![Millman’s Electronic Devices and Circuits
6
or
v V
= ¥
5.93 105
1
2
(1.13)
Thus, if an electron “falls” through a difference of only 1 V, its final speed is 5.93 ¥ 105 m/sec, or
approximately 370 miles/sec. Despite this tremendous speed, the electron possesses very little kinetic
energy, because of its minute mass.
It must be emphasized that Eq. (1.13) is valid only for an electron starting at rest. If the electron
does not have zero initial velocity or if the particle involved is not an electron, the more general formula
[Eq. (1.11)] must be used.
1.5 The eV Unit of Energy
The joule (J) is the unit of energy in the mks system. In some engineering power problems this unit is
very small, and a factor of 103 or 106 is introduced to convert from watts (1 W = 1 J/sec) to kilowatts
or megawatts, respectively. However, in other problems, the joule is too large a unit, and a factor of
10−7 is introduced to convert from joules to ergs. For a discussion of the energies involved in electronic
devices, even the erg is much too large a unit. This statement is not to be construed to mean that only
minute amounts of energy can be obtained from electron devices. It is true that each electron possesses
a tiny amount of energy, but as previously pointed out (Sec. 1.1), an enormous number of electrons is
involved even in a small current, so that considerable power may be represented.
A unit of work or energy, called the electron volt (eV), is defined as follows:
1 eV ∫ 1.60 ¥ 10−19 J
Of course, any type of energy, whether it be electric, mechanical, thermal, etc., may be expressed in
electron volts.
The name electron volt arises from the fact that, if an electron falls through a potential of one volt,
its kinetic energy will increase by the decrease in potential energy, or by
eV = (1.60 ¥ 10−19 C)(lV) = 1.60 ¥ 10−19 J = 1 eV
However, as mentioned above, the electron-volt unit may be used for any type of energy, and is not
restricted to problems involving electrons.
The abbreviations MeV and BeV are used to designate 1 million and 1 billion electron volts, respectively.
1.6 Relationship between Field Intensity and Potential
The definition of potential is expressed mathematically by Eq. (1.9). If the electric field is uniform, the
integral may be evaluated to the form
- - -
Ú e e
x
x
x
z o
dx x x V
o
= ( ) =
which shows that the electric field intensity resulting from an applied potential difference V between
the two plates of the capacitor illustrated in Fig. 1.1 is given by
ex
o
V
x x
V
d
=
-
-
= - (1.14)
where ex is in volts per meter, and d is the distance between plates, in meters.
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![9
Electron Ballistics and Applications
Solution The velocity of the hydrogen ion along the X axis is
v
qV
m
ox
h
=
Ê
Ë
Á
ˆ
¯
˜ =
¥ ¥ ¥
¥
Ê
Ë
Á
ˆ
¯
˜ =
-
-
2 2 1 602 10 100
1 676 10
4 3
1
2 19
27
1
2
.
.
. 7
7 105
¥ m/sec.
Note that we have used q = e = 1.602 ¥ 10-19 C as the charge and mh = (Atomic mass of hydrogen) ¥ 1.660 ¥
10-27 kg = 1.01 ¥ 1.660 ¥ 10-27 kg = 1.677 ¥ 10-27 kg as the mass of a hydrogen ion in the above calculation.
The potential difference Vd (in volts) is given by
V t
t t t
t t
d =
Ê
Ë
Á
ˆ
¯
˜ £ £
Ï
Ì
Ô
Ó
Ô
50
0
0
1
1
1
;
;
where t1 = 10-7 sec. Since the electric field e = -
V
d
d
is in the - Y direction, there is no force along the X or Z direc-
tions on the ion and thus the velocity component vox along the X direction remains unchanged.
It may be observed that at t = t1, the displacement in the X direction is
x1 = vox t1 = 4.37 ¥ 105 ¥ 10-7 = 4.37 ¥ 10-2 m
which is less than l = 5 cm. Therefore, it is clear that when the electric field becomes zero, the ion must be in
between the plates at a point below the X axis whose displacement along the X axis is x1 from the center point O .
Since, the hydrogen ion has positive charge, a force will act on the ion in the - Y direction (i.e. opposite to that
of an electron) which is given as
f m
dv
dt
q
eV
d
t
y h
y d
= = = - =
-
¥ ¥ ¥
¥
= - ¥
-
-
e
( . ) ( )
( .
1 602 10 5 10
2 10
4 0 10
19 8
2
-
-
£
Ï
Ì
Ô
Ó
Ô
9
1
1
0
0
) ;
;
]
t t t
t t
where the negative sign indicates that the force is acting on the ion in the - Y direction. Now, applying the initial
condition vy = 0 at t = 0 in the above differential equation, the velocity of the ion for 0 £ t £ t1 is given as
v
dy
dt
t t
y = = -
¥
¥ ¥
Ê
Ë
Á
ˆ
¯
˜ = - ¥
-
-
4 10
2 1 676 10
1 19 10
9
27
2 18 2
.
( . ) m/sec
With the initial condition y = 0 at t = 0, the displacement in the - Y direction is given as
y t t t
= -
¥
Ê
Ë
Á
ˆ
¯
˜ £ £
1 19 10
3
0
18
3
1
.
;
Hence at t = t1, the displacement is
y1
18
7
3
4
1 19 10
3
10 3 96 10 0 0396
= -
¥
Ê
Ë
Á
ˆ
¯
˜ ¥ ( ) = ¥ =
- -
.
. .
m cm
Note that the force in the -Y direction becomes zero for t t1. This implies that the velocity along the
-Y direction becomes v
dy
dt
t t t
oy = = - ¥ = - ¥ =
( . ) . /sec ,
1 19 10 1 19 10
18
1
2 4
m constantfor 1 which is same as the
velocity vy at t = t1. Thus, subject to the initial condition y = y1 at t = t1, the displacement of the ion from the X axis
for t t1 is given by
y = voy (t - t1) + y1
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![11
Electron Ballistics and Applications
v
eV
m
ox
a
=
2
(1.21)
on the assumption that the initial velocities of emission of the electrons from the cathode are negligible.
Since no field is supposed to exist in the region from the anode to the point O, the electrons will
move with a constant velocity vox in a straight-line path. In the region between the plates the electrons
will move in the parabolic path given by y a v x
y ox
= 1
2
2
( / ) 2
according to Eq. (1.20). The path is a straight
line from the point of emergence M at the edge of the plates to the point P¢ on the screen, since this
region is field-free.
The straight-line path in the region from the deflecting plates to the screen is, of course, tangent to
the parabola at the point M. The slope of the line at this point, and so at every point between M and P¢,
is [from Eq. (1.20)]
tan q =
˘
˚
˙ =
=
dy
dx
a l
v
x l
y
ox
2
From the geometry of the figure, the equation of the straight line MP¢ is found to be
y
a l
v
x
l
y
ox
= -
Ê
Ë
Á
ˆ
¯
˜
2 2
(1.22)
since x = l and y a l v
y ox
= 1
2
2
2
/ at the point M.
When y = 0, x = l/2, which indicates that when the straight line MP ¢ is extended backward, it will
intersect the tube axis at the point O¢, the center point of the plates. This result means that O¢ is, in
effect,
a virtual cathode, and regardless of the applied potentials Va and Vd, the electrons appear to emerge from
this “cathode” and move in a straight line to the point P¢.
At the point P¢, y = D, and x L l
= + 1
2
. Equation (1.22) reduces to
D
a lL
v
y
ox
= 2
By inserting the known values of ay (= eVd/dm) and vox, this becomes
D
lLV
dV
d
a
=
2
(1.23)
This result shows that the deflection on the screen of a cathode-ray tube is directly proportional to the
deflecting voltage Vd applied between the plates. Consequently, a cathode-ray tube may be used as a
linear-voltage indicating device.
Fig. 1.4 Electrostatic deflection in a cathode-ray tube.
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rights
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![AgO S2O2.
But AgO S2O2 plainly equals AgS, or Sulphuret of Silver, and SO3,
or Sulphuric Acid. The acid reaction assumed by the supernatant
liquid is due therefore to Sulphuric Acid, and the black substance
formed is Sulphuret of Silver. The yellow and orange-yellow
compounds are earlier stages of the decomposition, but their exact
nature is uncertain.
The instability of Hyposulphite of Silver is principally seen when it
is in an isolated state: the presence of an excess of Hyposulphite of
Soda renders it more permanent, by forming a double salt, as
already described.
In fixing Photographic prints, this brown deposit of Sulphuret of
Silver is very liable to form in the Bath and upon the picture;
particularly so when the temperature is high. To obviate it, observe
the following directions:—It is especially in the reaction between
Nitrate of Silver and Hyposulphite of Soda that the blackening is
seen; the Chloride and other insoluble Salts of Silver being dissolved,
even to saturation, without any decomposition of the Hyposulphite
formed. Hence if the print be washed in water to remove the soluble
Nitrate, a very much weaker fixing Bath than usual may be
employed. But if the proofs are taken at once from the printing
frame and immersed in a dilute Bath of Hyposulphite (one part of
the salt to six or eight of water), a shade of brown may often be
observed to pass over the surface of the print, and a large deposit of
Sulphuret of Silver soon forms as the result of the decomposition.
On the other hand, with a strong Hyposulphite Bath there is little or
no discoloration, and the black deposit is absent.
The print must also be left for a sufficient time in the fixing bath,
or some appearance of brown patches,[18] visible by transmitted
light, may occur. Each atom of Nitrate of Silver requires three atoms
of Hyposulphite of Soda to form the sweet and soluble double salt,
and hence, if the action be not continued sufficiently long, another](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-47-320.jpg)
![compound will be formed almost tasteless and insoluble (p. 44).
Even immersion in a new Bath of Hyposulphite of Soda does not fix
the print when once the yellow stage of decomposition has been
established. This yellow salt is insoluble in Hyposulphite of Soda, and
consequently remains in the paper.
[18] The writer has noticed that when sensitive paper is kept
for some time before being used for printing, these yellow
patches of imperfect fixation are very liable to occur. The Nitrate
of Silver appears gradually to enter into combination with the
organic matter of the size of the paper, and cannot then be so
easily extracted by the fixing bath.
In fixing prints by Ammonia the Author has found that the same
rule may be applied as in the case of Hyposulphite of Soda, viz. that
if the process be not properly performed, the white parts of the print
will appear spotted when held up to the light, from a portion of
insoluble Silver Salt remaining in the paper. Prints imperfectly fixed
by Ammonia are also usually brown and discoloured upon the
surface of the paper.
More exact directions as to the strength of the fixing bath and
the time occupied in the process, will be given in the Second Part of
the Work; at present it may be noticed only that Albuminized paper,
from the horny nature of its surface-coating, requires a longer
treatment with the Hyposulphite than the plain paper.
THE SALTS OF GOLD AS TONING AGENTS FOR
PHOTOGRAPHIC PRINTS.
The Salts of Gold have been successfully applied to the
improvement of the tones obtained by simply fixing the proof in
Hyposulphite of Soda. The following are the principal modes
followed:—
M. Le Grey's Process.—The print, having been exposed to light
until it becomes very much darker than it is intended to remain, is
washed in water to remove the excess of Nitrate of Silver. It is then](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-48-320.jpg)
![although darkened considerably, is less reduced in intensity, and the
same amount of over-printing is not required. The chemical changes
which ensue are different from before: they may be described as
follows:—
Chloride of Gold, added to Hyposulphite of Soda, is converted
into Hyposulphite of Gold, Tetrathionate of Gold, and (if the Chloride
of Gold be free from excess of acid) a red compound, containing
more of the metal than, either of the others, but the exact nature of
which is uncertain. Each of these three Gold Salts possesses the
property of darkening the print, but not to the same extent. The
activity is less as the stability of the salt is greater, and hence the red
compound, which is so highly unstable that it cannot be preserved
many hours without decomposing and precipitating metallic Gold, is
far more active than the Hyposulphite of Gold, which, when
associated with an excess of Hyposulphite of Soda, is comparatively
permanent.
When rapidity of colouring is an object it will therefore be
advisable to add Chloride of Gold to the fixing Bath of Hyposulphite
rather than an equivalent quantity of Sel d'or; and by dropping a
little Ammonia into the Chloride of Gold so as to precipitate
fulminating gold[19] (a compound which dissolves in Hyposulphite
of Soda with considerable formation of the unstable red salt), the
activity of the Bath will be promoted.
[19] Read the observations on the Explosive Properties of
Fulminating Gold in the Vocabulary, Part III.
The Author explains the action of these Salts of Gold upon the
Positive print as follows:—they are unstable, and contain an excess
of Sulphur loosely combined; hence, when placed in contact with the
image, which has an affinity for Sulphur, the existing compound is
broken up, and Sulphuret of Silver, Sulphuric Acid, and metallic Gold
are the results. That a minute proportion of Sulphuret of Silver is
formed seems certain; but the change must be superficial, as the](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-50-320.jpg)
![c. Temperature of the solution.—In cold weather, the
thermometer standing at 32° to 40°, the Bath works more slowly
than usual; whereas in the height of summer, and especially in hot
climates, it occasionally becomes quite unmanageable. The best
temperature for operating successfully appears to be about 60° to
65° Fahrenheit; if higher than this the solutions must be employed
more dilute.
d. Addition of Iodide of Silver.—Some operators associate Iodide
with Chloride in the preparation of sensitive paper for printing.
Another source of the same salts is the admixture of a portion of the
fixing Bath used for Negatives with the Positive toning solution. The
presence of Iodides in the fixing and toning Bath is injurious: when
in large excess, they dissolve the image, or produce yellow patches
of Iodide of Silver on the lights; in smaller quantity, the deposition of
the Gold is hindered, and the action proceeds more slowly. Bromides
and Chlorides have not the same effect.
e. Mode of preparing the paper.—The rapidity of toning varies
with causes independent of the Bath: thus, plain paper prints are
toned more quickly than prints upon albuminized paper, and the use
of English paper sized with Gelatine retards the action. Foreign
papers rendered sensitive with Ammonio-Nitrate tone the most
quickly.
On certain states of the fixing and toning Bath which are
injurious to the proofs.—The object of using the Hyposulphite Bath is
to fix the proof and to tone it by means of Gold. But it is a fact
familiar to the photographic chemist, that Positives can also be toned
by a sulphuretting action, and that the colours so obtained are not
very different from those which follow the employment of Gold.[20]
Now the Hyposulphite of Soda is a substance which can be very
readily made to yield up Sulphur to any bodies which possess an
affinity for that element, and as the reduced Silver compound in the
print has such an affinity, there is always a tendency to absorption of
Sulphur when the proofs are immersed in the Bath. Consequently in](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-53-320.jpg)
![many cases a sulphur toning-process is set up, and as the picture is
improved by it in appearance, losing its brick-red colour and
assuming a purple shade, it was at first adopted by Photographers.
Experience however has shown that colours brightened in this way
are less permanent than others, and are liable to fade unless kept
perfectly dry. Hence the process will be discarded by all careful
operators, and the object will be to avoid sulphuration as far as
possible. This can be done to a great extent, and, when the Bath is
properly managed, the prints will be toned almost entirely by Gold,
and will, with care, be permanent.
[20] For a more detailed account of the toning process by
Sulphur, see the Third Section of this Chapter, page 145. The
instability of sulphuretted prints is shown in the fourth Section.
Some of the conditions which facilitate a sulphuretting action
upon the proof are as follows:—
a. The addition of an Acid to the Bath.—It was at one time
common to add a few drops of Acetic Acid to the fixing Bath of
Hyposulphite of Soda, immediately before immersing the proofs. The
Bath then assumes an opalescent appearance in the course of a few
minutes, and, when this milkiness is perceptible, the print begins to
tone rapidly and becomes nearly black.
The chemical changes produced in a Hyposulphite Bath by
addition of acid, may be explained thus:—The acid first displaces the
feeble Hyposulphurous acid from its combination with Soda.
Acetic Acid +Hyposulphite Soda.
=Acetate Soda+Hyposulphurous Acid.
Then the Hyposulphurous Acid, not being a stable substance
when isolated, begins spontaneously to decompose, and splits up
into Sulphurous Acid—which remains dissolved in the liquid,
communicating the characteristic odour of burning Sulphur—and
Sulphur, which separates in a finely divided state and forms a milky
deposit.[21]](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-54-320.jpg)
![[21] From the Vocabulary, Part III., it will be seen that
commercial Chloride of Gold usually contains free Hydrochloric
Acid; hence a considerable deposit of Sulphur takes place on
adding it to the Hyposulphite solution, and the liquid must not be
used immediately.
Observe therefore that free acids of all kinds must be excluded
from the fixing Bath, or, if inadvertently added, the liquid must be
set aside for some hours until the Hyposulphurous Acid has
decomposed, and, the Sulphur having settled to the bottom, the
Bath has regained its original neutral condition.[22]
[22] The chemical reader will understand the decomposition of
free Hyposulphurous Acid by the following equation:—S2O2 = SO2
and S.
b. Decomposition of the Bath by constant use.—It has long been
known that a solution of Hyposulphite of Soda undergoes a peculiar
change in properties when much used in fixing. When first prepared
it leaves the image of a red tone, the characteristic colour of the
reduced Silver Salt, but soon acquires the property of darkening this
red colour by a subsequent communication of Sulphur. Hence a
simple fixing Bath becomes at last an active toning bath, without any
addition of Gold.
This change of properties will be found more fully explained in
the abstract of the Author's researches given in the next Section (p.
156). At present we remark only that it is due principally to a
reaction between Nitrate of Silver and Hyposulphite of Soda,
attended with decomposition of Hyposulphite of Silver (p. 130); and
hence, if the prints are washed in water before immersion in the
Bath, the solution will be less quickly liable to change.
Many operators state that the toning Bath having at first been
prepared with Chloride of Gold, no further addition of this substance
will be required. This no doubt is correct, but in such case the proofs
will at last be toned by Sulphur more than by Gold, and will not
possess the same stability; the Bath will also, after long use, be](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-55-320.jpg)
![found to acquire a distinct acid reaction to test-paper, the acidity
being due to a peculiar principle generated by decomposing
Hyposulphite of Silver, and which is shown to have an injurious
action upon the print (p. 158). To avoid this the solution should be
kept neutral to test-paper by means of a drop of Ammonia, if
required; and when it begins to be exhausted, and does not tone
(quickly) a print from which the free Nitrate of Silver has been
removed by washing, a fresh quantity of Chloride of Gold should be
added.
c. Tetrathionate in the Hyposulphite Bath.—The Author has
shown that the Tetrathionates, which are analogous to the
Hyposulphites, have an active sulphuretting action upon Positive
prints (see the papers in the next Section). Very fine colours can be
obtained in this way; but toning by Sulphur having been proved to
be wrong in principle, the formulæ given in the first two editions of
this Work have been omitted.[23]
[23] The preparation of a toning bath by Tetrathionate,
without Gold, is described in the next Section, but it is not
recommended for practical use.
The bodies which produce Tetrathionate when added to a
solution of Hyposulphite of Soda, and hence are inadmissible in the
toning process, are as follows:—Free Iodine, Perchloride of Iron,
Chloride of Copper, Acids of all kinds (in the latter case the acid first
produces Sulphurous Acid, and the Sulphurous Acid, if present in any
quantity, by reacting upon Hyposulphite of Soda, forms Tetrathionate
and Trithionate of Soda).
Chloride of Gold also produces a mixed Tetrathionate of Gold and
Soda when added to the fixing Bath (p. 133); but as the quantity of
Chloride used is small, the prints are far less sulphuretted than in the
case of toning Baths prepared by Tetrathionate without Gold.
SECTION III.
The Author's Researches in Photographic Printing.](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-56-320.jpg)
![3rd. The developing agent employed.—An organic developing
agent like Pyrogallic Acid may be expected to produce a Collodion
image more intense, but less metallic, than an inorganic developer,
such as the Protosulphate of Iron.
4th. The length of time during which the light has acted.—Over-
action of the light favours the production of an image which is dark
by reflection and brown or red by transmission, corresponding in
these particulars to what may be termed the non-metallic image
containing an oxide of Silver.
5th. The stage of the development.—The red image first formed
on the application of the developer to a gelatinized or albuminized
surface of Iodide of Silver is less metallic, and more easily injured by
destructive tests, than the black image, which is the result of
prolonging the action. Developed photographs which are of a bright
red colour after fixing, correspond in properties to images obtained
by the direct action of light on paper prepared with Chloride of
Silver, more nearly than to Collodion, or even to fully developed
Talbotype Negatives.
To conclude the Paper, the following may be offered in the way of
recapitulation:—An image consisting of metallic silver, as a rule,
reflects white light, and shows as a positive when laid on black
velvet; but a non-metallic organic image is dark, and represents the
shadows of a picture. Collodion positives developed with protosalts
of Iron are nearly or quite metallic. Photographs on Albumen or
Gelatine less so than those on Collodion. Developed Photographs
contain more Silver than others, if the development has been
prolonged. The half shadows of the image in a Positive Print are
especially liable to suffer under injurious conditions, since they
contain the Silver in a less perfect state of reduction.[24]
[24] The Author omits, in this place, all mention of molecular
conditions affecting intensity, inasmuch as at the present time
nothing positive has been determined with regard to them. It is
however known that in the use of the protosalts of Iron as
developing agents, the appearance of the image is much](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-62-320.jpg)
![These facts prove that Oxygen has an influence in accelerating
the destructive action of the Sulphur compounds upon Positive
prints; and this idea is borne out by the results of further
experiments, for it is found that moist Sulphuretted Hydrogen has
little or no effect in darkening the colour when every trace of air is
excluded. When prints are washed in water they are exposed to the
influence of the dissolved air which water always contains, and
hence the change from black to yellow is produced.[25]
[25] Further remarks upon the action of damp air upon
Positives toned by Sulphur are given at p. 153.
There are some substances which facilitate the yellow
degeneration of Positives toned by Sulphur, a knowledge of which
will be useful: they are—1st, powerful oxidizers, such as Chlorine,
Permanganate of Potash, and Chromic Acid; these, even when highly
diluted, act with great rapidity: 2nd, bodies which dissolve Oxide of
Silver, as soluble Cyanides, Hyposulphites, Ammonia; also acids of
various kinds, and hence the frequency of yellow finger impressions
upon old sulphuretted prints, which are probably caused by a trace
of organic (Lactic?) Acid left by contact with the warm hand.
It was at one time supposed that the Photograph in the stage at
which it appears blackened by Sulphur, consisted of Sulphuret of
Silver, and that this black Sulphuret became yellow by absorption of
Oxygen and conversion into Sulphate. MM. Davanne and Girard, who
examined the subject, thought that there might be two isomeric
forms of Sulphuret of Silver, a black and a yellow form; the former of
which passing gradually into the latter produced the fading of the
impression. But neither of these views are correct; for it is proved by
careful experiment, that the Sulphuret of Silver is a highly stable
compound, not prone to oxidize, and, further, that the change of
colour from black to yellow has no reference to a modification of this
salt. The truth appears to be that the image whilst in the black stage
contains other elements besides Sulphur and Silver, but when it has
become yellow by the continued action of the sulphuretting
compound, it is then a true Sulphuret.](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-64-320.jpg)
![Effect of Oxidizing Agents upon Positive Prints.—It appeared of
importance to ascertain to what extent Photographic Prints are
susceptible of oxidation; on account of the atmospheric influences to
which they are necessarily exposed. In experimenting upon this
subject the following results have been obtained.
Powerful oxidizers destroy Positive Prints rapidly; the action
usually commencing at the corners and edges of the paper, or at any
isolated point, such as a metallic speck or particle of extraneous
matter, which can serve as a centre of chemical action. This same
fact is often noticed in the fading of Positives by long keeping, and
therefore since other destructive actions (with the exception of that
of Chlorine) do not appear to follow the same rule, it is an argument
in addition to others which can be adduced, that Photographic Prints
are frequently destroyed by oxidation.
Air which has been Ozonized by Phosphorus, and in which blue
litmus-paper becomes reddened, quickly bleaches the Positive
image. Oxygen gas, obtained by voltaic decomposition of acidified
water and which should contain Ozone, did not appear to have an
equal amount of effect, the action being comparatively slight, or
altogether wanting.
Peroxide of Hydrogen obtained in solution, and in conjunction
with Acetate of Baryta, by adding Peroxide of Barium to dilute Acetic
Acid,[26] bleaches darkened Positive paper; but the effect is slow,
and does not take place to a very perceptible extent if the liquid be
kept alkaline to test-paper.
[26] Hydrochloric Acid, which is usually recommended in place
of Acetic Acid, cannot be employed in this experiment; it seems to
cause a liberation of free Chlorine, which bleaches the print
instantly.
Nitric Acid applied in a concentrated form acts immediately upon
the darkened surface, bleaching every part of the print with the
exception of the bronzed shadows, which usually retain a slight
residual colour. A solution of Chromic Acid is still more active. This](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-67-320.jpg)
![the point at which the paper begins to char, when it resumes its
original red tone, becoming at the same time faint and indistinct.
The Products of Combustion of Coal-gas a cause of Fading.—
Coal-gas contains Sulphur compounds, which in combustion are
oxidized into Sulphurous and Sulphuric Acids; other substances of a
deleterious nature may also be present. A plate of polished silver
suspended in a glass tube, through which was directed the current
of heated air rising from a small gas jet, became tarnished with a
white film in the course of twenty-four hours. Positive prints exposed
to the same, absorbed moisture and faded; the action resembling
that of oxidation, in being preceded by a general darkening in colour.
Of four prints exposed, an Iodide-developed print was the least
injured, and next, a print upon Albuminized paper.
ON THE ACTION OF DAMP AIR UPON POSITIVE
PRINTS.
In order to ascertain this point, more than six dozen Positives,
printed on every variety of paper, were mounted in new and
perfectly clean stoppered glass bottles, at the bottom of each of
which was placed a little distilled water, to keep the contained air
always moist. They were removed at the expiration of three months,
having been kept during that time, some in the dark, and others
exposed to the light. As the prints were prepared by various
methods, toned in different ways, and mounted with or without
substances likely to exercise a deleterious action, this series of
experiments will possess considerable value in determining some of
the intrinsic causes of fading of Positives.[27]
[27] For a more detailed account of the experiments, see the
original paper in the 'Photographic Journal,' vol. iii.
The general results obtained were as follows:—Positives which
had been simply fixed in Hyposulphite of Soda remained quite
uninjured. Whether developed by Gallic Acid on either of the three](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-72-320.jpg)
![An examination of the various modes employed for coating
Positives, in order to exclude the atmosphere, showed that many of
them were not fitted to fulfil the purpose intended. Waxed prints
faded quite as much when exposed to moisture as others not waxed.
White wax is a substance often adulterated, and Oil of Turpentine
has been shown to contain a body resembling Ozone in properties,
and possessing the power of bleaching a dilute solution of Sulphate
of Indigo. Spirit varnish applied to the surface of the picture after re-
sizing with Gelatine was plainly superior to white wax, but
nevertheless it did not obviate the fading effect of the moisture upon
an unstable Positive which had been toned by sulphuration. Its
protective influence is therefore limited.
ON THE CHANGE IN COMPOSITION WHICH
HYPOSULPHITE OF SODA EXPERIENCES BY USE IN
FIXING PAPER PROOFS.[28]
[28] These observations are condensed and re-arranged from
the papers published by the Author in the 'Photographic Journal'
for September and October, 1854.
It was remarked by Photographers at an early period that the
properties of the Fixing Bath of Hyposulphite of Soda became altered
by constant use; that it gradually acquired the power of darkening
the colour of the Positive image. This change was at first referred to
the accumulation of Salts of Silver in the Bath, and hence directions
were given to dissolve a portion of blackened Chloride of Silver in
the Hyposulphite in preparing a new solution.
Careful experiments performed by the Author convinced him that
an error had been entertained; since it was found that the simple
solution of Chloride of Silver in Hyposulphite of Soda had no power
of yielding the black tones. But it afterwards appeared that if the
fixing Bath, containing dissolved Silver Salts, were set aside for a few
weeks, a decomposition occurred in it, evidenced by the formation of](https://image.slidesharecdn.com/87398-250330124022-b709f0de/85/Millman-s-Electronics-Devices-and-Circuits-3rd-Edition-Jacob-Millman-75-320.jpg)
Millman s Electronics Devices and Circuits 3rd Edition Jacob Millman
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- 4. Millman’s Electronic Devices and Circuits Third Edition Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 5. About the Authors Jacob Millman was born in Russia in 1911, and came to the United States in 1913. He received his PhD from the Massachusetts Institute of Technology (MIT) in 1935. Except for three years during World War II, when he was a scientist with the Radiation Laboratory at MIT, he was a professor of engineering at City College of NewYork from 1936 to 1952. From 1952 until he retired in 1976, he taught at Columbia University. He was named Chairman of the Department of Electrical Engineering in 1965 and, at his retirement, became the Charles Bachelor Professor Emeri- tus of Electrical Engineering. His areas of expertise were radars, electronic circuits, and pulse-circuit techniques. Between 1941 and 1987, Prof. Millman wrote eight textbooks on electronics, which are perhaps some of the most widely used, and enduring, textbooks, on electronic devices and circuits, in the world. Another of his most notable achievements was the formulation of Millman’s Theorem (otherwise known as the Parallel generator theorem), which is named after him. Prof. Millman died in 1991. In 1992, the IEEE Education Society established the IEEE Education Society McGraw-Hill Jacob Millman award in his memory, to recognize an author who has written an exceptional textbook relating to the field of Electrical Engineering. Christos C Halkias is currently the Dean Emeritus at Athens Information Technology, National Technical University of Athens, Greece. He received his bachelor’s degree in electrical engineering from the City University of NewYork in 1957, and his MS and PhD degrees from Columbia University, in 1958 and 1962, respectively. During his long-running teach- ing career, Halkias has taught at many prestigious colleges and universities like the City College of NewYork, Columbia UniversityandtheNationalTechnicalUniversityofAthens.From1973,hehasbeenwiththeNationalTechnicalUniversity of Athens. Prof. Halkias has been a member of various academic and research administration boards, such as the Greek National ResearchAdvisory Board; the Ministry of Industry, Energy, Research and Technology; ISTA G, European Com- munity; and is a member of the Board of Directors, Research and Education Society in Information Technologies since 2001. He has co-authored four books in the area of electronic circuits, and has contributed articles for the McGraw-Hill Encyclopedia of Science and Technology. Besides these, he has six patents. Prof. Halkias was awarded the IEEE Centen- nial Medal, 1984 for ‘Extraordinary Achievements in the field of Electronics’, and he received ‘The Presidential Seal of Honor2000’oftheAmericanBiographicalInstitutefor‘ExemplaryAchievementsinthefieldofInformationTechnology’. Satyabrata Jit earned his BE in Electronics and Telecommunication Engineering from the Bengal Engineering College (presently known as Bengal Engineering and Science University, Shibpore) of the University of Calcutta in 1993; MTech in Communication Systems from the Indian Institute of Technology, Kanpur, in 1995 and then a PhD in Electronics Engineering from the Institute of Technology-Banaras Hindu University (IT-BHU),Varanasi, in 2002. Dr Jit has served as Lecturer in the Department of Electronics and Communication Engineering, G B Pant Engineering College, Uttaranchal, during 1995–1998. He joined the Department of Electronics Engineering, IT-BHU as Lecturer in 1998 where he has been working as Associate Professor since June 2007. He is a recipient of the INSA Visiting Fellowship for the session 2006–07. He has served as a Postdoctoral Researcher in the Optoelectronics Laboratory, Georgia State University, USA, during March–August, 2007. Dr Jit has published more than 40 research papers in various peer-reviewed international journals and conference proceedings. He is one of the editors of two books entitled Advanced Optoelectronic Materials and Devices and Emerging TrendsinElectronicandPhotonicDevicesandSystems.Hehasworkedasreviewerofanumberofnationalandinternational journals like IETE Journal of Research, IETE Technical Review, IEEE Transactions on Electron Devices, IEEE Journal of Quantum Electronics, IET (formerly IEE) Circuits, Devices and Systems, Solid-Sate Electronics, etc. His name was included in the Golden List of Reviewers of the IEEE Transactions on Electron Devices for the years 2004, 2005, 2006 and 2008. His research interests include optical bistability and switching, microwave photonics, terahertz detectors, SOI- MESFETs, nanochannel multiple gate SOI MOSFETs, and optically controlled MESFETs. Dr Jit is also a life member of the Institution of Electronics and Telecommunication Engineers (IETE), India. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 6. Tata McGraw Hill Education Private Limited NEW DELHI McGraw-Hill Offices New Delhi New York St Louis San Francisco Auckland Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto Late Jacob Millman Professor of Electrical Engineering Columbia University Christos C Halkias Dean Emeritus Athens Information Technology National Technical University of Athens Greece Satyabrata Jit Associate Professor Department of Electronics Engineering Institute of Technology Banaras Hindu University Varanasi Millman’s Electronic Devices and Circuits Third Edition Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 7. Published by The Tata McGraw Hill Education Private Limited, 7 West Patel Nagar, New Delhi 110 008. Electronic Devices and Circuits, 3e Copyright © 2010, 2007, by Tata McGraw Hill Education Private Limited No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they may not be reproduced for publication. This edition can be exported from India only by the publishers, Tata McGraw Hill Education Private Limited. ISBN-13: 978-0-07-070021-5 ISBN-10: 0-07-070021-4 Managing Director: Ajay Shukla Head—Higher Education Publishing and Marketing: Vibha Mahajan Manager—Sponsoring SEM & Tech Ed: Shalini Jha Assoc. Sponsoring Editor: Suman Sen Development Editor: Manish Choudhary Executive—Editorial Services: Sohini Mukherjee Senior Production Manager: P L Pandita Dy. Marketing Manager—SEM & Tech Ed: Biju Ganesan General Manager—Production: Rajender P Ghansela Asst. General Manager—Production: B L Dogra Information contained in this work has been obtained by Tata McGraw-Hill, from sources believed to be reliable. However, neither Tata McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither Tata McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that Tata McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. Typeset at Tulyasys Technologies, No. 1 Arulananthammal Nagar, Thanjavur 613 007, and printed at Rajkamal Electric Press, Plot No. 2, Phase IV, HSIIDC Kundli, Sonepat, Haryana, 131 028 Cover: Rajkamal Electric Press DZXQCRAZRYLCL Tata McGraw-Hill Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 9. Contents Preface to the Third Edition xiv Preface to the First Edition xvii 1. Electron Ballistics and Applications 1 1.1 Charged Particles 1 1.2 The Force on Charged Particles in an Electric Field 2 1.3 Constant Electric Field 3 1.4 Potential 4 1.5 The eV Unit of Energy 6 1.6 Relationship between Field Intensity and Potential 6 1.7 Two-dimensional Motion 7 1.8 Electrostatic Deflection in a Cathode-ray Tube 10 1.9 The Cathode-ray Oscilloscope 14 1.10 Relativistic Variation of Mass with Velocity 15 1.11 Force in a Magnetic Field 16 1.12 Current Density 17 1.13 Motion in a Magnetic Field 18 1.14 Magnetic Deflection in a Cathode-ray Tube 20 1.15 Magnetic Focusing 22 1.16 Parallel Electric and Magnetic Fields 24 1.17 Perpendicular Electric and Magnetic Fields 26 1.18 The Cyclotron 31 References 34 Problems 34 Open-Book Exam Questions 41 2. Energy Levels and Energy Bands 42 2.1 The Nature of the Atom 42 2.2 Atomic Energy Levels 44 2.3 The Photon Nature of Light 46 2.4 Ionization 47 2.5 Collisions of Electrons with Atoms 47 2.6 Collisions of Photons with Atoms 48 2.7 Metastable States 49 2.8 Wave Properties of Matter 49 2.9 Electronic Structure of the Elements 53 2.10 The Energy-band Theory of Crystals 55 2.11 Insulators, Semiconductors, and Metals 56 References 58 Problems 58 Open-Book Exam Questions 59 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 10. vii Contents 3. Conduction in Metals 60 3.1 Mobility and Conductivity 60 3.2 The Energy Method of Analyzing the Motion of a Particle 63 3.3 The Potential-energy Field in a Metal 65 3.4 Bound and Free Electrons 67 3.5 Energy Distribution of Electrons 68 3.6 The Density of States 71 3.7 Work Function 74 3.8 Thermionic Emission 75 3.9 Contact Potential 76 3.10 Energies of Emitted Electrons 76 3.11 Accelerating Fields 78 3.12 High-field Emission 79 3.13 Secondary Emission 79 References 80 Problems 80 Open-Book Exam Questions 83 4. Conduction in Semiconductors 84 4.1 Electrons and Holes in an Intrinsic Semiconductor 84 4.2 Conductivity of a Semiconductor 86 4.3 Carrier Concentrations in an Intrinsic Semiconductor 87 4.4 Donor and Acceptor Impurities 96 4.5 Charge Densities in a Semiconductor 98 4.6 Fermi Level in a Semiconductor Having Impurities 100 4.7 Diffusion 102 4.8 Carrier Lifetime 103 4.9 The Continuity Equation 104 4.10 The Hall Effect 107 References 110 Problems 111 Open-Book Exam Questions 111 5. Semiconductor-Diode Characteristics 113 5.1 Qualitative Theory of the p-n Junction 113 5.2 The p-n Junction as a Diode 115 5.3 Band Structure of an Open-Circuited p-n Junction 117 5.4 The Current Components in a p-n Diode 120 5.5 Quantitative Theory of the p-n Diode Currents 121 5.6 The Volt-Ampere Characteristic 126 5.7 The Temperature Dependence of p-n Characteristics 128 5.8 Diode Resistance 130 5.9 Space-Charge, or Transition, Capacitance CT 131 5.10 Diffusion Capacitance 138 5.11 p-n Diode Switching Times 141 5.12 Breakdown Diodes 143 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 11. viii Contents 5.13 The Tunnel Diode 150 5.14 Characteristics of a Tunnel Diode 155 5.15 The p-i-n Diode 157 5.16 Characteristics of a p-i-n Diode 161 5.17 The Point Contact Diode 163 5.18 The Schottky Barrier Diode 164 5.19 The Schottky Effect 171 5.20 Current-Voltage Relation of a Schottky Barrier Diode 173 References 177 Problems 177 Open-Book Exam Questions 182 6. Applications of Diode 183 6.1 A Half-Wave Rectifier 183 6.2 Ripple Factor 189 6.3 A Full-Wave Rectifier 190 6.4 A Bridge Rectifier 193 6.5 The Rectifier Voltmeter 196 6.6 The Harmonic Components in Rectifier Circuits 197 6.7 Inductor Filters 198 6.8 Capacitor Filters 202 6.9 Approximate Analysis of Capacitor Filters 205 6.10 L-Section Filter 209 6.11 Multiple L-Section Filter 213 6.12 II-Section Filter 214 6.13 II-Section Filter with a Resistor Replacing the Inductor 217 6.14 Summary of Filters 217 6.15 Voltage Regulation Using Zener Diode 218 6.16 Clipping Circuits 227 6.17 Clamper Circuits 239 6.18 The Envelope Detector Circuit 242 6.19 The Peak-To-Peak Detector Circuit 243 6.20 Voltage Multipliers 244 6.21 Variable Tuning Circuit Using a Varactor Diode 247 References 250 Problems 250 Open-Book Exam Questions 254 7. Transistor Characteristics 255 7.1 The Junction Transistor 255 7.2 Transistor Current Components 257 7.3 The Transistor as an Amplifier 259 7.4 Transistor Construction 259 7.5 Detailed Study of the Currents in a Transistor 261 7.6 The Transistor Alpha 263 7.7 The Common-Base Configuration 264 7.8 The Common-Emitter Configuration 266 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 12. ix Contents 7.9 The CE cutoff Region 268 7.10 The CE Saturation Region 271 7.11 Large-Signal, dc, and Small-Signal CE Values of Current Gain 272 7.12 The Common-Collector Configuration 274 7.13 Graphical Analysis of the CE Configuration 274 7.14 Analytical Expressions for Transistor Characteristics 276 7.15 Analysis of Cutoff and Saturation Regions 280 7.16 Typical Transistor-Junction Voltage Values 283 7.17 Determination of the Cut-off, Saturation and Active Retgions of Generalized Transistor Circuit 284 7.18 Transistor as a Switch 293 7.19 Transistor Switching Times 299 7.20 Maximum Voltage Rating 301 References 302 Problems 303 Open-Book Exam Questions 306 8. Transistor Biasing and Thermal Stabilization 307 8.1 The Operating Point 307 8.2 Bias Stability 310 8.3 Collector-to-Base Bias or Collector-Feedback Bias 312 8.4 Emitter-Feedback Bias 314 8.5 Collector-Emitter Feedback Bias 318 8.6 Self-Bias, Emitter Bias, or Voltage-Divide Bias 320 8.7 Stabilization against Variations in VBE and ß for the Self-Bias Circuit 324 8.8 General Remarks on Collector-Current Stability 328 8.9 Bias Compensation 331 8.10 Biasing Circuits for Linear Integrated Circuits 332 8.11 Thermistor and Sensistor Compensation 333 8.12 Thermal Runaway 334 8.13 Thermal Stability 336 8.14 Some General Design Guidelines for Self-Bias Circuits 338 References 345 Problems 345 Open-Book Exam Questions 348 9. Small-Signal Low-Frequency ac Models of Transistors 349 9.1 The ac Analysis of a Small-Signal Low-Frequency Common-Emitter Transistor Amplifier 349 9.2 The ac Model of Transistors Based on r′e-Parameter 358 9.3 Analysis of a Generalized Amplifier Circuit using �-Model 359 9.4 Drawbacks, Limitations and Modifications of r′e -Parameter Based ac Models 372 9.5 Two-Port Devices and the Hybrid Model 372 9.6 Transistor Hybrid Model 374 9.7 Determination of the h Parameters from the Characteristics 376 9.8 Measurement of h Parameters 379 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 13. x Contents 9.9 Conversion Formulas for the Parameters of the Three Transistor Configurations 381 9.10 Analysis of a Transistor Amplifier Circuit using h-Parameters 383 9.11 Comparison of Transistor Amplifier Configurations 387 9.12 Linear Analysis of a Transistor Circuit 391 9.13 The Physical Model of a CB Transistor 391 References 394 Problems 394 Open-Book Exam Questions 397 10. Low-Frequency Transistor Amplifier Circuits 398 10.1 Cascading Transistor Amplifiers 398 10.2 n-Stage Cascaded Amplifier 401 10.3 The Decibel 405 10.4 Simplified Common-Emitter Hybrid Model 406 10.5 Simplified Calculations for the Common-Collector Configura tion 412 10.6 Simplified Calculations for the Common-Base Configuration 414 10.7 The Common-Emitter Amplifier with an Emitter Resistance 415 10.8 The Emitter Follower 419 10.9 Miller’s Theorem 422 10.10 High-Input-Resistance Transistor Circuits 423 10.11 The Cascode Transistor Configuration 430 10.12 Difference Amplifiers 431 References 435 Problems 436 Open-Book Exam Questions 439 11. The High-Frequency Transistor 440 11.1 The High-Frequency T Model 440 11.2 The Common-Base Short-Circuit-Current Frequency Response 441 11.3 The Alpha Cutoff Frequency 442 11.4 The Common-Emitter Short-Circuit-Current Frequency Response 445 11.5 The Hybrid-pi (II) Common-Emitter Transistor Model 446 11.6 Hybrid-pi Conductances in Terms of Low-Frequency h Parameters 447 11.7 The CE Short-Circuit Current Gain Obtained with the Hybrid-pi Model 452 11.8 Current Gain with Resistive Load 455 11.9 Transistor Amplifier Response, Taking Source Resistance into Account 456 References 459 Problems 459 Open-Book Exam Questions 461 12. Field-Effect Transistors 462 12.1 The Junction Field-Effect Transistor 462 12.2 The Pinch-Off Voltage VP 465 12.3 The JFET Volt-Ampere Characteristics 467 12.4 The FET Small-Signal Model 469 12.5 The Insulated-Gate FET (MOSFET) 472 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 14. xi Contents 12.6 The Common-Source Amplifier 475 12.7 The Common-Drain Amplifier, or Source Follower 479 12.8 A Generalized FET Amplifier 480 12.9 Biasing the FET 486 12.10 Unipolar-Bipolar Circuit Applications 491 12.11 The FET as a Voltage-Variable Resistor (VVR) 492 12.12 The Unijunction Transistor 494 References 495 Problems 495 Open-Book Exam Questions 499 13. Integrated Circuits 500 13.1 Basic Monolithic Integrated Circuits 500 13.2 Epitaxial Growth 503 13.3 Masking and Etching 504 13.4 Diffusion of Impurities 505 13.5 Transistors for Monolithic Circuits 509 13.6 Monolithic Diodes 513 13.7 Integrated Resistors 514 13.8 Integrated Capacitors and Inductors 516 13.9 Monolithic Circuit Layout 517 13.10 Integrated Field-Effect Transistors 521 13.11 Additional Isolation Methods 522 References 524 Problems 524 Open-Book Exam Questions 527 14. Untuned Amplifiers 529 14.1 Classification of Amplifiers 529 14.2 Distortion in Amplifiers 530 14.3 Frequency Response of an Amplifier 531 14.4 The RC-Coupled Amplifier 533 14.5 Low-Frequency Response of an RC-Coupled Stage 533 14.6 High-Frequency Response of a FET Stage 536 14.7 Cascaded CE Transistor Stages 538 14.8 Step Response of an Amplifier 543 14.9 Bandpass of Cascaded Stages 546 14.10 Effect of an Emitter (or a Source) Bypass Capacitor on Low-Frequency Response 548 14.11 Noise 552 References 556 Problems 557 Open-Book Exam Questions 559 15. Feedback Amplifiers and Oscillators 560 15.1 Classification of Amplifiers 560 15.2 The Feedback Concept 563 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 15. xii Contents 15.3 General Characteristics of Negative-Feedback Amplifiers 567 15.4 Effect of Negative Feedback Upon Output and Input Resistances 569 15.5 Voltage-Series Feedback 571 15.6 A Voltage-Series Feedback Pair 578 15.7 Current-Series Feedback 580 15.8 Current-Shunt Feedback 584 15.9 Voltage-Shunt Feedback 586 15.10 The Operational Amplifier 589 15.11 Basic Characteristics of Practical Operational Amplifiers 597 15.12 Basic Applications of Operational Amplifier 599 15.13 Electronic Analog Computation 609 15.14 Feedback and Stability 610 15.15 Gain and Phase Margins 612 15.16 Sinusoidal Oscillators 613 15.17 The Phase-ShiftOscillator 615 15.18 Resonant-Circuit Oscillators 618 15.19 A General Form of Oscillator Circuit 620 15.20 Crystal Oscillators 622 15.21 Frequency Stability 624 15.22 Negative Resistance in Oscillators 625 References 626 Problems 627 Open-Book Exam Questions 635 16. Large-Signal Amplifiers 636 16.1 Class A Large-Signal Amplifiers 636 16.2 Second-Harmonic Distortion 638 16.3 Higher-Order Harmonic Generation 640 16.4 The Transformer-Coupled Audio Power Amplifier 643 16.5 Shift of Dynamic Load Line 648 16.6 Efficiency 648 16.7 Push-Pull Amplifiers 655 16.8 Class B Amplifiers 656 16.9 Class AB Operation 660 References 661 Problems 662 Open-Book Exam Questions 664 17. Photoelectric Devices 665 17.1 Photoemissivity 665 17.2 Photoelectric Theory 667 17.3 Definitions of Some Radiation Terms 669 17.4 Phototubes 670 17.5 Applications of Photodevices 672 17.6 Multiplier Phototubes 674 17.7 Photoconductivity 676 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 16. xiii Contents 17.8 The Semiconductor Photodiode 677 17.9 Multiple-Junction Photodiodes 680 17.10 The Photovoltaic Effect 681 17.11 The p-i-n Photodetector 683 17.12 The Avalanche Photodiode (APD) 689 References 694 Problems 695 Open-Book Exam Questions 697 18. Regulated Power Supplies 699 18.1 Elements of a Regulated Power Supply System 699 18.2 Stabilization 700 18.3 Emitter-follower Regulator 701 18.4 Series Voltage Regulation 702 18.5 Practical Considerations 706 18.6 Monolithic Linear Regulators 707 18.7 Performance Parameters of 3-Terminal IC Regulators 711 18.8 LM723/LM723C General Purpose Voltage Regulator 712 18.9 Shunt Voltage Regulators 713 References 715 Problems 716 Open-Book Exam Questions 717 Appendix-A 719 Appendix-B 720 Appendix-C 721 Appendix-D 722 Appendix-E 729 Appendix-F 740 Index 743 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 17. Preface to the Third Edition The overwhelming response received by the second edition of this book has motivated me to bring out the third edition. The objective of the third edition is to provide additional useful information (including new illustrative examples wherever needed in the text) to make the contents of the book up-to-date, self- explanatory, interesting and useful to both the students and instructors of the basic course on electronic devices and circuits. The book has been revised on the basis of the feedback received from teachers and students using this book. Utmost care has been taken to revise all the chapters of the book in order to cover the syllabi of major Indian universities. The new illustrative examples have been worked out in detail in the text. It is believed that the revised edition will help students use the book for self-study; and instructors will find the text useful regarding suitable explanations of the behavioral characteristics of many electronic circuits and systems using semiconductor devices. New to this Edition Thoroughly revised chapters on Transistor Characteristics, Transistor Biasing and Thermal Stabilization, and Small Signal Low-Frequency Transistor Model New topics on AC Model of Transistors, DC and AC Equivalent Circuits, Design Guidelines for Self-Bias Circuits, and AC Model of Transistor Based on r-Parameter New Appendix on General Purpose Transistors (NPN Silicon) and their Characteristics Addition of more than 150 solved problems and exercises Open book exam questions, with suitable hints, placed at the end of each chapter Chapter Organization The book is organized in 18 chapters. Chapter 1 presents the fundamental physical and mathematical theory of the motion of charged particles in electric and magnetic force. Some important devices such as the cathode-ray oscilloscope and cyclotron whose operations are based on the above theory are also introduced briefly. Chapter 2 begins with a review of the basic atomic properties of matter leading to the discrete electronic energy levels in atoms. The wave properties of matter, the Schrödinger wave equation and the Pauli Exclusion Principle are also introduced in this chapter. Finally, the formation of energy bands from discrete atomic energy levels in a crystal is presented to distinguish between an insulator, a semiconductor, and a metal. Chapter 3 includes the discussion on the basic principles that characterize the movement of elec trons within a metal.The laws governing the emission of electrons from the surface of a metal are also presented. Chapter 4 presents the application of the energy band concept developed in Chapter 2 to determine the conduction properties of a semiconductor. Special emphasis is given for the determination of electron Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 18. and hole concentrations in a semiconductor. The effect of carrier concentration on the Fermi level and the transport of holes and electrons by conduction or diffusion are also discussed. Chapter 5 begins with a qualitative theory of the p-n junction diode. Then the quantitative derivation of the volt-ampere characteristics of a p-n junction diode is discussed in detail. The capacitance across the p-n junction is also calculated. The characteristics of some special types of diodes, namely, the breakdown diode, tunnel diode, point contact diode, p-i-n diode and Schottky diode are considered in detail to complete the chapter. Chapter6includestheapplicationsofdiodeasanelementinvariouselectroniccircuits.Thechapterstarts with the discussion on rectifier circuits followed by different types of filters. These circuits are used to obtain a dc power source from the conventional ac power line. A large number of other diode circuits such as the voltage regulators using a Zener diode, clippers, clampers, envelope detec tors, peak-to-peak detectors, volt- age multipliers, and variable tuning circuits using a varactor diode are also discussed in detail in this chapter. Chapter 7, devoted to the bipolar junction transistor (BJT) characteristics, has been thoroughly revised in this edition. Two new sections containing the theoretical analysis for determining the active, cutoff and saturation conditions of a generalized BJT circuit; and the operation of the BJTs as a switch have been added in this chapter. Chapter 8 includes different biasing techniques for establishing the quiescent operating point of a transistor amplifier. The effect of temperature on the operating point followed by the compensation techniques used for the quiescent-point stabilization is also presented. A new section has been included in Chapter 8 to present some general guidelines for the designing of self-bias circuits using a BJT. Chapter 9 has been thoroughly revised by incorporating four new sections on the analysis of small-signal low-frequency BJT amplifier circuits using simplified r-parameter models. The concepts of ac and dc load lines are introduced. The analysis of a generalized amplifier circuit using the simplified r-parameter based ac model of a BJT has been presented. The relations between the r-parameters and h-parameters of a BJT are also discussed. Chapter 10 includes the discussion of cascaded amplifiers where a number of single stage amplifiers are connected in cascade to amplify a low frequency signal from a source to a desired level. In addition, various special transistor circuits of practical importance are examined in detail. Chapter 11 introduces the high-frequency model of a transistor where the internal capacitances play an important role in determining the frequency characteristics of an electronic circuit designed with a transistor as a circuit component. Different approximation techniques are discussed in detail for the simplification of transistorized circuit analysis at high frequencies of operation. Chapter 12 introduces the basic principles of operation of the junction field-effect transistors (JFETs) and metal-oxide semiconductor FETs (MOSFETs). The generalized circuit model of a FET is also presented. Finally, representative circuits making use of FETs are also discussed. Chapter 13 describes the basic concepts of an integrated circuit that consists of single-crystal chip of silicon, containing both the active and passive elements and their interconnections. The basic processes involved in fabricating an integrated circuit are presented in this chapter. Chapter 14 deals with the problem of the amplification with a minimum of a distortion of a low-level input waveform which is not necessarily sinusoidal but may contain frequency components from a few hertz to a few megahertz. It also presents many topics associated with general problem of amplification, such as the classification of amplifiers, noise in amplifiers etc. xv Preface to the Third Edition Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 19. xvi Preface to the Third Edition Chapter 15 introduces the concept of feedback techniques used to modify the characteristics of an amplifier by combining a portion of the output signal with the external signal. The chapter also presents the basic characteristics and applications of an integrated operational amplifier circuit. Examples of various feedback amplifiers and oscillator circuits are also discussed in detail. Chapter 16 considers the large-signal audio-frequency amplifiers. Particular emphasis is placed on the types of circuit used and calculations of distortion components, the power output, and the efficiency. Chapter 17 discusses photoelectric theory, considers some practical photodevices, and shows how these are used in a circuit.The semiconductor photodetectors like the p-i-n photodetector and ava lanche photodi- ode which are used to convert optical signal into electrical signal in an optical receiver, are also discussed. Chapter 18 describes the concept of designing a regulated power supply by using the discrete com ponents as well as monolithic ICs. The series and shunt voltage regulators using transistor as the main controlling element are discussed here. Using commercially available voltage regulator ICs, some fixed and adjustable power supplies with single or dual regulated outputs are also presented. Web Supplements Thewebsupplementscanbeaccessedathttp://www.mhhe.com/milman/edc3eandcontainsthefollowing: Instructor resources Solution Manual Power Point Lecture Slides Student resources MultiSIM based simulation exercises Web Links for further reading material Additional questions Acknowledgements The constant inspiration, help and moral support from my beloved wife, Urmila, during the preparation of the revised manuscript is highly appreciable. I am indebted to her for relieving me from all my family responsibilities and thereby helping me in devoting more time towards the development of the manu- script. Needless to say, without her help and support, preparation of the manuscript would not have been possible. I am thankful to my daughter Sushmita and son Soumik for bearing the loss of togetherness of many evenings, weekends, and even holidays. Last but not the least; I would like to thank my parents whose blessings, inspiration and moral support have made my efforts successful. My sincere thanks are due to the reviewers for their valuable comments and suggestions. The help and support provided by the entire editorial and production staff at Tata McGraw-Hill is highly appreciated. Any suggestion/comment from the readers regarding the improvement of the technical quality of the book will be highly appreciated. Satyabrata Jit Publisher’s Note Tata McGraw-Hill invites comments, views and suggestions from readers, all of which can be sent to tmh.ecefeedback@gmail.com. Piracy-related issues may also be reported. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 20. Electron Ballistics and Applications In this chapter we present the fundamental physical and mathematical theory of the motion of charged particles in electric and magnetic fields of force. In addition, we discuss a number of the more important electronic devices that depend on this theory for their operation. The motion of a charged particle in electric and magnetic fields is presented, starting with simple paths and proceeding to more complex motions. First a uniform electric field is considered, and then the analysis is given for motions in a uniform magnetic field. This discussion is followed, in turn, by the motion in parallel electric and magnetic fields and in perpendicular electric and magnetic fields. 1.1 Charged Particles The charge, or quantity, of negative electricity of the electron has been found by numerous experiments to be 1.602 ¥ 10−19 C (coulomb). The values of many important physical constants are given in Appendix A. Some idea of the number of electrons per second that represents current of the usual order of magnitude is readily possible. For example, since the charge per electron is 1.602 ¥ 10−19 C, the number of electrons per coulomb is the reciprocal of this number, or approxi- mately, 6 ¥ 1018. Further, since a current of 1 A (ampere) is the flow of 1 C/sec, then a current of only 1 pA (1 picoampere, or 10−12 A) represents the motion of approximately 6 million electrons per second. Yet a current of 1 pA is so small that considerable difficulty is experienced in attempting to measure it. Inadditiontoitscharge,theelectronpossessesadefinitemass.Adirect measurement of the mass of an electron cannot be made, but the ratio e/m of the charge to the mass has been determined by a number of experimenters using independent methods. The most probable value for this ratio is 1.759 ¥ 1011 C/kg. From this value of e/m and the value of e, the charge on the electron, the mass of the electron is calculated to be 9.109 ¥ 10−31 kg. The charge of a positive ion is an integral multiple of the charge of the electron, although it is of opposite sign. For the case of singly ionized particles, the charge is equal to that of the electron. For the case of doubly ionized particles, the ionic charge is twice that of the electron. The mass of an atom is expressed as a number that is based on the choice of the atomic weight of oxygen equal to 16. The mass of a hypothetical atom of atomic Chapter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 21. Millman’s Electronic Devices and Circuits 2 weight unity is, by this definition, one-sixteenth that of the mass of monatomic oxygen. This has been calculated to be 1.660 ¥ 10−27 kg. Hence, in order to calculate the mass in kilograms of any atom, it is necessary only to multiply the atomic weight of the atom by 1.660 ¥ 10−27 kg. A table of atomic weights is given in Appendix C. The radius of the electron has been estimated as 10−15 m, and that of an atom as 10−10 m. These are so small that all charges are considered as mass points in the following sections. Classical and Wave-mechanical Models of the Electron The foregoing description of the electron (or atom) as a tiny particle possessing a definite charge and mass is referred to as the classical model. If this particle is subjected to electric, magnetic, or gravitational fields, it experiences a force, and hence is accelerated. The trajectory can be determined precisely using Newton’s laws, provided that the forces acting on the particle are known. In this chapter we make exclusive use of the classical model to study electron ballistics. The term electron ballistics is used because of the existing analogy between the motion of charged particles in a field of force and the motion of a falling body in the earth’s gravitational field. For large-scale phenomena, such as electronic trajectories in a vacuum tube, the classical model yields accurate results. For small-scale systems, however, such as an electron in an atom or in a crystal, the classical model treated by Newtonian mechanics gives results which do not agree with experiment. To describe such subatomic systems properly it is found necessary to attribute to the electron a wavelike property which imposes restrictions on the exactness with which the electronic motion can be predicted. This wavemechanical model of the electron is considered in Chap. 2. 1.2 The Force on Charged Particles in an Electric Field The force on a unit positive charge at any point in an electric field is, by definition, the electric field intensity e at that point. Consequently, the force on a positive charge q in an electric field of intensity e is given by qe, the resulting force being in the direction of the electric field. Thus, fq = q e (1.1) where fq is in newtons, q is in coulombs, and e is in volts per meter. Boldface type is employed wherever vector quantities (those having both magnitude and direction) are encountered. The mks (meter-kilogram-second) rationalized system of units is found most convenient for the subsequent studies. Therefore, unless otherwise stated, this system of units is employed. In order to calculate the path of a charged particle in an electric field, the force, given by Eq. (1.1), must be related to the mass and the acceleration of the particle by Newton’s second law of motion. Hence f q ma m dv dt q = = = e (1.2) where m = mass, kg a = acceleration, m/sec2 v = velocity, m/sec The solution of this equation, subject to appropriate initial conditions, gives the path of the particle resulting from the action of the electric forces. If the magnitude of the charge on the electron is e, the force on an electron in the field is f = − ee (1.3) The minus sign denotes that the force is in the direction opposite to the field. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 22. 3 Electron Ballistics and Applications In investigating the motion of charged particles moving in externally applied force fields of electric and magnetic origin, it is implicitly assumed that the number of particles is so small that their presence does not alter the field distribution. 1.3 Constant Electric Field Suppose that an electron is situated between the two plates of a parallel-plate capacitor which are contained in an evacuated envelope, as illustrated in Fig. 1.1. A difference of potential is applied between the two plates, the direction of the electric field in the region between the two plates being as shown. If the distance between the plates is small compared with the dimensions of the plates, the electric field may be considered to be uniform, the lines of force pointing along the negative X direction. That is, the only field that is present is e along the − X axis. It is desired to investigate the characteristics of the motion, subject to the initial conditions vx = vox x = xo when t = 0 (1.4) This means that the initial velocity vox is chosen along e, the lines of force, and that the initial position xo of the electron is along the X axis. Since there is no force along the Y or Z directions, Newton’s law states that the acceleration along these axes must be zero. However, zero acceleration means constant velocity; and since the velocity is initially zero along these axes, the particle will not move along these directions. That is, the only possible motion is one-dimensional, and the electron moves along the X axis. Newton’s law applied to the X direction yields ee = max or a e m x = = const e (1.5) where e represents the magnitude of the electric field. This analysis indicates that the electron will move with a constant acceleration in a uniform electric field. Consequently, the problem is analogous to that of a freely falling body in the uniform gravitational field of the earth. The solution of this problem is given by the well-known expressions for the velocity and displacement,viz., v v a t x x v t a t x ox x o ox x = = + + + 1 2 2 (1.6) provided that ax = const, independent of the time. It is to be emphasized that, if the acceleration of the particle is not a constant but depends upon the time, Eqs (1.6) are no longer valid. Under these circumstances the motion is determined by integrating the equations dv dt a dx dt v x x x = and = (1.7) These are simply the definitions of the acceleration and the velocity, respectively. Equations (1.6) follow directly from Eqs (1.7) by integrating the latter equations subject to the condition of a constant acceleration. Fig. 1.1 The one-dimensional electric field between the plates of a parallel-plate capacitor. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 23. Millman’s Electronic Devices and Circuits 4 Example 1.1 An electron starts at rest on one plate of a plane-parallel capacitor whose plates are 5 cm apart. The applied voltage is zero at the instant the electron is released, and it increases linearly from zero to 10 V in 0.1 msec.† a. If the opposite plate is positive, what speed will the electron attain in 50 nsec? b. Where will it be at the end of this time? c. With what speed will the electron strike the positive plate? Solution Assume that the plates are oriented with respect to a cartesian system of axes as illustrated in Fig. 1.1. The magnitude of the electric field intensity is (a) e = ¥ ¥ ¥ - - 10 5 10 10 2 7 t t = 2 10 V/m 9 Hence a dv dt f m e m t t x x x = = (1.76 10 ) (2 10 ) =3.52 10 m/sec 11 9 20 2 = = ¥ ¥ ¥ e Upon integration, we obtain for the speed At v a dt t t v x x t x 1.76 10 5 10 sec, = 4.40 10 m/se 20 2 5 = = ¥ = ¥ ¥ Ú - 0 8 c c. (b) Integration of vx with respect to t, subject to the condition that x = 0 when t = 0, fields At x v dt t dt t t x t t = = 10 = 5.87 10 = 5 10 sec, 20 2 19 3 0 0 8 1 76 Ú Ú ¥ ¥ ¥ - . = 7.32 10 m = 0.732 cm. x ¥ -3 (c) To find the speed with which the electron strikes the positive plate, we first find the time t it takes to reach that plate, or t x = 5 87 10 0 05 5 87 10 9 46 10 19 1 3 19 1 3 8 . . . . sec ¥ Ê Ë Á ˆ ¯ ˜ = ¥ Ê Ë Á ˆ ¯ ˜ = ¥ - Hence vx = 1.76 ¥ 1020t2 = 1.76 ¥ 1020(9.46 ¥ 10−8)2 = 1.58 ¥ 10 m/sec 1.4 Potential The discussion to follow need not be restricted to uniform fields, but ex may be a function of distance. However, it is assumed that ex is not a function of time. Then, from Newton’s second law, † 1 msec = 1 microsecond = 10−6 sec. 1 nsec = 1 nanosecond = 10−9 sec. Conversion factors and prefixes are given in Appendix B. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 24. 5 Electron Ballistics and Applications - e m dv dt x x e = Multiply this equation by dx = vx dt, and integrate. This leads to - = Ú Ú e m dx v dv x x x x x v v ox x e 0 (1.8) The definite integral ex x x dx o Ú is an expression for the work done by the field in carrying a unit positive charge from the point xo to the point x. By definition, the potential V (in volts) of point x with respect to point xo is the work done against the field in taking a unit positive charge from xo to x. Thus † V dx x x x o ∫ - Ú e (1.9) By virtue of Eq. (1.9), Eq. (1.8) integrates to eV m v v x ox = ( ) 1 2 2 2 - (1.10) where the energy eV is expressed in joules. Equation (1.10) shows that an electron that has “fallen” through a certain difference of potential V in going from point xo to point x has acquired a specific value of kinetic energy and velocity, independent of the form of the variation of the field distribution between these points and dependent only upon the magnitude of the potential difference V. Although this derivation supposes that the field has only one component, namely, ex along the X axis, the final result given by Eq. (1.10) is simply a statement of the law of conservation of energy. This law is known to be valid even if the field is multidimensional. This result is extremely important in electronic devices. Consider any two points A and B in space, with point B at a higher potential than point A by Vba . Stated in its most general form, Eq. (1.10) becomes qV mv mv BA A B = 1 2 1 2 2 2 - (1.11) where q is the charge in coulombs, qVBA is in joules, and vA and vb are the corresponding initial and final speeds in meters per second at the points A and B, respectively. By definition, the potential energy between two points equals the potential multiplied by the charge in question. Thus the left-hand side of Eq. (1.11) is the rise in potential energy from A to B. The right-hand side represents the drop in kinetic energy from A to B. Thus Eq. (1.11) states that the rise in potential energy equals the drop in kinetic energy, which is equivalent to the statement that the total energy remains unchanged. It must be emphasized that Eq. (1.11) is not valid if the field varies with time. If the particle is an electron, then −e must be substituted for q. If the electron starts at rest, its final speed v, as given by Eq. (1.11) with va = 0, vB = v, and VBA = V, is v eV m = 2 1 2 (1.12) † The symbol ∫ is used to designate “equal to by definition.” Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 25. Millman’s Electronic Devices and Circuits 6 or v V = ¥ 5.93 105 1 2 (1.13) Thus, if an electron “falls” through a difference of only 1 V, its final speed is 5.93 ¥ 105 m/sec, or approximately 370 miles/sec. Despite this tremendous speed, the electron possesses very little kinetic energy, because of its minute mass. It must be emphasized that Eq. (1.13) is valid only for an electron starting at rest. If the electron does not have zero initial velocity or if the particle involved is not an electron, the more general formula [Eq. (1.11)] must be used. 1.5 The eV Unit of Energy The joule (J) is the unit of energy in the mks system. In some engineering power problems this unit is very small, and a factor of 103 or 106 is introduced to convert from watts (1 W = 1 J/sec) to kilowatts or megawatts, respectively. However, in other problems, the joule is too large a unit, and a factor of 10−7 is introduced to convert from joules to ergs. For a discussion of the energies involved in electronic devices, even the erg is much too large a unit. This statement is not to be construed to mean that only minute amounts of energy can be obtained from electron devices. It is true that each electron possesses a tiny amount of energy, but as previously pointed out (Sec. 1.1), an enormous number of electrons is involved even in a small current, so that considerable power may be represented. A unit of work or energy, called the electron volt (eV), is defined as follows: 1 eV ∫ 1.60 ¥ 10−19 J Of course, any type of energy, whether it be electric, mechanical, thermal, etc., may be expressed in electron volts. The name electron volt arises from the fact that, if an electron falls through a potential of one volt, its kinetic energy will increase by the decrease in potential energy, or by eV = (1.60 ¥ 10−19 C)(lV) = 1.60 ¥ 10−19 J = 1 eV However, as mentioned above, the electron-volt unit may be used for any type of energy, and is not restricted to problems involving electrons. The abbreviations MeV and BeV are used to designate 1 million and 1 billion electron volts, respectively. 1.6 Relationship between Field Intensity and Potential The definition of potential is expressed mathematically by Eq. (1.9). If the electric field is uniform, the integral may be evaluated to the form - - - Ú e e x x x z o dx x x V o = ( ) = which shows that the electric field intensity resulting from an applied potential difference V between the two plates of the capacitor illustrated in Fig. 1.1 is given by ex o V x x V d = - - = - (1.14) where ex is in volts per meter, and d is the distance between plates, in meters. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 26. 7 Electron Ballistics and Applications In the general case, where the field may vary with the distance, this equation is no longer true, and the correct result is obtained by differentiating Eq. (1.9). We obtain ex dV dx = - (1.15) The minus sign shows that the electric field is directed from the region of higher potential to the region of lower potential. 1.7 Two-dimensional Motion Suppose that an electron enters the region between the two parallel plates of a parallel-plate capacitor which are oriented as shown in Fig. 1.2 with an initial velocity in the +X direction. It will again be assumed that the electric field between the plates is uniform. Then, as chosen, the electric field e is in the direction of the −Y axis, no other fields existing in this region. The motion of the particle is to be investigated, subject to the initial conditions v v x v y v z t x ox y z = = = = = = ¸ ˝ Ô ˛ Ô 0 0 0 0 0 when = 0 (1.16) Since there is no force in the Z direction, the acceleration in that direction is zero. Hence the component of velocity in the Z direction remains constant. Since the initial velocity in this direction is assumed to be zero, the motion must take place entirely in one plane, the plane of the paper. For a similar reason, the velocity along the X axis remains constant and equal to vox. That is, vx = vox from which it follows that x = vox t (1.17) On the other hand, a constant acceleration exists along the Y direction, and the motion is given by Eq. (1.6), with the variable x replaced by y: v a t y a t y y y = = 1 2 2 (1.18) where a e m eV md y y d = - = e (1.19) and where the potential across the plates is V = Vd These equations indicate that in the region between the plates the electron is accelerated upward, the velocity component vy varying from point to point, whereas the velocity component vx remains unchanged in the passage of the electron between the plates. The path of the particle with respect to the point O is readily determined by combining Eqs (1.17) and (1.18), the variable t being eliminated. This leads to the expression y a v x y ox = Ê Ë Á ˆ ¯ ˜ 1 2 2 2 (1.20) which shows that the particle moves in a parabolic path in the region between the plates. Fig. 1.2 Two dimensional electronic motion in a uniform electric field. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 27. Millman’s Electronic Devices and Circuits 8 Example 1.2 Hundred-volt electrons are introduced at A into a uniform electric field of 104 V/m, as shown in Fig. 1.3. The electrons are to emerge at the point B in time 4.77 nsec. (a) What is the distance AB? (b) What angle does the electron beam make with the horizontal? Solution The path of the electrons will be a parabola, as shown by the dashed curve in Fig. 1.3. This problem is analogous to the firing of a gun in the earth’s gravitational field. The bullet will travel in a parabolic path, first rising because of the muzzle velocity of the gun and then falling because of the downward attractive force of the earth. The source of the charged particles is called an electron gun, or an ion gun. The initial electron velocity is found using Eq. (1.13). vo = 5.93 = 5.93 10 m/sec 6 ¥ ¥ 10 100 5 Since the speed along the X direction is constant, the distance AB = x is given by x = (vo cos q )t = (5.93 ¥ 106 cos q )(4.77 ¥ 10−9) = 2.83 ¥ 10−2 cos q Hence we first must find q before we can solve for x. Since the acceleration ay in the Y direction is constant, then y v t a t o y ( sin ) = - q 1 2 2 and y B v a t e m t o y = = = Ê Ë Á ˆ ¯ ˜ = ¥ 0 1 2 1 2 1 2 at point or sin (1.76 10 )(10 11 , q e 4 4 9 6 )(4.77 10 ) 4.20 10 m/sec ¥ = ¥ - (b) sin = 0.707 or 45 q q = ¥ ¥ = 4 20 10 5 93 10 6 6 . . and (a) x = 2.83 ¥ 10−2 ¥ 0.707 = 2.00 ¥ 10−2 m = 2.00 cm Example 1.3 A 100 eV hydrogen ion is released in the center O of the plates in the coordinate system as shown in Fig. 1.2. The voltage Vd between the plates varies linearly from 0 to 50 V in 10-7 sec and then drops immediately to zero and remains at zero. The separation between the plates d = 2 cm and length of the plates l = 5 cm. If the ion enters the region between the plates at time t = 0, how far will it be displaced from the X axis upon emergence from between the plates? Fig. 1.3 Parabolic path of an electron in a uniform electric field. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 28. 9 Electron Ballistics and Applications Solution The velocity of the hydrogen ion along the X axis is v qV m ox h = Ê Ë Á ˆ ¯ ˜ = ¥ ¥ ¥ ¥ Ê Ë Á ˆ ¯ ˜ = - - 2 2 1 602 10 100 1 676 10 4 3 1 2 19 27 1 2 . . . 7 7 105 ¥ m/sec. Note that we have used q = e = 1.602 ¥ 10-19 C as the charge and mh = (Atomic mass of hydrogen) ¥ 1.660 ¥ 10-27 kg = 1.01 ¥ 1.660 ¥ 10-27 kg = 1.677 ¥ 10-27 kg as the mass of a hydrogen ion in the above calculation. The potential difference Vd (in volts) is given by V t t t t t t d = Ê Ë Á ˆ ¯ ˜ £ £ Ï Ì Ô Ó Ô 50 0 0 1 1 1 ; ; where t1 = 10-7 sec. Since the electric field e = - V d d is in the - Y direction, there is no force along the X or Z direc- tions on the ion and thus the velocity component vox along the X direction remains unchanged. It may be observed that at t = t1, the displacement in the X direction is x1 = vox t1 = 4.37 ¥ 105 ¥ 10-7 = 4.37 ¥ 10-2 m which is less than l = 5 cm. Therefore, it is clear that when the electric field becomes zero, the ion must be in between the plates at a point below the X axis whose displacement along the X axis is x1 from the center point O . Since, the hydrogen ion has positive charge, a force will act on the ion in the - Y direction (i.e. opposite to that of an electron) which is given as f m dv dt q eV d t y h y d = = = - = - ¥ ¥ ¥ ¥ = - ¥ - - e ( . ) ( ) ( . 1 602 10 5 10 2 10 4 0 10 19 8 2 - - £ Ï Ì Ô Ó Ô 9 1 1 0 0 ) ; ; ] t t t t t where the negative sign indicates that the force is acting on the ion in the - Y direction. Now, applying the initial condition vy = 0 at t = 0 in the above differential equation, the velocity of the ion for 0 £ t £ t1 is given as v dy dt t t y = = - ¥ ¥ ¥ Ê Ë Á ˆ ¯ ˜ = - ¥ - - 4 10 2 1 676 10 1 19 10 9 27 2 18 2 . ( . ) m/sec With the initial condition y = 0 at t = 0, the displacement in the - Y direction is given as y t t t = - ¥ Ê Ë Á ˆ ¯ ˜ £ £ 1 19 10 3 0 18 3 1 . ; Hence at t = t1, the displacement is y1 18 7 3 4 1 19 10 3 10 3 96 10 0 0396 = - ¥ Ê Ë Á ˆ ¯ ˜ ¥ ( ) = ¥ = - - . . . m cm Note that the force in the -Y direction becomes zero for t t1. This implies that the velocity along the -Y direction becomes v dy dt t t t oy = = - ¥ = - ¥ = ( . ) . /sec , 1 19 10 1 19 10 18 1 2 4 m constantfor 1 which is same as the velocity vy at t = t1. Thus, subject to the initial condition y = y1 at t = t1, the displacement of the ion from the X axis for t t1 is given by y = voy (t - t1) + y1 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 29. Millman’s Electronic Devices and Circuits 10 Now, the time required by the ion to travel a distance l along the - X direction is t = l vox = ¥ ¥ = ¥ - - 5 10 4 37 10 1 14 10 2 5 7 . . sec. Therefore, the total displacement from the X axis upon the emergence from between the plates may be obtained by putting t = t in the displacement equation of the ion along the - Y direction as y = voy (t - t1) + y1 = -1.19 ¥ 104 ¥ 1.4 ¥ 10-8 −3.96 ¥ 10-4 = -5.6 ¥ 10-4 m ª -0.056 cm Note that the negative sign indicates that the displacement is measured from the X axis along the −Y direction. Alternative Method For 0 £ x £ x1 = vox t1, the locus of the hydrogen ion may be obtained by substituting t x vox = in the displacement equation which is given as y v x x x x ox = - ¥ Ê Ë Á ˆ ¯ ˜ = - £ £ 1 19 10 3 4 75 0 18 3 3 3 1 . . ; . Since electric field becomes zero in the region x x1 (i.e. t = t1), no force acts on the ion in this region. The resultant velocity of the ion must be along the tangent to the above path at the point (x1, y1) and hence the path of the ion is described by the straight line y - y1 = tan q (x - x1) where, tan q is the slope of the tangent at (x1, y1) and is given by tan . q = = - = dy dx x x x1 14 26 1 2 Now, the total displacement at x = l = 5 cm is given by y x l x y (14.26 )( ) + 14.26 (4.37 10 ) (5 10 4.37 1 1 2 = - - = - ¥ ¥ ¥ ¥ - - - 1 2 2 2 ¥ ¥ - ¥ ¥ = - - - 10 ) 4.75 (4.37 10 ) 0.056 cm 3 2 2 1.8 Electrostatic Deflection in a Cathode-ray Tube The essentials of a cathode-ray tube for electrostatic deflection are illustrated in Fig. 1.4. The hot cathode K emits electrons which are accelerated toward the anode by the potential Va. Those electrons which are not collected by the anode pass through the tiny anode hole and strike the end of the glass envelope. This has been coated with a material that fluoresces when bombarded by electrons. Thus the positions where the electrons strike the screen are made visible to the eye. The displacement D of the electrons is determined by the potential Vd (assumed constant) applied between the deflecting plates, as shown. The velocity vox with which the electrons emerge from the anode hole is given by Eq. (1.12), viz., Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 30. 11 Electron Ballistics and Applications v eV m ox a = 2 (1.21) on the assumption that the initial velocities of emission of the electrons from the cathode are negligible. Since no field is supposed to exist in the region from the anode to the point O, the electrons will move with a constant velocity vox in a straight-line path. In the region between the plates the electrons will move in the parabolic path given by y a v x y ox = 1 2 2 ( / ) 2 according to Eq. (1.20). The path is a straight line from the point of emergence M at the edge of the plates to the point P¢ on the screen, since this region is field-free. The straight-line path in the region from the deflecting plates to the screen is, of course, tangent to the parabola at the point M. The slope of the line at this point, and so at every point between M and P¢, is [from Eq. (1.20)] tan q = ˘ ˚ ˙ = = dy dx a l v x l y ox 2 From the geometry of the figure, the equation of the straight line MP¢ is found to be y a l v x l y ox = - Ê Ë Á ˆ ¯ ˜ 2 2 (1.22) since x = l and y a l v y ox = 1 2 2 2 / at the point M. When y = 0, x = l/2, which indicates that when the straight line MP ¢ is extended backward, it will intersect the tube axis at the point O¢, the center point of the plates. This result means that O¢ is, in effect, a virtual cathode, and regardless of the applied potentials Va and Vd, the electrons appear to emerge from this “cathode” and move in a straight line to the point P¢. At the point P¢, y = D, and x L l = + 1 2 . Equation (1.22) reduces to D a lL v y ox = 2 By inserting the known values of ay (= eVd/dm) and vox, this becomes D lLV dV d a = 2 (1.23) This result shows that the deflection on the screen of a cathode-ray tube is directly proportional to the deflecting voltage Vd applied between the plates. Consequently, a cathode-ray tube may be used as a linear-voltage indicating device. Fig. 1.4 Electrostatic deflection in a cathode-ray tube. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 31. Millman’s Electronic Devices and Circuits 12 The electrostatic-deflection sensitivity of a cathode-ray tube is defined as the deflection (in meters) on the screen per volt of deflecting voltage. Thus S D V lL dV d a ∫ = 2 (1.24) An inspection of Eq. (1.24) shows that the sensitivity is independent of both the deflecting voltage Vd and the ratio e/m. Furthermore, the sensitivity varies inversely with the accelerating potential Va. The idealization made in connection with the foregoing development, viz., that the electric field between the deflecting plates is uniform and does not extend beyond the edges of the plates, is never met in practice. Consequently, the effect of fringing of the electric field may be enough to necessitate corrections amounting to as much as 40 percent in the results obtained from an application of Eq. (1.24). Typical measured values of sensitivity are 1.0 to 0.1 mm/V, corresponding to a voltage requirement of 10 to 100 V to give a deflection of 1 cm. Example 1.4 A sinusoidal voltage Vd (t) = Vm sin (w t) is applied across the deflecting plates of a cathode-ray tube where Vm and w are the amplitude and frequency of the applied potential. The transit time between the plates is t. The length of the line on the screen is A. If A0 is the line length when the transit time is negligible compared with the period of the applied voltage, show that A A = 0 2 2 sin( / ) ( / ) wt wt Solution Consider the coordinate system as shown in Fig. 1.4. Since the electric field is in the -Y direction, the force equation are given as f m d y dt eV t d eV t d f f y d m x z = = = = = 2 2 ( ) sin( ) w and 0 Subjecting to the initial conditions y = 0 and v dy dt y = = 0 at t = 0, the displacement equation of the electron in the Y direction is given by y eV dm t t m = - Ê Ë Á ˆ ¯ ˜ w w w sin( ) Since no force is acting on the electron along the X or Z direction, with the initial conditions vx = vox and vz = 0 at t = 0, the displacements along the X and Y directions are given as x = vox t and z = 0 Substituting t x vox = in the equation of y, the path of the electron is given as y eV dm x v x v m ox ox = - Ê Ë Á ˆ ¯ ˜ Ê Ë Á Á Á ˆ ¯ ˜ ˜ ˜ w w w sin Now, for x l, the path becomes a straight line MP¢(as shown in Fig.1.4) with slope Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 32. 13 Electron Ballistics and Applications tan sin ( cos( )) q w w t w wt = = - Ê Ë Á ˆ ¯ ˜ = - = dy dx eV d m v l v eV d m l x l m ox ox m 1 1 where t = l vox is the transit time. Now, the total deflection line-length PP¢ on the screen is given by A L l y eV L l d m l m = - Ê Ë Á ˆ ¯ ˜ + = - Ê Ë Á ˆ ¯ ˜ Ê Ë Á Á ˆ ¯ ˜ ˜ Ê Ë Á ˆ ¯ 2 2 2 1 2 tan sin q t w w t ˜ ˜ Ê Ë Á ˆ ¯ ˜ Ê Ë Á ˆ ¯ ˜ + sin w t w t 2 2 1 y where y1 is the displacement of the electron from the X axis at x = l which is written as y y eV d m eV d m m m = = - Ê Ë Á ˆ ¯ ˜ = - - + - 1 2 3 5 1 3 5 w t wt w t w w wt wt wt sin( ) ( ) ! ( ) ! … …… …… Ê Ë Á ˆ ¯ ˜ Ï Ì Ô Ó Ô ¸ ˝ Ô ˛ Ô = - + Ê Ë Á ˆ ¯ ˜ eV d m m ( ) ! ( ) ! wt t wt t 2 3 2 3 5 Since wt p t = Ê Ë Á ˆ ¯ ˜ 2 T where T is the period of the applied voltage, y1 ª 0 for t T. However, for higher frequencies of the applied voltage, where T is very small but t is comparable with T resulting in the finite value of wt, y1 again becomes very small because of the very small values of t. Thus, we may say that for any finite frequency of the applied voltage, y1 can always be neglected as compared to the total deflection of the beam on the screen. Therefore, the total deflection line-length on the screen may be approximately written as A eV L l d m l m ª - Ê Ë Á ˆ ¯ ˜ Ê Ë Á Á ˆ ¯ ˜ ˜ Ê Ë Á ˆ ¯ ˜ Ê Ë Á ˆ ¯ ˜ Ê Ë t w w t w t w t 2 2 2 2 2 sin sin Á Á ˆ ¯ ˜ For, t T sin w t w t 2 2 1 Ê Ë Á ˆ ¯ ˜ Ê Ë Á ˆ ¯ ˜ ª hence the line-length A0 can be given by Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 33. Millman’s Electronic Devices and Circuits 14 A eV L l d m l m 0 2 2 2 ª - Ê Ë Á ˆ ¯ ˜ Ê Ë Á Á ˆ ¯ ˜ ˜ Ê Ë Á ˆ ¯ ˜ t w w t sin Now, the line-length on the screen A for all values of t and T may be expressed in the form of the desired result as A A = = ( ) ( ) 0 2 2 sin w t w t 1.9 The Cathode-ray Oscilloscope An electrostatic tube has two sets of deflecting plates which are at right angles to each other in space (as indicated in Fig. 1.5). These plates are referred to as the vertical-deflection and horizontal-deflection plates because the tube is oriented in space so that the potentials applied to these plates result in verti- cal and horizontal deflections, respectively. The reason for having two sets of plates is now discussed. Suppose that the sawtooth waveform of Fig. 1.6 is impressed across the horizontal-deflection plates. Since this voltage is used to sweep the electron beam across the screen, it is called a sweep voltage. The electrons are deflected linearly with time in the horizontal direction for a time T. Then the beam returns to its starting point on the screen very quickly as the sawtooth voltage rapidly falls to its initial value at the end of each period. If a sinusoidal voltage is impressed across the vertical-deflection plates when,simultaneously,thesweepvolt- ageisimpressedacrossthehorizontal- deflection plates, the sinusoidal voltage, which of itself would give rise to a vertical line, will now be spread out and will appear as a sinusoidal trace on the screen.The pattern will appear stationary only if the time T is equal to, or is some multiple of, the time for one cycle of the wave on the vertical plates. It is then necessary that the frequency of the sweep circuit be adjusted to synchronize with the frequency of the applied signal. Actually, of course, the voltage impressed on the vertical plates may have any waveform. Consequently, a system of this type provides an almost inertialess oscilloscope for viewing arbitrary waveshapes. This is one of the most common uses for cathode-ray tubes. If a nonrepeating sweep voltage Fig. 1.5 A waveform to be displayed on the screen of a cathode-ray tube is applied to the vertical- deflection plates, and simultaneously a sawtooth voltage is applied to the horizontal-deflection plates. Fig. 1.6 Sweep or sawtooth voltage for a cathode-ray tube. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 34. 15 Electron Ballistics and Applications is applied to the horizontal plates, it is possible to study transients on the screen. This requires a system for synchronizing the sweep with the start of the transient.† A commercial oscilloscope has many refinements not indicated in the schematic diagram of Fig. 1.5. The sensitivity is greatly increased by means of a high-gain amplifier interposed between the input signal and the deflection plates. The electron gun is a complicated structure which allows for accelerating the electrons through a large potential, for varying the intensity of the beam, and for focusing the electrons into a tiny spot. Controls are also provided for positioning the beam as desired on the screen. 1.10 Relativistic Variation of Mass with Velocity The theory of relativity postulates an equivalence of mass and energy according to the relationship W = mc2 (1.25) where W = total energy, J m = mass, kg c = velocity of light in vacuum, m/sec According to this theory, the mass of a particle will increase with its energy, and hence with its speed. If an electron starts at the point A with zero velocity and reaches the point B with a velocity v, then the increase in energy of the particle must be given by the expression eV, where V is the difference of potential between the points A and B. Hence eV = mc2 − moc2 (1.26) where moc2 is the energy possessed at the point A. The quantity mo is known as the rest mass, or the electrostatic mass, of the particle, and is a constant, independent of the velocity. The total mass m of the particle is given by m m v c o = - 1 2 2 / (1.27) This result, which was originally derived by Lorentz and then by Einstein as a consequence of the theory of special relativity, predicts an increasing mass with an increasing velocity, the mass approaching an infinite value as the velocity of the particle approaches the velocity of light. From Eqs (1.26) and (1.27), the decrease in potential energy, or equivalently, the increase in kinetic energy, is eV m c v c = - - Ê Ë Á Á ˆ ¯ ˜ ˜ 0 2 2 2 1 1 1 / (1.28) This expression enables one to find the velocity of an electron after it has fallen through any potential difference V. By defining the quantity vN as the velocity that would result if the relativistic variation in mass were neglected, i.e., v eV m N o ∫ 2 (1.29) † Superscript numerals are keyed to the References at the end of the chapter. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 35. Millman’s Electronic Devices and Circuits 16 then Eq. (1.28) can be solved for v, the true velocity of the particle. The result is v c v c N = - + È Î Í Í ˘ ˚ ˙ ˙ 1 1 1 2 2 1 2 2 2 ( / ) (1.30) This expression looks imposing at first glance. It should, of course, reduce to v = vn for small velocities. That it does so is seen by applying the binomial expansion to Eq. (1.30). The result becomes v v v c N N = - + Ê Ë Á ˆ ¯ ˜ 1 3 8 2 2 . . . (1.31) From this expression it is seen that, if the speed of the particle is much less than the speed of light, the second and all subsequent terms in the expansion can be neglected, and then v = vN, as it should. This equation also serves as a criterion to determine whether the simple classical expression or the more formidable relativistic one must be used in any particular case. For example, if the speed of the electron is one-tenth of the speed of light, Eq. (1.31) shows that an error of only three-eighths of 1 percent will result if the speed is taken as vN instead of v. For an electron, the potential difference through which the particle must fall in order to attain a velocity of 0.1c is readily found to be 2,560 V. Thus, if an electron falls through a potential in excess of about 3 kV, the relativistic corrections should be applied. If the particle under question is not an electron, the value of the nonrelativistic velocity is first calculated. If this is greater than 0.1c, the calculated value of vn must be substituted in Eq. (1.30) and the true value of v then calculated. In cases where the speed is not too great, the simplified expression (1.31) may be used. The accelerating potential in high-voltage cathode-ray tubes is sufficiently high to require that relativistic corrections be made in order to calculate the velocity and mass of the particle. Other devices employing potentials that are high enough to require these corrections are x-ray tubes, the cyclotron, and other particle-accelerating machines. Unless specifically stated otherwise, nonrelativistic conditions are asumed in what follows. 1.11 Force in a Magnetic Field To investigate the force on a moving charge in a magnetic field, the well-known motor law is recalled. It has been verified by experiment that, if a conductor of length L, carrying a current of I, is situated in a magnetic field of intensity B, the force fm acting on this conductor is fm = BIL (1.32) where fm is in newtons, B is in webers per square meter (Wb/m2), † I is in amperes, and L is in meters. Equation (1.32) assumes that the directions of I and B are perpendicular to each other. The direction of this force is perpendicular to the plane of I and B and has the direction of advance of a right-handed screw which is placed at O and is rotated from I to B through 90°, as illustrated in Fig. 1.7. If I and B are not perpendicular to each other, only the component of I perpendicular to B contributes to the force. Some caution must be exercised with regard to the meaning of Fig. 1.7. If the particle under consid- eration is a positive ion, then I is to be taken along the direction of its motion. This is so because the † One weber per square meter (also called a tesla) equals 104 G. A unit of more practical size in most applications is the milliweber per square meter (mWb/m2), which equals 10 G. Other conversion factors are given in Appendix B. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 36. 17 Electron Ballistics and Applications conventional direction of the current is taken in the direction of flow of positive charge. If the current is due to the flow of electrons, the direction of I is to be taken as opposite to the direction of the motion of the electrons. If, therefore, a negative charge moving with a velocity v− is under consideration, one must first draw I antiparallel to v− as shown and then apply the “direction rule.” If N electrons are contained in a length L of conductor (Fig. 1.8) and if it takes an electron a time T sec to travel a distance of L m in the conductor, the total number of electrons passing through any cross section of wire in unit time is N/T. Thus the total charge per second passing any point, which, by definition, is the current in amperes, is I Ne T = (1.33) The force in newtons on a length L m (or the force on the N conduction charges contained therein) is BIL BVeL T = Furthermore, since L/T is the average, or drift, speed v m/sec of the electrons, the force per electron is fm = eBv (1.34) The subscript m indicates that the force is of magnetic origin. To summarize: The force on a negative charge e (coulombs) moving with a component of velocity v−(meters per second) normal to a field B (webers per square meter) is given by eBv−(newtons) and is in a direction perpendicular to the plane of B and v−, as noted in Fig. 1.7. † 1.12 Current Density Before proceeding with the discussion of possible motions of charged particles in a magnetic field, it is convenient to introduce the concept of current density. This concept is very useful in many later applications. By definition, the current density, denoted by the symbol J, is the current per unit area of the conducting medium. That is, assuming a uniform current distribution, J I A ∫ (1.35) where J is in amperes per square meter, and A is the cross-sectional area in square meter of the conductor. This becomes, by Eq. (1.33), Fig. 1.7 Pertaining to the determination of the direction of the force fm on a charged particle in a magnetic field. Fig. 1.8 Pertaining to the determination of the magnitude of the force fm on a charged particle in a magnetic field. † In the cross-product notation of vector analysis, fm = eB ¥ v−. For a positive ion moving with a velocity v+, the force is fm = ev+ ¥ B. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 37. Millman’s Electronic Devices and Circuits 18 J Ne TA ∫ But it has already been pointed out that T = L/v. Then J Nev LA = (1.36) From Fig. 1.8 it is evident that LA is simply the volume containing the N electrons, and so N/LA is the electron concentration n (in electrons per cubic meter). Thus n N LA = (1.37) and Eq. (1.36) reduces to J = nev = rv (1.38) where r ∫ ne is the charge density, in coulombs per cubic meter, and v is in meters per second. This derivation is independent of the form of the conducting medium. Consequently, Fig. 1.8 does not necessarily represent a wire conductor. It may represent equally well a portion of a gaseous-discharge tube or a volume element in the space-charge cloud of a vacuum tube or a semiconductor. Furthermore, neither r nor v need be constant, but may vary from point to point in space or may vary with time. Numerous occasions arise later in the text when reference is made to Eq. (1.38). 1.13 Motion in a Magnetic Field The path of a charge particle that is moving in a magnetic field is now investigated. Consider an electron to be placed in the region of the magnetic field. If the particle is at rest, fm = 0 and the particle remains at rest. If the initial velocity of the particle is along the lines of the magnetic flux, there is no force acting on the particle, in accordance with the rule associated with Eq. (1.34). Hence a particle whose initial velocity has no component normal to a uniform magnetic field will continue to move with constant speed along the lines of flux. Now consider an electron moving with a speed vo to enter a constant uniform magnetic field normally, as shown in Fig. 1.9. Since the force fm is perpendicular to v and so to the motion at every instant, no work is done on the electron.This means that its kinetic energy is not increased, and so its speed remains unchanged. Further, since v and B are each constant in magnitude, then fm is constant in magnitude and perpendicular to the direction of motion of the particle. This type of force results in motion in a circular path with con- stant speed. It is analogous to the problem of a mass tied to a rope and twirled around with constant speed. The force (which is the tension in the rope) remains constant in magnitude and is always directed toward the center of the circle, and so is normal to the motion. To find the radius of the circle, it is recalled that a particle moving in a circular path with a constant speed v has an acceleration toward the center of the circle of magnitude v2/R, where R is the radius of the path in meters. Then Fig. 1.9 Circular motion of an electron in a transverse magnetic field. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 38. 19 Electron Ballistics and Applications mv R eBv 2 = from which R mv eB = (1.39) The corresponding angular velocity in radians per second is given by w = = v R eB m (1.40) The time in seconds for one complete revolution, called the period, is T m eB = = 2 2 p w p (1.41) For an electron, this reduces to T B = ¥ - 3 57 10 11 . (1.42) In these equations, e/m is in coulombs per kilogram and B in webers per square meter. It is noticed that the radius of the path is directly proportional to the speed of the particle. Further, the period and the angular velocity are independent of speed or radius. This means, of course, that faster-moving particles will traverse larger circles in the same time that a slower particle moves in its smaller circle. This very important result is the basis of operation of numerous devices, for example, the cyclotron and magnetic-focusing apparatus. Example 1.5 Calculate the deflection of a cathode-ray beam caused by the earth’s magnetic field. Assume that the tube axis is so oriented that it is normal to the field, the strength of which is 0.6 G. The anode potential is 400 V; the anode-screen distance is 20 cm (Fig. 1.10). Solution According to Eq. (1.13), the velocity of the electrons will be vox = ¥ = ¥ 5.93 10 m/sec 5 400 1 19 107 . Since 1 Wb/m2 = 104 G, then B = 6 ¥ 10−5 Wb/m2. From Eq. (1.39) the radius of the circular path is R v e m B ox = = ¥ ¥ ¥ ¥ = = - ( / ) . . . 1 19 10 2 76 10 6 10 1 12 112 7 11 5 m cm Furthermore, it is evident from the geometry of Fig. 1.10 that (in centimeters) 1122 = (112 − D)2 + 202 from which it follows that D2 − 224D + 400 = 0 The evaluation of D from this expression yields the value D = 1.8 cm. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 39. Millman’s Electronic Devices and Circuits 20 This example indicates that the earth’s magnetic field can have a large effect on the position of the cathode-beam spot in a low-voltage cathode-ray tube. If the anode voltage is higher than the value used in this example, or if the tube is not oriented normal to the field, the deflection will be less than that calculated. In any event, this calculation indicates the advisability of carefully shielding a cathode-ray tube from stray magnetic fields. 1.14 Magnetic Deflection in a Cathode-ray Tube The illustrative example in Sec. 1.13 immediately suggests that a cathode-ray tube may employ a magnetic as well as an electric field in order to accomplish the deflection of the electron beam. However, since it is not feasible to use a field extending over the entire length of the tube, a short coil furnishing a transverse field in a limited region is employed, as shown in Fig. 1.11. The magnetic field is taken as pointing out of the paper, and the beam is deflected upward. It is assumed that the magnetic field intensity B is uniform in the restricted region shown and is zero outside of this area. Hence the electron moves in a straight line from the cathode to the boundary O of the magnetic field. In the region of the uniform magnetic field the electron experiences a force of magnitude eBv, where v is the speed. The path OM will be the arc of a circle whose center is at Q. The speed of the particles will remain constant and equal to v v eV m ox a = = 2 (1.43) The angle j is, by definition of radian measure, equal to the length of the arc OM divided by R, the radius of the circle. If we assume a small angle of deflection, then j ª l R (1.44) where, by Eq. (1.39), R mv eB = (1.45) In most practical cases, L is very much larger than l, so that little error will be made in assuming that the straight line MP¢, if projected backward, will pass through the center O¢ of the region of the magnetic field. Then D ª L tan j ª Lj (1.46) Fig. 1.10 The circular path of an electron in a cathode-ray tube, resulting from the earth’s transverse magnetic field (normal to the plane of the paper). This figure is not drawn to scale. Fig. 1.11 Magneticdeflectionina cathode‑ray tube. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 40. 21 Electron Ballistics and Applications By Eqs (1.43) to (1.45), Eq. (1.46) now becomes D L lL R lLeB mv lLB V e m a ª = = = j 2 The deflection per unit magnetic field intensity, D/B, given by D B lL V e m a = 2 (1.47) is called the magnetic-deflection sensitivity of the tube. It is observed that this quantity is independent of B. This condition is analogous to the electric case for which the electrostatic sensitivity is independent of the deflecting potential. However, in the electric case, the sensitivity varies inversely with the anode voltage, whereas it here varies inversely with the square root of the anode voltage. Another important difference is in the appearance of e/m in the expression for the magnetic sensitivity, whereas this ratio did not enter into the final expression for the electric case. Because the sensitivity increases with L, the deflecting coils are placed as far down the neck of the tube as possible, usually directly after the accelerating anode. Deflection in a Television Tube A modern TV tube has a screen diameter comparable with the length of the tube neck. Hence the angle j is too large for the approximation tan j ª j to be valid. Under these circumstances it is found that the deflection is no longer proportional to B. If the magnetic- deflection coil is driven by a sawtooth current waveform (Fig. 1.6), the deflection of the beam on the face of the tube will not be linear with time. For such wide-angle deflection tubes, special linearity- correcting networks must be added. A TV tube has two sets of magnetic-deflection coils mounted around the neck at right angles to each other, corresponding to the two sets of plates in the oscilloscope tube of Fig. 1.5. Sweep currents are applied to both coils, with the horizontal signal much higher in frequency than that of the vertical sweep. The result is a rectangular raster of closely spaced lines which cover the entire face of the tube and impart a uniform intensity to the screen. When the video signal is applied to the electron gun, it modulates the intensity of the beam and thus forms the TV picture. Example 1.6 Show that the magnetic deflection in a TV tube having a screen diameter comparable with the length of the tube neck is given by D lLB e m V e m Bl a = - / ( / )( ) 2 2 Solution Consider the coordinate system as shown in Fig. 1.11. Since, Q (0, R) is the center of the circular path of the electron due to the magnetic field under consideration, the path is described by the equation x2 + (y − R)2 = R2 Note that at x l y y R R l R = = = - - ( ) , 1 2 2 , where R mv eB = . Now, differentiating the above equation, the slope of the tangent at x = l is given by tan j = = - = dy dx l R l x l 2 2 Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 41. Millman’s Electronic Devices and Circuits 22 Thus, the total deflection may be approximately given by D L lL m v e B l ª = - tan j 2 2 2 2 2 Substituting v v eV m ox a = = 2 in the above equation, we get the desired result as D lL m e B eV m l lL V e m Bl e m B lLB e m V e m a a a = - = - ( )( ) ( ) = - ( 2 2 2 2 2 2 2 1 2 2 / / / / ) )( ) Bl 2 1.15 Magnetic Focusing As another application of the theory developed in Sec. 1.13, one method of measuring e/m is discussed. Imagine that a cathode-ray tube is placed in a constant longitudinal magnetic field, the axis of the tube coinciding with the direction of the magnetic field. A magnetic field of the type here considered is obtained through the use of a long solenoid, the tube being placed within the coil. Inspection of Fig. 1.12 reveals the motion. The Y axis represents the axis of the cathode-ray tube. The origin O is the point at which the electrons emerge from the anode. The velocity of the origin is vo, the initial transverse velocity due to the mutual repulsion of the electrons being vox. It is now shown that the resulting motion is a helix, as illustrated. The electronic motion can most easily be analyzed by resolving the velocity into two components, vy and vq, along and transverse to the magnetic field, respectively. Since the force is perpendicular to B, there is no acceleration in the Y direction. Hence vy is constant and equal to voy. A force eBvq normal to the path will exist, resulting from the transverse velocity. This force gives rise to circular motion, the radius of the circle being mvq /eB, with vq a constant, and equal to vox. The resultant path is a helix whose axis is parallel to the Y axis and displaced from it by a distance R along the Z axis, as illustrated. The pitch of the helix, defined as the distance travelled along the direction of the magnetic field in one revolution, is given by p = voyT where T is the period, or the time for one revolution. It follows from Eq. (1.41) that p m eB voy = 2p (1.48) If the electron beam is defocused, a smudge is seen on the screen when the applied magnetic field is zero. This means that the various electrons in the beam pass through the anode hole with different transverse velocities vox, and so strike the screen at different points. This accounts for the appearance of a broad, faintly illuminated area instead of a bright point on the screen. As the magnetic field is increased from zero the electrons will move in helices of different radii, since the velocity vox that controls the Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 42. 23 Electron Ballistics and Applications radius of the path will be different for different electrons. However, the period, or the time to trace out the path, is independent of vox, and so the period will be the same for all electrons. If, then, the distance from the anode to the screen is made equal to one pitch, all the electrons will be brought back to the Y axis (the point O¢ in Fig. 1.12), since they all will have made just one revolution. Under these condi- tions an image of the anode hole will be observed on the screen. As the field is increased from zero, the smudge on the screen resulting from the defocused beam will contract and will become a tiny sharp spot (the image of the anode hole) when a critical value of the field is reached. This critical field is that which makes the pitch of the helical path just equal to the anode- screen distance, as discussed above. By continuing to increase the strength of the field beyond this critical value, the pitch of the helix decreases, and the electrons travel through more than one complete revolution. The electrons then strike the screen at various points, so that a defocused spot is again visible. A magnetic field strength will ultimately be reached at which the electrons make two complete revolutions in their path from the anode to the screen, and once again the spot will be focused on the screen. This process may be continued, numerous foci being obtainable. In fact, the current rating of the solenoid is the factor that generally furnishes a practical limitation to the order of the focus. The foregoing considerations may be generalized in the following way: If the screen is perpendicular to the Y axis at a distance L from the point of emergence of the electron beam from the anode, then, for an anode-cathode potential equal to Va, the electron beam will come to a focus at the center of the screen provided that L is an integral multiple of p. Under these conditions, Eq. (1.48) may be rearranged to read e m V n L B a = 8 2 2 2 2 p (1.49) where n is an integer representing the order of the focus. It is assumed, in this development, that eV mv a oy = 1 2 2 , or that the only effect of the anode potential is to accelerate the electron along the tube axis. This implies that the transverse velocity vox, which is variable and unknown, is negligible in com- parison with voy. This is a justifiable assumption. This arrangement was suggested by Busch, and has been used2 to measure the ratio e/m for electrons very accurately. A Short Focusing Coil The method described above of employing a longitudinal mag- netic field over the entire length of a commercial tube is not too practical. Hence, in a commercial tube, a short coil is wound around the neck of the tube. Because of the fringing of the magnetic lines of flux, a radial component of B exists in addition to the component along the tube axis. Hence there are now two components of force on the electron, one due to the axial component of velocity and the radial component of the field, and the second due to the radial component of the velocity Fig. 1.12 The helical path of an electron introduced at an angle (not 90°) with a constant magnetic field. Copyright © 2010. Tata McGraw-Hill. All rights reserved.
- 43. Millman’s Electronic Devices and Circuits 24 and the axial component of the field. The analysis is complicated,3 but it can be seen qualitatively that the motion will be a rotation about the axis of the tube and, if conditions are correct, the electron on leaving the region of the coil may be turned sufficiently so as to move in a line toward the center of the screen. A rough adjustment of the focus is obtained by positioning the coil properly along the neck of the tube. The fine adjustment of focus is made by controlling the coil current. Example 1.7 Consider the magnetic focusing system described by the Fig. 1.12. Show that the coordinates of the electron on the screen (placed perpendicular to the Y axis at a distance L from the point of emergence of the electron beam) are given by x v L v z v L v ox oy ox oy = = - a a a a sin ( cos ) and 1 where a = eBL mvoy Solution Since there is no force acting on the electron along the Y direction, the time required by the electron to travel a distance L along the Y axis is given by t L voy = Subjecting to the circular motion in the X-Z plane with radius R mv eB ox = and angular velocity w = = v R eB m ox , the angle rotated from the Z axis during time t is given as q w a = = = t eBL mvoy Since the screen is parallel to the X-Z plane and electron performs motion in a circular path in X-Z plane in the clockwise direction with radius R and center at (0, R) (see Fig. 1.15), the coordinates at time t can be written in the desired forms as x R mv eB v L v mv eBL v L v ox ox oy oy ox oy = = = = sin sin sin sin q a a a a and y R R mv v ox oy = - = - cos ( cos ) q a a 1 1.16 Parallel Electric and Magnetic Fields Consider the case where both electric and magnetic fields exist simultaneously, the fields being in the same or in opposite directions. If the initial velocity of the electron either is zero or is directed along the fields, the magnetic field exerts no force on the electron, and the resultant motion depends solely upon Copyright © 2010. Tata McGraw-Hill. All rights reserved.
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- 45. of a brown tone, or with a shade of purple when the gold Bath is newly made and active; pure blacks are not easily obtained. Iceland Moss affects the colour of the proof to a certain extent, but less than Albumen; the finished prints are nearly black if the paper is highly salted. The Gelatinous sizing used for the English papers, and obtained by boiling hides in water, and hardening the product by an admixture of Alum, has a reddening influence upon reduced Silver salts, analogous to that of Albumen, or of Caseine, the characteristic animal principle of milk. Positives printed upon English paper, commonly assume some shade of brown more or less removed from black; the darker tones being more readily obtained upon the foreign papers. Citrates and Tartrates have a marked effect upon the colour of prints. Paper prepared with Citrate, in addition to Chloride of Silver, darkens to a fine purple colour which changes to brick-red in the fixing Bath. The Positives, when toned, are usually of a violet-purple or of a bistre tint, with a general aspect of warmth and transparency. SECTION II. The Processes for Fixing and Toning the Proof. This part of the operation is one to which great attention should be paid, in order to secure bright and lasting colours: it involves more of delicate chemical change than perhaps any other department of the Art. The first point requiring explanation is the process of fixing; to which (p. 41) brief reference has already been made. The methods adopted to improve the tint of the finished picture will then be described. CONDITIONS OF A PROPER FIXING OF THE PROOF.
- 46. This subject is not always understood by operators, and consequently they have no certain guide as to how long the prints should remain in the fixing Bath. The time occupied in fixing will of course vary with the strength of the solution employed; but there are simple rules which may be usefully followed. In the act of dissolving the unaltered Chloride of Silver in the proof, the fixing solution of Hyposulphite of Soda converts it into Hyposulphite of Silver (p. 43), which is soluble in an excess of Hyposulphite of Soda. But if there be an insufficient excess,—that is, if the Bath be too weak, or the print removed from it too speedily,—then the Hyposulphite of Silver is not perfectly dissolved, and begins by degrees to decompose, producing a brown deposit in the tissue of the paper. This deposit, which has the appearance of yellow spots and patches, is not usually seen upon the surface of the print, but becomes very evident when it is held up to the light, or if it be split in half, which can be readily done by gluing it between two flat surfaces of deal, and then forcing them asunder. The reaction of Hyposulphite of Soda with Nitrate of Silver.—In order to understand more fully how decomposition of Hyposulphite of Silver may affect the process of fixing, the peculiar properties of this salt should be studied. With this view Nitrate of Silver and Hyposulphite of Soda may be mixed in equivalent proportions, viz. about twenty-one grains of the former salt to sixteen grains of the latter, first dissolving each in separate vessels in half an ounce of distilled water. These solutions are to be added to each other and well agitated; immediately a dense deposit forms, which is Hyposulphite of Silver. At this point a curious series of changes commences. The precipitate, at first white and curdy, soon alters in colour: it becomes canary-yellow, then of a rich orange-yellow, afterwards liver-colour, and finally black. The rationale of these changes is explained to a certain extent by studying the composition of the Hyposulphite of Silver. The formula for this substance is as follows:—
- 47. AgO S2O2. But AgO S2O2 plainly equals AgS, or Sulphuret of Silver, and SO3, or Sulphuric Acid. The acid reaction assumed by the supernatant liquid is due therefore to Sulphuric Acid, and the black substance formed is Sulphuret of Silver. The yellow and orange-yellow compounds are earlier stages of the decomposition, but their exact nature is uncertain. The instability of Hyposulphite of Silver is principally seen when it is in an isolated state: the presence of an excess of Hyposulphite of Soda renders it more permanent, by forming a double salt, as already described. In fixing Photographic prints, this brown deposit of Sulphuret of Silver is very liable to form in the Bath and upon the picture; particularly so when the temperature is high. To obviate it, observe the following directions:—It is especially in the reaction between Nitrate of Silver and Hyposulphite of Soda that the blackening is seen; the Chloride and other insoluble Salts of Silver being dissolved, even to saturation, without any decomposition of the Hyposulphite formed. Hence if the print be washed in water to remove the soluble Nitrate, a very much weaker fixing Bath than usual may be employed. But if the proofs are taken at once from the printing frame and immersed in a dilute Bath of Hyposulphite (one part of the salt to six or eight of water), a shade of brown may often be observed to pass over the surface of the print, and a large deposit of Sulphuret of Silver soon forms as the result of the decomposition. On the other hand, with a strong Hyposulphite Bath there is little or no discoloration, and the black deposit is absent. The print must also be left for a sufficient time in the fixing bath, or some appearance of brown patches,[18] visible by transmitted light, may occur. Each atom of Nitrate of Silver requires three atoms of Hyposulphite of Soda to form the sweet and soluble double salt, and hence, if the action be not continued sufficiently long, another
- 48. compound will be formed almost tasteless and insoluble (p. 44). Even immersion in a new Bath of Hyposulphite of Soda does not fix the print when once the yellow stage of decomposition has been established. This yellow salt is insoluble in Hyposulphite of Soda, and consequently remains in the paper. [18] The writer has noticed that when sensitive paper is kept for some time before being used for printing, these yellow patches of imperfect fixation are very liable to occur. The Nitrate of Silver appears gradually to enter into combination with the organic matter of the size of the paper, and cannot then be so easily extracted by the fixing bath. In fixing prints by Ammonia the Author has found that the same rule may be applied as in the case of Hyposulphite of Soda, viz. that if the process be not properly performed, the white parts of the print will appear spotted when held up to the light, from a portion of insoluble Silver Salt remaining in the paper. Prints imperfectly fixed by Ammonia are also usually brown and discoloured upon the surface of the paper. More exact directions as to the strength of the fixing bath and the time occupied in the process, will be given in the Second Part of the Work; at present it may be noticed only that Albuminized paper, from the horny nature of its surface-coating, requires a longer treatment with the Hyposulphite than the plain paper. THE SALTS OF GOLD AS TONING AGENTS FOR PHOTOGRAPHIC PRINTS. The Salts of Gold have been successfully applied to the improvement of the tones obtained by simply fixing the proof in Hyposulphite of Soda. The following are the principal modes followed:— M. Le Grey's Process.—The print, having been exposed to light until it becomes very much darker than it is intended to remain, is washed in water to remove the excess of Nitrate of Silver. It is then
- 49. immersed in a dilute solution of Chloride of Gold, acidified by Hydrochloric Acid. The effect is to reduce the intensity considerably, and at the same time to change the dark shades to a violet or bluish tint. After a second washing with water, the proof is placed in plain Hyposulphite of Soda, which fixes it and alters the tone to a pure black or a blue-black, according to the manner of preparing the paper and the time of exposure to light. The rationale of the process appears to be as follows:— the Chlorine, previously combined with Gold, passes to the reduced Silver Salt; it bleaches the lightest shades, by converting them again into white Protochloride of Silver, and gives to the others a violet tint more or less intense according to the reduction. At the same time metallic Gold is deposited, the effect of which is not visible at this stage, since the same violet tint is perceived when a solution of Chlorine is substituted for Chloride of Gold. The Hyposulphite of Soda subsequently employed, decomposes the violet Subchloride of Silver, and leaves the surface of a black tint, due to the Gold and the reduced Silver Salt. M. Le Grey's process is objectionable on account of the excessive over-printing required. This however is to a great extent obviated by a modification of the process in which an alkaline instead of an acid solution of the Chloride is employed; one grain of Chloride of Gold is dissolved in about six ounces of water, to which are added twenty to thirty grains of the common Carbonate of Soda. The alkali moderates the violence of the action, so that the print washed with water and immersed in the Gold Bath, is less reduced in intensity, and does not acquire the same inky blueness. On subsequent fixing in the Hyposulphite, the tint changes from violet to a dark chocolate- brown, which is permanent. The Tetrathionate and Hyposulphite of Gold employed in toning. —After the discovery of Le Grey's mode, it was proposed, as an improvement, to add Chloride of Gold to the fixing solution, so as to obviate the necessity of using two Baths. The print, in that case,
- 50. although darkened considerably, is less reduced in intensity, and the same amount of over-printing is not required. The chemical changes which ensue are different from before: they may be described as follows:— Chloride of Gold, added to Hyposulphite of Soda, is converted into Hyposulphite of Gold, Tetrathionate of Gold, and (if the Chloride of Gold be free from excess of acid) a red compound, containing more of the metal than, either of the others, but the exact nature of which is uncertain. Each of these three Gold Salts possesses the property of darkening the print, but not to the same extent. The activity is less as the stability of the salt is greater, and hence the red compound, which is so highly unstable that it cannot be preserved many hours without decomposing and precipitating metallic Gold, is far more active than the Hyposulphite of Gold, which, when associated with an excess of Hyposulphite of Soda, is comparatively permanent. When rapidity of colouring is an object it will therefore be advisable to add Chloride of Gold to the fixing Bath of Hyposulphite rather than an equivalent quantity of Sel d'or; and by dropping a little Ammonia into the Chloride of Gold so as to precipitate fulminating gold[19] (a compound which dissolves in Hyposulphite of Soda with considerable formation of the unstable red salt), the activity of the Bath will be promoted. [19] Read the observations on the Explosive Properties of Fulminating Gold in the Vocabulary, Part III. The Author explains the action of these Salts of Gold upon the Positive print as follows:—they are unstable, and contain an excess of Sulphur loosely combined; hence, when placed in contact with the image, which has an affinity for Sulphur, the existing compound is broken up, and Sulphuret of Silver, Sulphuric Acid, and metallic Gold are the results. That a minute proportion of Sulphuret of Silver is formed seems certain; but the change must be superficial, as the
- 51. stability of the print is very little lessened when the process is properly performed. Sel Or employed as a toning agent.—This process, which was communicated to the 'Photographic Journal' by Mr. Sutton of Jersey, has been found serviceable. The prints are first washed in water, to which is added a little Chloride of Sodium, to decompose the free Nitrate of Silver. They are then immersed in a dilute solution of Sel d'or, or double Hyposulphite of Gold and Soda, which quickly changes the tint from red to purple without destroying any of the details or lighter shades. Lastly, the Hyposulphite of Soda is employed to fix the print in the usual way. This process differs theoretically from the last in some important particulars. The toning solution is applied to the print before fixing, which experience proves to have an important influence upon the result, it having been found that when the print is previously acted upon by Hyposulphite of Soda, the rapidity of deposition of the Gold is interfered with;—thus, a dilute solution of Sel d'or colours a print rapidly, but if to this same liquid a few crystals of Hyposulphite of Soda be added, the picture becomes red and may be kept in the Bath for comparatively a long time without acquiring the purple tones. As Hyposulphite of Soda in excess lessens the action of the Sel d'or, so on the other hand the addition of an acid increases it. The acid does not precipitate Sulphur, as might be expected from a knowledge of the reaction of Hyposulphite with acid bodies (p. 137), but it favours the reduction of metallic Gold. Hence it is usual to add a little Hydrochloric Acid to the toning solution of Sel d'or, to increase the rapidity and perfection of the colouring process. THE CONDITIONS WHICH AFFECT THE ACTION OF THE FIXING AND TONING BATH OF GOLD AND
- 52. HYPOSULPHITE OF SODA. Although the process of toning Positives by Sel d'or is very certain in its results and gives good tints, yet, as involving a somewhat greater expenditure of time and trouble, it is not at present universally adopted. The ordinary plan of fixing and toning in one bath has been proved to yield permanent prints if the proper precautions are observed, but it is quite necessary, in order to ensure success, that the conditions by which its action is modified should be understood. The more important of these are as follows:— a. The AGE of the Bath.—When Chloride of Gold is added to Hyposulphite of Soda, several unstable salts are produced, which decompose by keeping. Hence the solution is very active during the first few days after mixing; but at the expiration of some weeks or months, if not used, it becomes almost inert, a reddish deposit of Gold first forming, and eventually a mixture of black Sulphuret of Silver and Sulphur, the former of which often adheres to the sides of the bottle in dense shining laminæ. When the Bath is constantly kept in use there is a loss of Gold, which, although it is less perceived than it otherwise would be, from the fact that sulphuretting principles are formed (see next page) capable of replacing the Gold as toning agents—yet makes the Bath work more slowly, and hence over-printing is required. b. Presence of free Nitrate of Silver upon the surface of the proof. —This produces an accelerating effect, as may be shown by soaking the print in salt and water, to convert the Nitrate into Chloride of Silver; the action then takes place more slowly. The free Nitrate of Silver increases the instability of the Gold salts; but if present in too great an excess, it is apt to cause a decomposition of Hyposulphite of Silver, and consequent yellowness in the white parts of the proof. It is therefore particularly recommended to wash the print in water before immersing it in the fixing and toning Bath.
- 53. c. Temperature of the solution.—In cold weather, the thermometer standing at 32° to 40°, the Bath works more slowly than usual; whereas in the height of summer, and especially in hot climates, it occasionally becomes quite unmanageable. The best temperature for operating successfully appears to be about 60° to 65° Fahrenheit; if higher than this the solutions must be employed more dilute. d. Addition of Iodide of Silver.—Some operators associate Iodide with Chloride in the preparation of sensitive paper for printing. Another source of the same salts is the admixture of a portion of the fixing Bath used for Negatives with the Positive toning solution. The presence of Iodides in the fixing and toning Bath is injurious: when in large excess, they dissolve the image, or produce yellow patches of Iodide of Silver on the lights; in smaller quantity, the deposition of the Gold is hindered, and the action proceeds more slowly. Bromides and Chlorides have not the same effect. e. Mode of preparing the paper.—The rapidity of toning varies with causes independent of the Bath: thus, plain paper prints are toned more quickly than prints upon albuminized paper, and the use of English paper sized with Gelatine retards the action. Foreign papers rendered sensitive with Ammonio-Nitrate tone the most quickly. On certain states of the fixing and toning Bath which are injurious to the proofs.—The object of using the Hyposulphite Bath is to fix the proof and to tone it by means of Gold. But it is a fact familiar to the photographic chemist, that Positives can also be toned by a sulphuretting action, and that the colours so obtained are not very different from those which follow the employment of Gold.[20] Now the Hyposulphite of Soda is a substance which can be very readily made to yield up Sulphur to any bodies which possess an affinity for that element, and as the reduced Silver compound in the print has such an affinity, there is always a tendency to absorption of Sulphur when the proofs are immersed in the Bath. Consequently in
- 54. many cases a sulphur toning-process is set up, and as the picture is improved by it in appearance, losing its brick-red colour and assuming a purple shade, it was at first adopted by Photographers. Experience however has shown that colours brightened in this way are less permanent than others, and are liable to fade unless kept perfectly dry. Hence the process will be discarded by all careful operators, and the object will be to avoid sulphuration as far as possible. This can be done to a great extent, and, when the Bath is properly managed, the prints will be toned almost entirely by Gold, and will, with care, be permanent. [20] For a more detailed account of the toning process by Sulphur, see the Third Section of this Chapter, page 145. The instability of sulphuretted prints is shown in the fourth Section. Some of the conditions which facilitate a sulphuretting action upon the proof are as follows:— a. The addition of an Acid to the Bath.—It was at one time common to add a few drops of Acetic Acid to the fixing Bath of Hyposulphite of Soda, immediately before immersing the proofs. The Bath then assumes an opalescent appearance in the course of a few minutes, and, when this milkiness is perceptible, the print begins to tone rapidly and becomes nearly black. The chemical changes produced in a Hyposulphite Bath by addition of acid, may be explained thus:—The acid first displaces the feeble Hyposulphurous acid from its combination with Soda. Acetic Acid +Hyposulphite Soda. =Acetate Soda+Hyposulphurous Acid. Then the Hyposulphurous Acid, not being a stable substance when isolated, begins spontaneously to decompose, and splits up into Sulphurous Acid—which remains dissolved in the liquid, communicating the characteristic odour of burning Sulphur—and Sulphur, which separates in a finely divided state and forms a milky deposit.[21]
- 55. [21] From the Vocabulary, Part III., it will be seen that commercial Chloride of Gold usually contains free Hydrochloric Acid; hence a considerable deposit of Sulphur takes place on adding it to the Hyposulphite solution, and the liquid must not be used immediately. Observe therefore that free acids of all kinds must be excluded from the fixing Bath, or, if inadvertently added, the liquid must be set aside for some hours until the Hyposulphurous Acid has decomposed, and, the Sulphur having settled to the bottom, the Bath has regained its original neutral condition.[22] [22] The chemical reader will understand the decomposition of free Hyposulphurous Acid by the following equation:—S2O2 = SO2 and S. b. Decomposition of the Bath by constant use.—It has long been known that a solution of Hyposulphite of Soda undergoes a peculiar change in properties when much used in fixing. When first prepared it leaves the image of a red tone, the characteristic colour of the reduced Silver Salt, but soon acquires the property of darkening this red colour by a subsequent communication of Sulphur. Hence a simple fixing Bath becomes at last an active toning bath, without any addition of Gold. This change of properties will be found more fully explained in the abstract of the Author's researches given in the next Section (p. 156). At present we remark only that it is due principally to a reaction between Nitrate of Silver and Hyposulphite of Soda, attended with decomposition of Hyposulphite of Silver (p. 130); and hence, if the prints are washed in water before immersion in the Bath, the solution will be less quickly liable to change. Many operators state that the toning Bath having at first been prepared with Chloride of Gold, no further addition of this substance will be required. This no doubt is correct, but in such case the proofs will at last be toned by Sulphur more than by Gold, and will not possess the same stability; the Bath will also, after long use, be
- 56. found to acquire a distinct acid reaction to test-paper, the acidity being due to a peculiar principle generated by decomposing Hyposulphite of Silver, and which is shown to have an injurious action upon the print (p. 158). To avoid this the solution should be kept neutral to test-paper by means of a drop of Ammonia, if required; and when it begins to be exhausted, and does not tone (quickly) a print from which the free Nitrate of Silver has been removed by washing, a fresh quantity of Chloride of Gold should be added. c. Tetrathionate in the Hyposulphite Bath.—The Author has shown that the Tetrathionates, which are analogous to the Hyposulphites, have an active sulphuretting action upon Positive prints (see the papers in the next Section). Very fine colours can be obtained in this way; but toning by Sulphur having been proved to be wrong in principle, the formulæ given in the first two editions of this Work have been omitted.[23] [23] The preparation of a toning bath by Tetrathionate, without Gold, is described in the next Section, but it is not recommended for practical use. The bodies which produce Tetrathionate when added to a solution of Hyposulphite of Soda, and hence are inadmissible in the toning process, are as follows:—Free Iodine, Perchloride of Iron, Chloride of Copper, Acids of all kinds (in the latter case the acid first produces Sulphurous Acid, and the Sulphurous Acid, if present in any quantity, by reacting upon Hyposulphite of Soda, forms Tetrathionate and Trithionate of Soda). Chloride of Gold also produces a mixed Tetrathionate of Gold and Soda when added to the fixing Bath (p. 133); but as the quantity of Chloride used is small, the prints are far less sulphuretted than in the case of toning Baths prepared by Tetrathionate without Gold. SECTION III. The Author's Researches in Photographic Printing.
- 57. Having been long engaged in conducting experiments upon the composition and properties of the reduced material forming the Photographic image, and especially with a view of determining the exact conditions under which the picture may be considered permanent, the Author has thought it advisable to give the results of these researches in the form of an abstract of the original papers read at the meetings of the Photographic Society. A previous perusal of these papers will put the reader in possession of the principal facts upon which are founded the precautions advised in the next Section for the preservation of Photographic prints. In order to keep the Work as nearly as possible within its original limits, and also for the purpose of distinguishing the present Section from the others, as one referring principally to scientific details, the type has been reduced to the size of that used in the Appendix. ON THE CHEMICAL COMPOSITION OF THE PHOTOGRAPHIC IMAGE. The determination of the chemical nature of the Photographic image in its various forms is a point of much importance, both as indicating the conditions required for the preservation of works of art of that class, and also as a guide to the experimenter in selecting bodies likely to have an effect as chemical agents in Photography. It has been stated by some who have given attention to the subject, that the image is formed in all cases of pure metallic Silver, and that any observable variations in its colour and properties, are due to a difference in the molecular arrangement of the particles. But this hypothesis, although involving much that is correct, yet does not contain the whole truth, for it is evident that the chemical properties of the Photographic image often bear no resemblance to those of a metal. One Photograph may also differ essentially from another, so that we are led to infer the existence of two varieties, the first of which is less of a metallic nature than the second.
- 58. In investigating the subject, the principal point appeared to be to examine the action of light upon Chloride of Silver, and afterwards to associate the Chloride with organic matter in order to imitate the conditions under which Photographs are obtained. The following is an epitome of the conclusions arrived at:— Action of Light upon Chloride of Silver.—The process is accompanied by a separation of Chlorine, but its product is not a mere mixture of Chloride of Silver and Metallic Silver; if it were so, we cannot suppose that the darkening would take place beneath the surface of Nitric Acid, which it is found to do. A definite Subchloride of Silver seems to be formed, the most important property of which is its decomposition by fixing agents, such as Ammonia, and Hyposulphite of Soda, both of which destroy the violet colour, dissolving out Protochloride of Silver, and leaving a small quantity of a grey residue of metallic Silver. Inasmuch therefore as all Photographic pictures require fixing, we may conclude that if they could be produced upon pure and isolated Chloride of Silver (which however is not the case), they would consist solely of metallic Silver. Decomposition of organic Salts of Silver by Light.—Compounds of Oxide of Silver with organic bodies, are as a rule darkened by exposure to light, but the process does not always consist in a simple reduction to the metallic state. This assertion is proved by the employment of the following tests. a. Mercury.—Little or no amalgamation takes place on triturating the darkened salt with this metal. b. Ammonia and fixing agents.—These usually produce only a limited amount of action. Thus, the Albuminate of Protoxide of Silver is perfectly soluble in Ammonia; but after having been reddened by exposure to light, it is little or not at all affected.
- 59. c. Potash.—Animal matters coagulated by Nitrate of Silver, and reduced by the sun's rays, are dissolved by boiling Potash, the solution being clear and of a blood-red colour. Metallic Silver, it is presumed, if present, would remain insoluble. d. Boiling Water.—Gelatine treated with Nitrate of Silver and exposed to light, loses its characteristic property of dissolving in hot water. This experiment is conclusive. The above facts justify us in supposing the existence of combinations of organic matter with a low Oxide of Silver; and analysis indicates further that the relative proportion of each constituent in these compounds may vary. For instance, when Citrate of Silver is reduced by light, and acted on with Ammonia, a black powder remains, which was found to contain as much as 95 per cent, real Silver; but Albuminate of Silver treated in the same way yields on analysis less of metallic Silver, and more volatile and carbonaceous matter. The use of Ammonio-Nitrate of Silver in preparing the salt tends also to increase the relative quantity of metal left in the compound after reduction and fixing. The length of time during which the light has acted, has also a modifying effect of the same kind,—the product of reduction by a powerful light being more nearly in the state of metal, and containing less both of Oxygen and organic matter. Action of Light upon Chloride of Silver associated with organic matter.—Photographs formed on Chloride of Silver alone, would, after fixing, consist of metallic Silver, but such a process could not be carried out in practice. The addition of organic matter is absolutely necessary in order to increase the sensitiveness, and to prevent the image from being dissolved in the Bath of Hyposulphite of Soda. The blue Subchloride of Silver is decomposed by fixing, a very scanty proportion of grey metallic Silver remaining insoluble; but the red compound of Suboxide of Silver with organic matter is almost unaffected by Hyposulphite of Soda, or Ammonia.
- 60. The increase of sensitiveness and intensity produced by the use of organic matter is accompanied also by a change in the composition of the picture; the image losing the metallic character which it possesses when formed on pure Chloride of Silver, and resembling in every respect the product of the action of light upon organic Salts of Silver. There are certain characteristic tests which may usefully be employed in distinguishing the metallic image from what may be termed the organic or non-metallic image. One of these tests is Cyanide of Potassium. An image formed upon pure Chloride of Silver, although pale and feeble, may, after fixing, be immersed ill dilute solution of Cyanide of Potassium without injury. But a photograph on Chloride of Silver supported by an organic basis, is much acted upon by Cyanide of Potassium, quickly losing its finer details. A second test is the Hydrosulphate of Ammonia. If no organic matter be employed, the image becomes darker and more intense by treatment with a soluble Sulphuret; whilst the non-metallic image, formed on an organic surface, is quickly bleached and faded. The action of Sulphur upon the image is indeed a mode of determining the real quantity of Silver present. When existing in a very finely divided layer, Sulphuret of Silver often appears yellow; but in a thicker layer it is black. Hence the colour of the Photograph, after treatment with Sulphuretted Hydrogen, is an indication of the proportion of metal present, and the reason of the organic image becoming so perfectly faded is because it contains a minimum of Silver in relation to the intensity. We see, therefore, that the addition of organic matter to Chloride of Silver does not so much increase the actual quantity of Silver reduced by light, as it adds to its opacity by associating other elements with the Silver, and altogether modifying the composition of the image. The employment of oxidizing agents shows also that in an ordinary Photographic process by the direct action of light, other elements besides Silver assist in forming the image: the pictures
- 61. being found to be easily susceptible of oxidation, whereas the metallic image formed on pure Chloride of Silver resists oxidation. Composition of developed images.—By exposing sensitive layers of the Iodide, the Bromide, and the Chloride of Silver to the light for a short time only, and subsequently developing with Gallic Acid, Pyrogallic Acid, and the protosalts of Iron, a variety of images may be obtained, which differ from each other materially in every important particular, and a comparison of which assists the determination of the disputed point. The appearance and properties of the developed Photograph are found to vary with the existence of the following conditions. 1st. The surface used to sustain the sensitive layer.—There is a peculiarity in the image formed on Collodion. Collodion contains Pyroxyline, a substance which behaves towards the salts of Silver in a manner different from that of most organic bodies, exhibiting no tendency to assist their reduction by light. Hence Chloride of Silver on Collodion darkens far more slowly than the same salt upon Albumen, and the image, after fixing, is feeble and metallic. Iodide of Silver on Collodion, exposed and developed, gives usually a more metallic image, with less intensity, than Iodide of Silver upon Albumen, or on paper sized with Gelatine. By adding to the Collodion a body which has an affinity for low oxides of Silver, such for instance as Glycyrrhizine, the opacity of the developed image is increased. 2nd. The nature of the sensitive salt.—When Iodide of Silver is used to receive the latent impression, the image after development, although lacking intensity of colour by reflected light, is more nearly in the condition of metallic Silver than if Bromide or Chloride of Silver be substituted; and of the three salts, the Chloride gives the most intensity, with the least quantity of metallic Silver. This rule applies especially when organic matters, Gelatine, Glycyrrhizine, etc., are present.
- 62. 3rd. The developing agent employed.—An organic developing agent like Pyrogallic Acid may be expected to produce a Collodion image more intense, but less metallic, than an inorganic developer, such as the Protosulphate of Iron. 4th. The length of time during which the light has acted.—Over- action of the light favours the production of an image which is dark by reflection and brown or red by transmission, corresponding in these particulars to what may be termed the non-metallic image containing an oxide of Silver. 5th. The stage of the development.—The red image first formed on the application of the developer to a gelatinized or albuminized surface of Iodide of Silver is less metallic, and more easily injured by destructive tests, than the black image, which is the result of prolonging the action. Developed photographs which are of a bright red colour after fixing, correspond in properties to images obtained by the direct action of light on paper prepared with Chloride of Silver, more nearly than to Collodion, or even to fully developed Talbotype Negatives. To conclude the Paper, the following may be offered in the way of recapitulation:—An image consisting of metallic silver, as a rule, reflects white light, and shows as a positive when laid on black velvet; but a non-metallic organic image is dark, and represents the shadows of a picture. Collodion positives developed with protosalts of Iron are nearly or quite metallic. Photographs on Albumen or Gelatine less so than those on Collodion. Developed Photographs contain more Silver than others, if the development has been prolonged. The half shadows of the image in a Positive Print are especially liable to suffer under injurious conditions, since they contain the Silver in a less perfect state of reduction.[24] [24] The Author omits, in this place, all mention of molecular conditions affecting intensity, inasmuch as at the present time nothing positive has been determined with regard to them. It is however known that in the use of the protosalts of Iron as developing agents, the appearance of the image is much
- 63. influenced by the rapidity with which the reduction is effected— the particles of Silver being larger and more metallic when the development is conducted slowly. The process of electro-plating and other chemical operations of a similar kind prove that the physical properties of metals precipitated from solutions of their salts, vary greatly with the degree of fineness and arrangement of their particles. ON THE VARIOUS AGENCIES DESTRUCTIVE TO PHOTOGRAPHIC PRINTS. Action of Sulphuretting Compounds upon Positive Prints.—It was first noticed by Mr. T. A. Malone, that the most intense Photograph might be destroyed by acting upon it with solution of Sulphuretted Hydrogen or a soluble Sulphuret, for a sufficient length of time. The changes produced by a sulphuretting compound acting upon the red image of a simply fixed print are these:—the colour is first darkened, and a degree of brilliancy imparted to it; this is the effect termed toning. Then the warm tint by degrees alters to a colder shade, the intensity of the whole image is lessened, and the half- tones turn yellow. Lastly, the full shadows pass also from black to yellow, and the print fades. Now in this peculiar reaction we notice the following points of interest. If at that particular stage at which the print has reached its maximum of blackness, it be raised partially out of the liquid and allowed to project into the air, the part so treated becomes yellow before that which remains immersed. Again, if a print toned by Sulphur be placed in a pan of water to wash, after the lapse of several hours it is apt to assume a faded appearance in the half- tones. The full shadows, in which the reduced Silver salt is thicker and more abundant, retain their black colour for a longer time, but if the action of the sulphuretting Bath be continued, every portion of the print becomes yellow.
- 64. These facts prove that Oxygen has an influence in accelerating the destructive action of the Sulphur compounds upon Positive prints; and this idea is borne out by the results of further experiments, for it is found that moist Sulphuretted Hydrogen has little or no effect in darkening the colour when every trace of air is excluded. When prints are washed in water they are exposed to the influence of the dissolved air which water always contains, and hence the change from black to yellow is produced.[25] [25] Further remarks upon the action of damp air upon Positives toned by Sulphur are given at p. 153. There are some substances which facilitate the yellow degeneration of Positives toned by Sulphur, a knowledge of which will be useful: they are—1st, powerful oxidizers, such as Chlorine, Permanganate of Potash, and Chromic Acid; these, even when highly diluted, act with great rapidity: 2nd, bodies which dissolve Oxide of Silver, as soluble Cyanides, Hyposulphites, Ammonia; also acids of various kinds, and hence the frequency of yellow finger impressions upon old sulphuretted prints, which are probably caused by a trace of organic (Lactic?) Acid left by contact with the warm hand. It was at one time supposed that the Photograph in the stage at which it appears blackened by Sulphur, consisted of Sulphuret of Silver, and that this black Sulphuret became yellow by absorption of Oxygen and conversion into Sulphate. MM. Davanne and Girard, who examined the subject, thought that there might be two isomeric forms of Sulphuret of Silver, a black and a yellow form; the former of which passing gradually into the latter produced the fading of the impression. But neither of these views are correct; for it is proved by careful experiment, that the Sulphuret of Silver is a highly stable compound, not prone to oxidize, and, further, that the change of colour from black to yellow has no reference to a modification of this salt. The truth appears to be that the image whilst in the black stage contains other elements besides Sulphur and Silver, but when it has become yellow by the continued action of the sulphuretting compound, it is then a true Sulphuret.
- 65. Comparative permanence of Photographs under the action of Sulphur.—Developed Positives, as a rule, stand better than those printed by direct exposure to light; but much depends upon the nature of the negative process followed; and hence no general statement can be made which will not be liable to many exceptions. The mode of conducting the development must not be overlooked. The prints, which become very red in the Hyposulphite fixing Bath from the action of the developer having been stopped at too early a period, are often sulphuretted and destroyed even more readily than a vigorous sun-print obtained by direct exposure to light. A point of even greater importance is the nature of the sensitive surface which receives the latent image. It is the print developed upon Iodide of Silver which especially resists sulphuration. In that case, not only is the preliminary toning effect of the Sulphur more slow than usual, but the impression cannot be made to fade by any continuance of the action. It loses much of its brilliancy, and is reduced in intensity, but it is not so completely destroyed as to be useless. The reason of this, as shown in the last paper, depends upon the fact that the Talbotype proofs contain the largest amount of Silver in the image. The employment of Gold in toning does not render an ordinary sun-print as permanent as a Positive developed upon Iodide of Silver. The deep shadows of the picture are protected by the Gold, but the lighter shades not so perfectly. Hence after the Sulphur has acted, in place of the universal yellow and faded aspect presented by the simple untoned print, the Positive fully toned by Gold has black shadows with yellow half-tones. Therefore, whilst recommending the use of Gold as a toning agent, it does not seem advisable to lay too much stress upon it as a preservative from the destructive action of Sulphur. Exposure of Positive Prints to a Sulphuretting Atmosphere.—In testing the action of a solution of Sulphuretted Hydrogen upon paper Positives, it did not appear that the conditions under which the prints were placed bore a sufficiently close resemblance to the case of
- 66. Positives exposed to an atmosphere contaminated with minute traces of the gas; and this more particularly because it is known that dry Sulphuretted Hydrogen has comparatively little effect upon Photographic Prints. The experiments were therefore repeated in a somewhat different form. A number of Positives (about three dozen) printed in various ways, were suspended in a glass case, measuring 2½ feet by 21 inches, and containing 7½ cubic feet of air; into which was introduced, occasionally, a few bubbles of Sulphuretted Hydrogen, just sufficient to keep the air of the chamber smelling perceptibly of the gas. A polished Daguerreotype plate was hung up in the centre, to serve as a guide to the progress of the sulphuretting action. By the second day the metal plate had acquired a faint yellow hue, not easily seen except in certain positions; but the Positives were unaffected. At the expiration of three days the majority of the pictures exhibited no signs of change, but a few untoned prints of a pale red colour, some of which had been printed by development, and others by direct exposure to light, had perceptibly darkened. After the eighth day, the action, appearing to progress more slowly than at first, was stopped, and the prints removed. The general results obtained were as follows:— The Daguerreotype plate had become strongly tarnished with a film of Sulphuret of Silver, which appeared yellowish-brown in some parts and steel-blue in others. The Positives were, as a rule, toned to a slightly colder shade, but many of them had scarcely changed. No obvious difference was observed between prints developed on paper prepared with Chloride of Silver, and others printed by direct exposure to light; but in all cases the prints obtained by those methods which give a very red image after fixing, were the first to show the change of colour due to sulphuration, the proofs submitted to the test having all been previously toned with Gold.
- 67. Effect of Oxidizing Agents upon Positive Prints.—It appeared of importance to ascertain to what extent Photographic Prints are susceptible of oxidation; on account of the atmospheric influences to which they are necessarily exposed. In experimenting upon this subject the following results have been obtained. Powerful oxidizers destroy Positive Prints rapidly; the action usually commencing at the corners and edges of the paper, or at any isolated point, such as a metallic speck or particle of extraneous matter, which can serve as a centre of chemical action. This same fact is often noticed in the fading of Positives by long keeping, and therefore since other destructive actions (with the exception of that of Chlorine) do not appear to follow the same rule, it is an argument in addition to others which can be adduced, that Photographic Prints are frequently destroyed by oxidation. Air which has been Ozonized by Phosphorus, and in which blue litmus-paper becomes reddened, quickly bleaches the Positive image. Oxygen gas, obtained by voltaic decomposition of acidified water and which should contain Ozone, did not appear to have an equal amount of effect, the action being comparatively slight, or altogether wanting. Peroxide of Hydrogen obtained in solution, and in conjunction with Acetate of Baryta, by adding Peroxide of Barium to dilute Acetic Acid,[26] bleaches darkened Positive paper; but the effect is slow, and does not take place to a very perceptible extent if the liquid be kept alkaline to test-paper. [26] Hydrochloric Acid, which is usually recommended in place of Acetic Acid, cannot be employed in this experiment; it seems to cause a liberation of free Chlorine, which bleaches the print instantly. Nitric Acid applied in a concentrated form acts immediately upon the darkened surface, bleaching every part of the print with the exception of the bronzed shadows, which usually retain a slight residual colour. A solution of Chromic Acid is still more active. This
- 68. liquid may usefully be applied to distinguish prints toned by Sulphur from others toned by Gold; the presence of metallic Gold protecting the shadows of the picture in some measure from the action of the acid. The solution should be prepared as follows:— Bichromate of Potash 6grains. Strong Sulphuric Acid 4minims. Water 12ounces. A solution of Permanganate of Potash is an energetic destroyer of paper positives; and, as it is a neutral substance, may conveniently be employed in testing the relative capability of withstanding oxidation possessed by different Photographic Prints. The solution should be dilute, of a pale pink hue, and the Positives must be moved occasionally, as the first effect is to decolorize a great portion of the liquid, the Permanganate oxidizing the size and organic tissue of the paper. After an immersion of twenty minutes to half an hour, varying with the degree of dilution, the half-tones of the picture begin to die out, and the full shadows become darker in colour; the bronzed portions of the print withstand the action longer, but at length the whole is changed to a yellow image much resembling in appearance the Photograph faded by Sulphur. Comparative permanence of Photographs treated with Permanganate of Potash.—Developed prints prepared by a Negative process withstand the action better than others. But to this rule there are exceptions; much depending upon the time of exposure to light, and the extent to which the development is carried. Those prints which, being exposed for a short time, and afterwards strongly developed, become dark in colour and vigorous in outline, are more permanent than others which having been over-exposed and under-developed, lose their dark colour and become red and comparatively faint in the Hyposulphite fixing Bath. Positives developed upon a surface of Chloride of Silver on plain paper do not resist the oxidizing action so perfectly as those on
- 69. Iodide of Silver. Prints developed upon paper prepared with Serum of Milk containing Caseine stand better than those on plain paper. Of prints obtained by the ordinary process of direct exposure to light, those on plain paper are the first to fade, the oxidizing action being most seen upon the half-tones. The use of Albumen gives a great advantage. Developed prints on Albumen stand far better than the same upon plain paper; and even the Albuminized sun prints are less injured by the Permanganate than the best of the Negative prints prepared without Albumen. Caseine has the same effect, but to a less extent; and as Serum of Milk almost invariably contains uncoagulated Caseine, its efficacy is thus explained. The manner of toning the print is a point of importance; previous sulphuration in an old Hyposulphite Bath always facilitating the oxidizing action. Action of Chlorine upon Positive Prints.—Aqueous solution of Chlorine destroys the Photographic image, changing it first to a violet tint (probably Subchloride), and subsequently obliterating it by conversion into white Chloride of Silver. The impression, although invisible, remains in the paper, and may be developed in the form of yellow or brown Sulphuret of Silver by the action of Sulphuretted Hydrogen. It also becomes visible on exposure to light, and assumes considerable intensity if the paper be previously brushed with free Nitrate of Silver. Sulphate of Iron produces no effect upon the invisible image of Chloride of Silver; but Gallic or Pyrogallic Acid, rendered alkaline by Potash, converts it into a black deposit. The Action of Chlorine water usually commences at the edges and corners of the print, in the same manner as that of oxidizing agents. The proofs upon Albumen are the least readily injured, and next, those developed on Iodide of Silver. Hydrochloric Acid.—The liquid acid of sp. gr. ·116, even when free from Chlorine, acts immediately upon the half-tones of a positive print, and destroys the full shadows in the course of a few
- 70. hours; a slight residual colour however usually remains in the darkest parts. The prints developed on Iodide of Silver are the most permanent. Sulphuric, Acetic Acids, etc.—Acids of all kinds appear to exert an injurious influence upon Positive prints, and especially so upon the half-tones of the image, the effect varying with the strength of the acid and the degree of dilution with water. Even a vegetable acid like Acetic gradually darkens the colour and destroys partially or entirely the faint outlines of the picture. Bichloride of Mercury.—The most important particulars relating to the action of this test upon Photographs are well known. The image is ultimately converted into a white powder, and hence, in the case of a Positive print, it becomes invisible; immersion in Ammonia or Hyposulphite of Soda however restores it in a form often resembling in tint the original impression. A point worthy of note is the protective effect of a deposit of Gold, which is very marked, the proof, after toning, resisting the action of the Bichloride for comparatively a long time. Ammonia.—The effect of Ammonia upon a print is rather to redden the image than to destroy it; the half-tones become pale and faint, but they do not disappear. Toning with Gold enables the proof to resist the action of the strongest solution of Ammonia, and hence Ammonia may safely be employed as a fixing agent after the use of the Sel d'or Bath. Hyposulphite of Soda.—A concentrated solution of Hyposulphite of Soda exercises a gradual solvent action upon the image of Photographic Prints, at the same time tending to communicate Sulphur and to darken the colour of the impression. A faint yellow outline of Sulphuret of Silver usually remains after the solution of the image is completed. Developed prints of all kinds, but in particular the Talbotype proofs upon Iodide of Silver, are less readily dissolved by
- 71. Hyposulphite of Soda than those obtained by the direct action of light. There is also a slight difference between plain and Albuminized prints, which is in favour of the former, the albuminized paper always losing somewhat more by immersion in the Hyposulphite Bath than plain Chloride paper sensitized by Nitrate of Silver. Cyanide of Potassium.—The solvent action of Cyanide of Potassium is most energetic upon Photographs formed on paper. These images, whether developed or not, do not withstand the test so well as the impressions on Collodion. Albuminized proofs are also somewhat more easily affected than prints on simple Chloride paper sensitized with Nitrate or Ammonio-Nitrate of Silver. Heat, moist and dry.—Long-continued boiling in distilled water has a reddening action upon Positive Prints. The image becomes at length pale and faint, resembling a print treated with Ammonia before toning. A deposit of Gold upon the image lessens, but does not altogether neutralize, the effect of the hot water. If the boiling be long continued, the violet-purple tone often imparted by the Gold invariably gives place to a chocolate-brown, which appears to be the most permanent colour. Prints developed by Gallic Acid upon paper prepared with Serum of Milk or with a Citrate, suffer as much as others obtained by direct action of light. Ammonio-Nitrate prints on highly salted paper, which become nearly black when toned with Gold, retain their original appearance the most perfectly; a slight diminution of brightness being the only observable difference after long boiling in water. Albumen proofs, and prints on English papers, or foreign papers prepared with Serum of Milk, Citrates, Tartrates, or any of those bodies which redden the reduced Salt, are, as a rule, rendered lighter in colour, and pass from purple to brown when boiled in water. Dry heat has an opposite effect to that of hot water, usually darkening the colour of the image. On exposing a plain paper print simply fixed, and thoroughly freed from Hyposulphite of Soda by washing, to a current of heated air, it changes gradually from red to dark brown, in which state it continues until the temperature rises to
- 72. the point at which the paper begins to char, when it resumes its original red tone, becoming at the same time faint and indistinct. The Products of Combustion of Coal-gas a cause of Fading.— Coal-gas contains Sulphur compounds, which in combustion are oxidized into Sulphurous and Sulphuric Acids; other substances of a deleterious nature may also be present. A plate of polished silver suspended in a glass tube, through which was directed the current of heated air rising from a small gas jet, became tarnished with a white film in the course of twenty-four hours. Positive prints exposed to the same, absorbed moisture and faded; the action resembling that of oxidation, in being preceded by a general darkening in colour. Of four prints exposed, an Iodide-developed print was the least injured, and next, a print upon Albuminized paper. ON THE ACTION OF DAMP AIR UPON POSITIVE PRINTS. In order to ascertain this point, more than six dozen Positives, printed on every variety of paper, were mounted in new and perfectly clean stoppered glass bottles, at the bottom of each of which was placed a little distilled water, to keep the contained air always moist. They were removed at the expiration of three months, having been kept during that time, some in the dark, and others exposed to the light. As the prints were prepared by various methods, toned in different ways, and mounted with or without substances likely to exercise a deleterious action, this series of experiments will possess considerable value in determining some of the intrinsic causes of fading of Positives.[27] [27] For a more detailed account of the experiments, see the original paper in the 'Photographic Journal,' vol. iii. The general results obtained were as follows:—Positives which had been simply fixed in Hyposulphite of Soda remained quite uninjured. Whether developed by Gallic Acid on either of the three
- 73. Salts of Silver usually employed, or printed by direct action of light, the result was the same. Hence we may infer that the darkened material which forms the image of Photographic Prints does not readily oxidize in a damp atmosphere. Toned Positives were found in many cases to be less permanent than Positives simply fixed. This was especially the case when the toning had been effected by Sulphur; all the sulphuretted prints, fixed in solution of Hyposulphite which had been long used, became yellow in the half-tones when exposed to moisture. Positives fixed and toned in Hyposulphite containing Gold were variously affected; some prepared when the solution was in an active state being unchanged, others losing a little half-tone, and others, again, fading badly. These latter were prepared in a Bath which had lost Gold and acquired sulphuretting properties; and it was noticed that they were more injured by the action of boiling water than those Positives which proved to be permanent under the influence of the moisture. Toning by means of Chloride of Gold appeared to be highly satisfactory, but the number of prints operated upon was small. The Sel d'or process also did not injure the integrity of the image, no commencing yellowness or bleaching of half-tones being visible after exposure to the moist air. This series of experiments confirmed the statement made in a former paper, that some tints obtained in Positive printing are more permanent than others. Violet tones produced by Sulphur invariably passed into a dull brown by the action of the moist air; and even when Gold was employed in toning, these same purple colours were usually reddened. This was especially the case when English papers were used, or foreign papers re-sized with Serum of Milk containing Caseine. The chocolate-brown tints which best stand the action of boiling water, and in particular those upon Ammonio-Nitrate paper, were least affected by the damp air; and indeed it was evident that the two agents, viz. moist air and hot water, acted alike in tending to redden the print, although the latter did so in the most marked manner.
- 74. It seemed also, from the results of these experiments, to be a point of great importance that the size should be removed from the print in order to render it indestructible by damp air. This was evidently seen in two cases where Positives, toned in an old Hyposulphite and Gold Bath, were divided into halves, one of which was treated with a strong solution of Ammonia. The result was that the halves in which the size was allowed to remain, faded, whilst the others were comparatively uninjured. The Albumen proofs especially suffered when the size was left in the paper, a destructive mouldiness forming, and fading the picture. The use of boiling water obviated this, and the prints so treated remained clean and bright. A partial decomposition of Albumen however occurred in some cases even when hot water was used, the gloss disappearing from the paper in isolated patches. With Caseine substituted for Albumen there was also a loss of half-tone; thus seeming to indicate that both these animal principles, although stable under ordinary conditions, will, even when coagulated by Nitrate of Silver, decompose if kept long in a moist state. The use of improper substances for mounting proved to be another determining cause of fading by oxidation. Those bodies which combine with Oxide of Silver, are likely upon theoretical grounds to destroy the half-tones of the image; and it was found, that if the picture were left in contact with Alum, Acetic Acid, etc., or with the substances which generate an acid by fermentation, such as paste or starch, it invariably faded. The supposed accelerating influence of Light upon the fading of Positives was not confirmed by these experiments, as far as they extended. Many of the bottles containing the Photographs were placed outside the window of a house with a southern aspect during the whole of the three months with the exception of two or three weeks, but no difference whatever could be detected between Positives so treated and others kept in total darkness. It will be proper however that this part of the investigation should be repeated, allowing a longer time.
- 75. An examination of the various modes employed for coating Positives, in order to exclude the atmosphere, showed that many of them were not fitted to fulfil the purpose intended. Waxed prints faded quite as much when exposed to moisture as others not waxed. White wax is a substance often adulterated, and Oil of Turpentine has been shown to contain a body resembling Ozone in properties, and possessing the power of bleaching a dilute solution of Sulphate of Indigo. Spirit varnish applied to the surface of the picture after re- sizing with Gelatine was plainly superior to white wax, but nevertheless it did not obviate the fading effect of the moisture upon an unstable Positive which had been toned by sulphuration. Its protective influence is therefore limited. ON THE CHANGE IN COMPOSITION WHICH HYPOSULPHITE OF SODA EXPERIENCES BY USE IN FIXING PAPER PROOFS.[28] [28] These observations are condensed and re-arranged from the papers published by the Author in the 'Photographic Journal' for September and October, 1854. It was remarked by Photographers at an early period that the properties of the Fixing Bath of Hyposulphite of Soda became altered by constant use; that it gradually acquired the power of darkening the colour of the Positive image. This change was at first referred to the accumulation of Salts of Silver in the Bath, and hence directions were given to dissolve a portion of blackened Chloride of Silver in the Hyposulphite in preparing a new solution. Careful experiments performed by the Author convinced him that an error had been entertained; since it was found that the simple solution of Chloride of Silver in Hyposulphite of Soda had no power of yielding the black tones. But it afterwards appeared that if the fixing Bath, containing dissolved Silver Salts, were set aside for a few weeks, a decomposition occurred in it, evidenced by the formation of
- 76. a black deposit of Sulphuret of Silver; and then it became active in toning the proofs. The presence of this deposit of Sulphuret of Silver indicated that a portion of Hyposulphite of Silver had spontaneously decomposed, and, knowing the products which are generated by the spontaneous decomposition of this salt, a clue to the difficulty was afforded. One atom of Hyposulphite of Silver includes the elements of one of Sulphuret of Silver and one of Sulphuric Acid. Sulphuric Acid in contact with Hyposulphite of Soda produces Sulphurous Acid by a process of displacement; and Plessy has shown that Sulphurous Acid reacts upon an excess of Hyposulphite of Soda, forming two of that interesting series of Sulphur compounds designated by Berzelius the Polythionic Acids. It appeared therefore probable, upon theoretical grounds, that the Penta-, Tetra-, and Trithionates might produce some effect in the Hyposulphite fixing Bath. Upon making the trial these expectations were verified; and it was found that Tetrathionate of Soda added to Hyposulphite of Soda yielded a fixing and toning Bath quite equal in activity to that produced by means of Chloride of Gold. It may be useful to review for an instant the composition of the Polythionic series of acids; it is thus represented:— Sulphur. Oxygen. Formulæ. Dithionic or Hyposulphuric Acid 2 atoms 5 atoms S2O5 Trithionic Acid 3 5 S3O5 Tetrathionic Acid 4 5 S4O5 Pentathionic Acid 5 5 S5O5 The amount of Oxygen in all is the same, that of the other element increases progressively; hence it is at once evident that the highest member of the series might by losing Sulphur descend gradually until it reached the condition of the lowest.
- 77. This transition is not only theoretically possible, but there is an actual tendency to it, all the acids being unstable with the exception of the Hyposulphuric. The Alkaline Salts of these acids are more unstable than the acids themselves; a solution of Tetrathionate of Soda becomes milky in the course of a few days from deposition of Sulphur, and, if tested, is then found to contain Trithionate and eventually Dithionate of Soda. The cause of the change in properties of the fixing Bath being thus clearly traced to a decomposition of Hyposulphite of Silver, and a consequent generation of unstable principles capable of imparting Sulphur to the immersed proofs, it seemed desirable to continue the experiments.— There is a peculiar acid condition commonly assumed by old fixing Baths, which could not be satisfactorily explained, since it was known that acids do not exist long in a free state in solution of Hyposulphite of Soda, but tend to neutralize themselves by displacing Hyposulphurous Acid spontaneously decomposable into Sulphurous Acid and Sulphur. This point is set at rest by the discovery of a peculiar reaction which takes place between certain salts of the Polythionic acids and Hyposulphite of Soda. A solution of Tetrathionate of Soda may be preserved for many hours unchanged; but if a few crystals of Hyposulphite of Soda be dropped in, it begins very shortly to deposit Sulphur, and continues to do so for several days. At the same time the liquid acquires an acid reaction to test- paper, and produces effervescence on the addition of Carbonate of Lime. It is evident that a Sulphur acid exists which has not hitherto been described, and that this acid is formed as one of the products of the decomposition of the Hyposulphite of Silver contained in the fixing Bath. The subject is an important one to Photographers, because it is found that Hyposulphite Baths which have acquired the acid reaction, although toning quickly, yield Positives which fade on keeping. The acid may perhaps combine with the reduced Silver
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