Secrets of RF Circuit Design 3rd ed Edition Joseph Carr

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Secrets of RF Circuit Design 3rd ed Edition Joseph Carr
Digital Instant Download
Author(s): Joseph Carr
ISBN(s): 9780071370677, 0071370676
Edition: 3rd ed
File Details: PDF, 5.81 MB
Year: 2001
Language: english

1
CHAPTER
Introduction to RF
electronics
Radio-frequency (RF) electronics differ from other electronics because the higher
frequencies make some circuit operation a little hard to understand. Stray
capacitance and stray inductance afflict these circuits. Stray capacitance is the
capacitance that exists between conductors of the circuit, between conductors or
components and ground, or between components. Stray inductance is the normal in-
ductance of the conductors that connect components, as well as internal component
inductances. These stray parameters are not usually important at dc and low ac
frequencies, but as the frequency increases, they become a much larger proportion
of the total. In some older very high frequency (VHF) TV tuners and VHF communi-
cations receiver front ends, the stray capacitances were sufficiently large to tune the
circuits, so no actual discrete tuning capacitors were needed.
Also, skin effect exists at RF. The term skin effect refers to the fact that ac flows
only on the outside portion of the conductor, while dc flows through the entire con-
ductor. As frequency increases, skin effect produces a smaller zone of conduction
and a correspondingly higher value of ac resistance compared with dc resistance.
Another problem with RF circuits is that the signals find it easier to radiate both
from the circuit and within the circuit. Thus, coupling effects between elements of
the circuit, between the circuit and its environment, and from the environment to
the circuit become a lot more critical at RF. Interference and other strange effects
are found at RF that are missing in dc circuits and are negligible in most low-
frequency ac circuits.
The electromagnetic spectrum
When an RF electrical signal radiates, it becomes an electromagnetic wave that
includes not only radio signals, but also infrared, visible light, ultraviolet light,
X-rays, gamma rays, and others. Before proceeding with RF electronic circuits,
therefore, take a look at the electromagnetic spectrum.
1
Source: Secrets of RF Circuit Design
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.

The electromagnetic spectrum (Fig. 1-1) is broken into bands for the sake of
convenience and identification. The spectrum extends from the very lowest ac fre-
quencies and continues well past visible light frequencies into the X-ray and gamma-
ray region. The extremely low frequency (ELF) range includes ac power-line
frequencies as well as other low frequencies in the 25- to 100-hertz (Hz) region. The
U.S. Navy uses these frequencies for submarine communications.
The very low frequency (VLF) region extends from just above the ELF region,
although most authorities peg it to frequencies of 10 to 100 kilohertz (kHz). The low-
frequency (LF) region runs from 100 to 1000 kHz—or 1 megahertz (MHz). The
medium-wave (MW) or medium-frequency (MF) region runs from 1 to 3 MHz. The
amplitude-modulated (AM) broadcast band (540 to 1630 kHz) spans portions of the
LF and MF bands.
The high-frequency (HF) region, also called the shortwave bands (SW), runs
from 3 to 30 MHz. The VHF band starts at 30 MHz and runs to 300 MHz. This region
includes the frequency-modulated (FM) broadcast band, public utilities, some tele-
vision stations, aviation, and amateur radio bands. The ultrahigh frequencies (UHF)
run from 300 to 900 MHz and include many of the same services as VHF. The mi-
crowave region begins above the UHF region, at 900 or 1000 MHz, depending on
source authority.
You might well ask how microwaves differ from other electromagnetic waves.
Microwaves almost become a separate topic in the study of RF circuits because at
these frequencies the wavelength approximates the physical size of ordinary elec-
tronic components. Thus, components behave differently at microwave frequencies
than they do at lower frequencies. At microwave frequencies, a 0.5-W metal film re-
sistor, for example, looks like a complex RLC network with distributed L and C val-
ues—and a surprisingly different R value. These tiniest of distributed components
have immense significance at microwave frequencies, even though they can be ig-
nored as negligible at lower RFs.
Before examining RF theory, first review some background and fundamentals.
Units and physical constants
In accordance with standard engineering and scientific practice, all units in
this book will be in either the CGS (centimeter-gram-second) or MKS (meter-
kilogram-second) system unless otherwise specified. Because the metric system de-
2 Introduction to RF electronics
1-1 The electromagnetic spectrum from VLF to X-ray. The RF region covers from less than
100 kHz to 300 GHz.
Introduction to RF electronics

pends on using multiplying prefixes on the basic units, a table of common metric
prefixes (Table 1-1) is provided. Table 1-2 gives the standard physical units. Table
1-3 gives physical constants of interest in this and other chapters. Table 1-4 gives
some common conversion factors.
Units and physical constants 3
Table 1-1. Metric prefixes
Metric prefix Multiplying factor Symbol
tera 1012
T
giga 109 G
mega 106
M
kilo 103 K
hecto 102 h
deka 10 da
deci 10⫺1 d
centi 10⫺2 c
milli 10⫺3
m
micro 10⫺6
u
nano 10⫺9
n
pico 10⫺12
p
femto 10⫺15
f
atto 10⫺18
a
Table 1-2. Units of measure
Quantity Unit Symbol
Capacitance farad F
Electric charge coulomb Q
Conductance mhos
Conductivity mhos/meter ⍀/m
Current ampere A
Energy joule (watt-second) j
Field volts/meter E
Flux linkage weber (volt/second)
Frequency hertz Hz
Inductance henry H
Length meter m
Mass gram g
Power watt W
Resistance ohm ⍀
Time second s
Velocity meter/second m/s
Electric potential volt V

Wavelength and frequency
For all wave forms, the velocity, wavelength, and frequency are related so that
the product of frequency and wavelength is equal to the velocity. For radiowaves,
this relationship can be expressed in the following form:
(1-1)
where
␭ ⫽ wavelength in meters (m)
F ⫽ frequency in hertz (Hz)
⫽ dielectric constant of the propagation medium
c ⫽ velocity of light (300,000,000 m/s).
The dielectric constant ( ) is a property of the medium in which the wave prop-
agates. The value of is defined as 1.000 for a perfect vacuum and very nearly 1.0 for
dry air (typically 1.006). In most practical applications, the value of in dry air is
taken to be 1.000. For media other than air or vacuum, however, the velocity of prop-
⑀
⑀
⑀
⑀
lF2⑀ ⫽ c,
Table 1-3. Physical constants
Constant Value Symbol
Boltzmann’s constant 1.38 ⫻ 10⫺23
J/K K
Electric chart (e⫺
) 1.6 ⫻ 10⫺19
C q
Electron (volt) 1.6 ⫻ 10⫺19 J eV
Electron (mass) 9.12 ⫻ 10⫺31
kg m
Permeability of free space 4␲ ⫻ 10⫺7 H/m U0
Permitivity of free space 8.85 ⫻ 10⫺12 F/m 0
Planck’s constant 6.626 ⫻ 10⫺34 J-s h
Velocity of electromagnetic waves 3 ⫻ 108
m/s c
Pi (␲) 3.1416 ...... ␲
⑀
Table 1-4. Conversion factors
1 inch ⫽ 2.54 cm
1 inch ⫽ 25.4 mm
1 foot ⫽ 0.305 m
1 statute mile ⫽ 1.61 km
1 nautical mile ⫽ 6,080 feet (6,000 feet)a
1 statute mile ⫽ 5,280 feet
1 mile ⫽ 0.001 in ⫽ 2.54 ⫻ 10⫺5
m
1 kg ⫽ 2.2 lb
1 neper ⫽ 8.686 dB
1 gauss ⫽ 10,000 teslas
a Some navigators use 6,000 feet for ease of calculation. The
nautical mile is 1/360 of the Earth’s circumference at the
equator, more or less.

agation is slower and the value of ⑀ relative to a vacuum is higher. Teflon, for exam-
ple, can be made with values from about 2 to 11.
Equation (1-1) is more commonly expressed in the forms of Eqs. (1-2) and
(1-3):
(1-2)
and
(1-3)
[All terms are as defined for Eq. (1-1).]
Microwave letter bands
During World War II, the U.S. military began using microwaves in radar and
other applications. For security reasons, alphabetic letter designations were adopted
for each band in the microwave region. Because the letter designations became in-
grained, they are still used throughout industry and the defense establishment. Un-
fortunately, some confusion exists because there are at least three systems currently
in use: pre-1970 military (Table 1-5), post-1970 military (Table 1-6), and the IEEE
and industry standard (Table 1-7). Additional confusion is created because the mili-
tary and defense industry use both pre- and post-1970 designations simultaneously
and industry often uses military rather than IEEE designations. The old military des-
ignations (Table 1-5) persist as a matter of habit.
Skin effect
There are three reasons why ordinary lumped constant electronic components
do not work well at microwave frequencies. The first, mentioned earlier in this chap-
ter, is that component size and lead lengths approximate microwave wavelengths.
F ⫽
c
l2⑀
.
l ⫽
c
F 2⑀
⑀
Microwave letter bands 5
Table 1-5. Old U.S. military
microwave frequency bands
(WWII–1970)
Band designation Frequency range
P 225–390 MHz
L 390–1550 MHz
S 1550–3900 MHz
C 3900–6200 MHz
X 6.2–10.9 GHz
K 10.9–36 GHz
Q 36–46 GHz
V 46–56 GHz
Q 56–100 GHz

The second is that distributed values of inductance and capacitance become signifi-
cant at these frequencies. The third is the phenomenon of skin effect. While dc cur-
rent flows in the entire cross section of the conductor, ac flows in a narrow band near
the surface. Current density falls off exponentially from the surface of the conductor
toward the center (Fig. 1-2). At the critical depth (␦, also called the depth of pene-
tration), the current density is 1/e ⫽ 1/2.718 ⫽ 0.368 of the surface current density.
Table 1-7. IEEE/Industry standard
frequency bands
HF 3–30 MHz
VHF 0–300 MHz
UHF 300–1000 MHz
L 1000–2000 MHz
S 2000–4000 MHz
C 4000–8000 MHz
X 8000–12000 MHz
Ku 12–18 GHz
K 18–27 GHz
Ka 27–40 GHz
Millimeter 40–300 GHz
Submillimeter ⬎300 GHz
Table 1-6. New U.S. military microwave
frequency bands (Post-1970)
A 100–250 MHz
B 250–500 MHz
C 500–1000 MHz
D 1000–2000 MHz
E 2000–3000 MHz
F 3000–4000 MHz
G 4000–6000 MHz
H 6000–8000 MHz
I 8000–10000 MHz
J 10–20 GHz
K 20–40 GHz
L 40–60 GHz
M 60–100 GHz

The value of ␦ is a function of operating frequency, the permeability (␮) of the con-
ductor, and the conductivity (␴). Equation (1-4) gives the relationship.
(1-4)
where
␦ ⫽ critical depth
F ⫽ frequency in hertz
␮ ⫽ permeability in henrys per meter
␴ ⫽ conductivity in mhos per meter.
RF components, layout, and construction
Radio-frequency components and circuits differ from those of other frequencies
principally because the unaccounted for “stray” inductance and capacitance forms a
significant portion of the entire inductance and capacitance in the circuit. Consider
a tuning circuit consisting of a 100-pF capacitor and a 1-␮H inductor. According to
an equation that you will learn in a subsequent chapter, this combination should res-
onate at an RF frequency of about 15.92 MHz. But suppose the circuit is poorly laid
out and there is 25 pF of stray capacitance in the circuit. This capacitance could
come from the interaction of the capacitor and inductor leads with the chassis or
with other components in the circuit. Alternatively, the input capacitance of a tran-
sistor or integrated circuit (IC) amplifier can contribute to the total value of the
“strays” in the circuit (one popular RF IC lists 7 pF of input capacitance). So, what
does this extra 25 pF do to our circuit? It is in parallel with the 100-pF discrete
␦ ⫽
B
1
2␲F␴␮
RF components, layout, and construction 7
1-2
In ac circuits, the current flows
only in the outer region of the
conductor. This effect is
frequency-sensitive and it
becomes a serious consideration
at higher RF frequencies.

capacitor so it produces a total of 125 pF. Reworking the resonance equation with
125 pF instead of 100 pF reduces the resonant frequency to 14.24 MHz.
A similar situation is seen with stray inductance. All current-carrying conduc-
tors exhibit a small inductance. In low-frequency circuits, this inductance is not suf-
ficiently large to cause anyone concern (even in some lower HF band circuits), but
as frequencies pass from upper HF to the VHF region, strays become terribly impor-
tant. At those frequencies, the stray inductance becomes a significant portion of to-
tal circuit inductance.
Layout is important in RF circuits because it can reduce the effects of stray ca-
pacitance and inductance. A good strategy is to use broad printed circuit tracks at
RF, rather than wires, for interconnection. I’ve seen circuits that worked poorly
when wired with #28 Kovar-covered “wire-wrap” wire become quite acceptable
when redone on a printed circuit board using broad (which means low-inductance)
tracks.
Figure 1-3 shows a sample printed circuit board layout for a simple RF amplifier
circuit. The key feature in this circuit is the wide printed circuit tracks and short
distances. These tactics reduce stray inductance and will make the circuit more
predictable.
Although not shown in Fig. 1-3, the top (components) side of the printed circuit
board will be all copper, except for space to allow the components to interface with
the bottom-side printed tracks. This layer is called the “ground plane” side of the
board.
Impedance matching in RF circuits
In low-frequency circuits, most of the amplifiers are voltage amplifiers. The re-
quirement for these circuits is that the source impedance must be very low com-
pared with the load impedance. A sensor or signal source might have an output
impedance of, for example, 25 ⍀. As long as the input impedance of the amplifier re-
ceiving that signal is very large relative to 25 ⍀, the circuit will function. “Very large”
typically means greater than 10 times, although in some cases greater than 100 times
is preferred. For the 25-⍀ signal source, therefore, even the most stringent case is
met by an input impedance of 2500 ⍀, which is very far below the typical input im-
pedance of real amplifiers.
RF circuits are a little different. The amplifiers are usually specified in terms of
power parameters, even when the power level is very tiny. In most cases, the RF cir-
cuit will have some fixed system impedance (50, 75, 300, and 600 ⍀ being common,
with 50 ⍀ being nearly universal), and all elements of the circuit are expected to
1-3
Typical RF printed circuit
layout.

match the system impedance. Although a low-frequency amplifier typically has a
very high input impedance and very low output impedance, most RF amplifiers will
have the same impedance (usually 50 ⍀) for both input and output.
Mismatching the system impedance causes problems, including loss of signal—
especially where power transfer is the issue (remember, for maximum power trans-
fer, the source and load impedances must be equal). Radio-frequency circuits very
often use transformers or impedance-matching networks to affect the match be-
tween source and load impedances.
Wiring boards
Radio-frequency projects are best constructed on printed circuit boards that are
specially designed for RF circuits. But that ideal is not always possible. Indeed, for
many hobbyists or students, it might be impossible, except for the occasional project
built from a magazine article or from this book. This section presents a couple of al-
ternatives to the use of printed circuit boards.
Figure 1-4 shows the use of perforated circuit wiring board (commonly called
perfboard). Electronic parts distributors, RadioShack, and other outlets sell various
versions of this material. Most commonly available perfboard offers 0.042⬙ holes
spaced on 0.100⬙ centers, although other hole sizes and spacings are available. Some
perfboard is completely blank, and other stock material is printed with any of several
different patterns. The offerings of RadioShack are interesting because several dif-
ferent patterns are available. Some are designed for digital IC applications and oth-
ers are printed with a pattern of circles, one each around the 0.042⬙ holes.
In Fig. 1-4, the components are mounted on the top side of an unprinted board.
The wiring underneath is “point-to-point” style. Although not ideal for RF circuits, it
will work throughout the HF region of the spectrum and possibly into the low VHF
(especially if lead lengths are kept short).
1-4 Perfboard layout.

Notice the shielded inductors on the board in Fig. 1-4. These inductors are slug-
tuned through a small hole in the top of the inductor. The standard pin pattern for
these components does not match the 0.100-hole pattern that is common to perf-
board. However, if the coils are canted about half a turn from the hole matrix, the
pins will fit on the diagonal. The grounding tabs for the shields can be handled in ei-
ther of two ways. First, bend them 90⬚ from the shield body and let them lay on the
top side of the perfboard. Small wires can then be soldered to the tabs and passed
through a nearby hole to the underside circuitry. Second, drill a pair of 1
⁄16⬙ holes (be-
tween two of the premade holes) to accommodate the tabs. Place the coil on the
board at the desired location to find the exact location of these holes.
Figure 1-5 shows another variant on the perfboard theme. In this circuit,
pressure-sensitive (adhesive-backed) copper foil is pressed onto the surface of the
perfboard to form a ground plane. This is not optimum, but it works for “one-off”
homebrew projects up to HF and low-VHF frequencies.
The perfboard RF project in Fig. 1-6 is a frequency translator. It takes two fre-
quencies (F1 and F2), each generated in a voltage-tuned variable-frequency oscilla-
tor (VFO) circuit, and mixes them together in a double-balanced mixer (DBM)
device. A low-pass filter (the toroidal inductors seen in Fig. 1-6) selects the differ-
ence frequency (F2-F1). It is important to keep the three sections (osc1, osc2, and
the low-pass filter) isolated from each other. To accomplish this goal, a shield parti-
tion is provided. In the center of Fig. 1-6, the metal package of the mixer is soldered
to the shield partition. This shield can be made from either 0.75⬙ or 1.00⬙ brass strip
stock of the sort that is available from hobby and model shops.
Figure 1-7 shows a small variable-frequency oscillator (VFO) that is tuned by an
air variable capacitor. The capacitor is a 365-pF “broadcast band” variable. I built this
circuit as the local oscillator for a high-performance AM broadcast band receiver
project. The shielded, slug-tuned inductor, along with the capacitor, tunes the 985-
to 2055-kHz range of the LO. The perfboard used for this project was a preprinted
RadioShack. The printed foil pattern on the underside of the perfboard is a matrix of
small circles of copper, one copper pad per 0.042⬙ hole. The perfboard is held off the
chassis by nylon spacers and 4-40 ⫻ 0.75⬙ machine screws and hex nuts.
1-5 Perfboard layout with RF ground plane.

Chassis and cabinets
It is probably wise to build RF projects inside shielded metal packages wherever
possible. This approach to construction will prevent external interference from
harming the operation of the circuit and prevent radiation from the circuit from in-
terfering with external devices. Figure 1-8 shows two views of an RF project built in-
side an aluminum chassis box; Fig. 1-8A shows the assembled box and Fig. 1-8B
shows an internal view. These boxes have flanged edges on the top portion that over-
lap the metal side/bottom panel. This overlap is important for interference reduc-
tion. Shun those cheaper chassis boxes that use a butt fit, with only a couple of
nipples and dimples to join the boxes together. Those boxes do not shield well.
The input and output terminals of the circuit in Fig. 1-8 are SO-239 “UHF” coax-
ial connectors. Such connectors are commonly used as the antenna terminal on
shortwave radio receivers. Alternatives include “RCA phono jacks” and “BNC” coax-
ial connectors. Select the connector that is most appropriate to your application.
RF shielded boxes
At one time, more than 2 decades ago, I loathed small RF electronic projects
above about 40-m as “too hard.” As I grew in confidence, I learned a few things about
1-6
The use of shielding on
perfboard.
1-7
VFO circuit build on perfboard.

RF construction (e.g., layout, grounding, and shielding) and found that by following
the rules, one can be as successful building RF stuff as at lower frequencies.
One problem that has always been something of a hassle, however, is the shield-
ing that is required. You could learn layout and grounding, but shielding usually re-
quired a better box than I had. Most of the low-cost aluminum electronic hobbyist
boxes on the market are alright for dc to the AM broadcast band, but as frequency
climbs into the HF and VHF region, problems begin to surface. What you thought
was shielded “t’ain’t.” If you’ve read my columns or feature articles over the years,
you will recall that I caution RF constructors to use the kind of aluminum box with
an overlapping flange of at least 0.25⬙, and a good tight fit. Many hobbyist-grade
boxes on the market just simply are not good enough.
Enter SESCOM, Inc. [Dept. JJC, 2100 Ward Drive, Henderson, NV, 89015-4249;
(702) 565-3400 and (for voice orders only) 1-800-634-3457 and (for FAX orders
only) 1-800-551-2749]. SESCOM makes a line of cabinets, 19⬙ racks, rack mount
boxes, and RF shielded boxes. Their catalog has a lot of interesting items for radio
and electronic hobbyist constructors. I was particularly taken by their line of RF
shielded boxes. Why? Because it seems that RF projects are the main things I’ve
built for the past 10 years.
Figure 1-9 shows one of the SESCOM RF shielded steel boxes in their SB-x line.
Notice that it uses the “finger” construction in order to get a good RF-tight fit be-
tween the lid and the body of the box. Also notice that the box comes with some
snap-in partitions for internal shielding between sections. The box body is punched
to accept the tabs on these internal partitions, which can then be soldered in place
for even better stability and shielding.
At first, I was a little concerned about the material; the boxes are made of hot
tin-plated steel rather than aluminum. The tin plating makes soldering easy, but steel
A
1-8 Shielded RF construction: (A) closed box showing dc connections
made via coaxial capacitors; (B) box opened.
B

is hard on drill bits. I found, however, in experimenting with the SB-5 box supplied
to me by SESCOM that a good-quality set of drill bits had no difficulty making a hole.
Sure, if you use old, dull drill bits and lean on the drill like Attila the Hun, then you’ll
surely burn it out. But by using a good-quality, sharp bit and good workmanship
practices to make the hole, there is no real problem.
The boxes come in 11 sizes from 2.1⬙ ⫻ 1.9⬙ footprint to a 6.4⬙ ⫻ 2.7⬙ footprint,
with heights of 0.63,⬙ 1.0, or 1.1⬙. Prices compare quite favorably with the prices of
the better-quality aluminum boxes that don’t shield so well at RF frequencies.
The small project in Fig. 1-10 is a small RF preselector for the AM broadcast
band. It boosts weak signals and reduces interference from nearby stations. The tun-
ing capacitor is mounted to the front panel and is fitted with a knob to facilitate tun-
ing. An on/off switch is also mounted on the front panel (a battery pack inside the
aluminum chassis box provides dc power). The inductor that works with the capac-
itor is passed through the perfboard (where the rest of the circuit is located) to the
rear panel (where its adjustment slug can be reached).
1-9 RF project box with superior shielding because of the finger-grip design of the top cover
(one of a series made by SESCOM).

The project in Fig. 1-11 is a test that I built for checking out direct-conversion
receiver designs. The circuit boards are designed to be modularized so that different
sections of the circuit can easily be replaced with new designs. This approach allows
comparison (on an “apples versus apples” basis) of different circuit designs.
Coaxial cable transmission line (“coax”)
Perhaps the most common form of transmission line for shortwave and
VHF/UHF receivers is coaxial cable. “Coax” consists of two conductors arranged
concentric to each other and is called coaxial because the two conductors share the
same center axis (Fig. 1-12). The inner conductor will be a solid or stranded wire,
and the other conductor forms a shield. For the coax types used on receivers, the
shield will be a braided conductor, although some multistranded types are also
sometimes seen. Coaxial cable intended for television antenna systems has a 75-⍀
characteristic impedance and uses metal foil for the outer conductor. That type of
outer conductor results in a low-loss cable over a wide frequency range but does not
work too well for most applications outside of the TV world. The problem is that the
foil is aluminum, which doesn’t take solder. The coaxial connectors used for those
antennas are generally Type-F crimp-on connectors and have too high of a casualty
rate for other uses.
The inner insulator separating the two conductors is the dielectric, of which
there are several types; polyethylene, polyfoam, and Teflon are common (although
the latter is used primarily at high-UHF and microwave frequencies). The velocity
factor (V) of the coax is a function of which dielectric is used and is outlined as fol-
lows:
Dielectric type Velocity factor
Polyethylene 0.66
Polyfoam 0.80
Teflon 0.70
1-10
Battery-powered RF project.

Coaxial cable is available in a number of characteristic impedances from about
35 to 125 ⍀, but the vast majority of types are either 52- or 75-⍀ impedances. Sev-
eral types that are popular with receiver antenna constructors include the following:
RG-8/U or RG-8/AU 52 ⍀ Large diameter
RG-58/U or RG-58/AU 52 ⍀ Small diameter
RG-174/U or RG-174/AU 52 ⍀ Tiny diameter
RG-11/U or RG-11/AU 75 ⍀ Large diameter
RG-59/U or RG-59/AU 75 ⍀ Small diameter
Although the large-diameter types are somewhat lower-loss cables than the
small diameters, the principal advantage of the larger cable is in power-handling ca-
pability. Although this is an important factor for ham radio operators, it is totally
unimportant to receiver operators. Unless there is a long run (well over 100 feet),
where cumulative losses become important, then it is usually more practical on
receiver antennas to opt for the small-diameter (RG-58/U and RG-59/U) cables; they
Coaxial cable transmission line (“coax”) 15
1-11
Receiver chassis used as a “test
bench” to try various
modifications to a basic design.
1-12 Coaxial cable (cut-away view).

are a lot easier to handle. The tiny-diameter RG-174 is sometimes used on receiver
antennas, but its principal use seems to be connection between devices (e.g., re-
ceiver and either preselector or ATU), in balun and coaxial phase shifters, and in in-
strumentation applications.
Installing coaxial connectors
One of the mysteries faced by newcomers to the radio hobbies is the small mat-
ter of installing coaxial connectors. These connectors are used to electrically and
mechanically fasten the coaxial cable transmission line from the antenna to the re-
ceiver. There are two basic forms of coaxial connector, both of which are shown in
Fig. 1-13 (along with an alligator clip and a banana-tip plug for size comparison). The
larger connector is the PL-259 UHF connector, which is probably the most-common
form used on radio receivers and transmitters (do not take the “UHF” too seriously,
it is used at all frequencies). The PL-259 is a male connector, and it mates with the
SO-239 female coaxial connector.
The smaller connector in Fig. 1-12 is a BNC connector. It is used mostly on elec-
tronic instrumentation, although it is used in some receivers (especially in handheld
radios).
The BNC connector is a bit difficult, and very tedious, to correctly install so I
recommend that most readers do as I do: Buy them already mounted on the wire.
But the PL-259 connector is another matter. Besides not being readily available al-
ready mounted very often, it is relatively easy to install.
Figure 1-14A shows the PL-259 coaxial connector disassembled. Also shown in
Fig. 1-14A is the diameter-reducing adapter that makes the connector suitable for
use with smaller cables. Without the adapter, the PL-259 connector is used for RG-
8/U and RG-11/U coaxial cable, but with the correct adapter, it will be used with
smaller RG-58/U or RG-59/U cables (different adapters are needed for each type).
1-13
Various types of coaxial
connectors, cable ends, and
adapters.

Coaxial cable transmission line (“coax”) 17
1-14 Installing the PL-259 UHF connector.
(A) Disassembled PL-29 connector
(B) Adapter and shield placed over the coax
(C) Coax stripped and shield laid
back onto adapter
(D) Adapter threaded into main barrel
and soldered through holes in barrel
(E) Finished connector.

The first step is to slip the adapter and thread the outer shell of the PL-259 over
the end of the cable (Fig. 1-14B). You will be surprised at how many times, after the
connector is installed, you find that one of these components is still sitting on the
workbench . . . requiring the whole job to be redone (sigh). If the cable is short
enough that these components are likely to fall off the other end, or if the cable is
dangling a particularly long distance, then it might be wise to trap the adapter and
outer shell in a knotted loop of wire (note: the knot should not be so tight as to kink
the cable).
The second step is to prepare the coaxial cable. There are a number of tools for
stripping coaxial cable, but they are expensive and not terribly cost-effective for
anyone who does not do this stuff for a living. You can do just as effective a job with
a scalpel or X-acto knife, either of which can be bought at hobby stores and some
electronics parts stores. Follow these steps in preparing the cable:
1. Make a circumscribed cut around the body of the cable 3
⁄4⬙ from the end, and
then make a longitudinal cut from the first cut to the end.
2. Now strip the outer insulation from the coax, exposing the shielded outer
conductor.
3. Using a small, pointed tool, carefully unbraid the shield, being sure to
separate the strands making up the shield. Lay it back over the outer
insulation, out of the way.
4. Finally, using a wire stripper, side cutters or the scalpel, strip 5
⁄8⬙ of the
inner insulation away, exposing the inner conductor. You should now have
5
⁄8⬙ of inner conductor and 3
⁄8⬙ of inner insulation exposed, and the outer
shield destranded and laid back over the outer insulation.
Next, slide the adapter up to the edge of the outer insulator and lay the un-
braided outer conductor over the adapter (Fig. 1-14C). Be sure that the shield
strands are neatly arranged and then, using side cutters, neatly trim it to avoid in-
terfering with the threads. Once the shield is laid onto the adapter, slip the connec-
tor over the adapter and tighten the threads (Fig. 1-14D). Some of the threads
should be visible in the solder holes that are found in the groove ahead of the
threads. It might be a good idea to use an ohmmeter or continuity connector to be
sure that there is no electrical connection between the shield and inner conductor
(indicating a short circuit).
Warning
Soldering involves using a hot soldering iron. The connector will become
dangerously hot to the touch. Handle the connector with a tool or cloth covering.
• Solder the inner conductor to the center pin of the PL-259. Use a
100-W or greater soldering gun, not a low-heat soldering pencil.
• Solder the shield to the connector through the holes in the groove.
• Thread the outer shell of the connector over the body of the con-
nector.
After you make a final test to make sure there is no short circuit, the connector
is ready for use (Fig. 1-14E).

2
CHAPTER
RF components
and tuned circuits
This chapter covers inductance (L) and capacitance (C), how they are affected by
ac signals, and how they are combined into LC-tuned circuits. The tuned circuit
allows the radio-frequency (RF) circuit to be selective about the frequency being
passed. Alternatively, in the case of oscillators, LC components set the operating
frequency of the circuit.
Tuned resonant circuits
Tuned resonant circuits, also called tank circuits or LC circuits, are used in the
radio front end to select from the myriad of stations available at the antenna. The
tuned resonant circuit is made up of two principal components: inductors and ca-
pacitors, also known in old radio books as condensers. This section examines induc-
tors and capacitors separately, and then in combination, to determine how they
function to tune a radio’s RF, intermediate-frequency (IF), and local oscillator (LO)
circuits. First, a brief digression is needed to discuss vectors because they are used
in describing the behavior of these components and circuits.
Vectors
A vector (Fig. 2-1A) is a graphical device that is used to define the magnitude
and direction (both are needed) of a quantity or physical phenomenon. The length
of the arrow defines the magnitude of the quantity, and the direction in which it
points defines the direction of action of the quantity being represented.
Vectors can be used in combination with each other. For example, Fig. 2-1B
shows a pair of displacement vectors that define a starting position (P1) and a final
position (P2) for a person traveling 12 miles north from point P1 and then 8 miles
east to arrive at point P2. The displacement in this system is the hypotenuse of the
19
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embraced him, crying: "More than a million! think of it! more than a
million!" and he began to dance more violently than ever.
"But come, she is waiting for you, come and embrace her, at least,"
and taking him by the shoulders he pushed Lesable before him, and
threw him like a ball into the apartment where Cora stood anxiously
waiting and listening.
The moment she saw her husband, she recoiled, stifled with a
sudden emotion. He stood before her, pale and severe. He had the
air of a judge, and she of a culprit. At last he said: "It seems that
you are pregnant."
She stammered in a trembling voice: "Yes, that seems to be the
case."
But Cachelin seized each of them by the neck, and, bringing them
face to face, cried: "Now kiss each other, by George! It is a fitting
occasion."
And after releasing them, he capered about like a schoolboy,
shouting: "Victory, victory, we have won our case! I say, Léopold, we
must purchase a country house; there, at least, you will certainly
recover your health." At this idea Lesable trembled. His father-in-law
continued: "We will invite M. Torchebeuf and his wife to visit us, and
as the under-chief is at the end of his term you may take his place.
That is the way to bring it about."
Lesable was now beginning to regard things from Cachelin's
standpoint, and he saw himself receiving his chief at a beautiful
country place on the banks of the river, dressed in coat of white
twill, with a Panama hat on his head.
Something sweet entered into his heart with this hope, something
warm and good seemed to melt within him, rendering him light of
heart and healthier in feeling. He smiled, still without speaking.
Cachelin, intoxicated with joy, transported at the thought of his fine
prospects, continued:

"Who knows, we may gain some political influence. Perhaps you will
be deputy. At all events, we can see the society of the
neighbourhood, and enjoy some luxuries. And you shall have a little
pony to convey you every morning to the station."
These images of luxury, of elegance and prosperity aroused the
drooping spirits of Lesable. The thought that he could be driven in
his own carriage, like the rich people he had so often envied, filled
him with satisfaction, and he could not refrain from exclaiming: "Ah,
that will be delightful indeed."
Cora, seeing him won over, smiled tenderly and gratefully, and
Cachelin, who saw no obstacles now in the way of indulgence,
declared: "We will dine at the restaurant, to celebrate the happy
event."
When they reached home, the two men were a little tipsy, and
Lesable, who saw double and whose ideas were all topsy-turvy,
could not find his bedroom. He made his way by mistake, or
forgetfulness, into the long vacant bed of his wife. And all night long
it seemed to him that the bed oscillated like a boat, rolling and
pitching as though it would upset. He was even a little seasick.
He was surprised on awaking to find Cora in his arms. She opened
her eyes with a smile and kissed him with a sudden effusion of
gratitude and affection. Then she said to him, in that caressing voice
which women employ in their cajoleries: "If you wish to be very nice,
you will not go to your office to-day. There is no need to be so
punctual now that we are going to be rich, and we will make a little
visit to the country, all by ourselves."
Lesable was content to remain quiet, with the feeling for self-
indulgence which follows an evening of excess, and the warmth of
the bed was grateful. He felt the drowsy wish to lie a long time, to
do nothing more but to live in tranquil idleness. An unusual sloth
paralyzed his soul and subdued his body, and one vague, happy, and
continuous thought never left him—"He was going to be rich,
independent."

But suddenly a fear seized him, and he whispered softly, as if he
thought the walls might hear him: "Are you very sure you are
pregnant, after all?"
She reassured him at once. "Oh, yes! I am certain of it. I could not
be mistaken."
And, as if still doubting, he traced the outline of her figure with his
hand, and feeling convinced declared: "Yes, it is true—but you will
not be brought to bed before the date. They will contest our right on
that account, perhaps."
At this supposition she grew angry.
"Oh, no indeed, they are not going to trick us now after so much
misery, so much trouble, and so many efforts. Oh, no, indeed!" She
was overwhelmed with indignation. "Let us go at once to the
notary," she said.
But his advice was to get a physician's certificate first, and they
presented themselves again to Dr. Lefilleul.
He recognized them immediately, and exclaimed:
"Ah well, have you succeeded?"
They both blushed up to their ears, and Cora a little shamefacedly
stammered: "I believe we have, doctor."
The doctor rubbed his hands, crying: "I expected it, I expected it.
The means I recommended to you never fail; at least, only from
some radical incapacity of one of the parties."
When he had made an examination of the young wife, he declared:
"It is true, bravo!" and he wrote on a sheet of paper:
"I, the undersigned, doctor of medicine, of the Faculty of Paris,
certify that Madame Léopold Lesable, née Cachelin, presents all the
symptoms of pregnancy, dating from over three months."
Then, turning toward Lesable: "And you," he said, "how is that chest
and that heart?" and having made an auscultation, he declared that

the patient was entirely cured. They set out happy and joyous, arm
in arm, with elastic steps. But on the route Léopold had an idea. "We
had better go home before we see the lawyer, and rearrange your
dress; you'll put two or three towels under your belt it will draw
attention to it and that will be better; he will not believe then that
we are trying to gain time."
They returned home, and he himself undressed his wife in order to
adjust the deception. Ten consecutive times Lesable changed the
position of the towels, and stepped back some paces to get the
proper effect, wishing to obtain an absolutely perfect resemblance.
Satisfied with the result at last, they set out again, and walked
proudly through the streets, Lesable carrying himself with the air of
one whose virility was established and patent to all the world.
The notary received them kindly. Then he listened to their
explanation, ran his eye over the certificate, and, as Lesable insisted,
"For the rest, Monsieur, it is only necessary to glance for a second,"
he threw a convinced look on the tell-tale figure of the young
woman.
There was a moment of anxious suspense, when the man of law
declared: "Assuredly, whether the infant is born or to be born, it
exists, it lives; so we will suspend the execution of the testament till
the confinement of Madame."
After leaving the office of the notary, they embraced each other on
the stairway, so exuberant was their joy.
VII
From the moment of this happy discovery, the three relatives lived in
the most perfect accord. They were good-humoured, reasonable,
and kind. Cachelin had recovered all his old gaiety, and Cora loaded
her husband with attentions. Lesable also seemed like another man,
and more gay than he had ever been in his life. Maze came less
often, and seemed ill at ease in the family circle; they received him

kindly, but with less warmth than formerly, for happiness is
egotistical and excludes strangers.
Cachelin himself seemed to feel a certain secret hostility against the
handsome clerk whom some months before he had introduced so
eagerly into his household. It was he who announced to this friend
the pregnancy of Cora. He said to him brusquely: "You know my
daughter is pregnant!"
Maze, feigning surprise, replied: "Ah, indeed! you ought to be very
happy."
Cachelin responded with a "Humph!" for he perceived that his
colleague, on the contrary, did not appear to be delighted. Men care
but little to see in this state (whether or not the cause lies with
them) women in whom they are interested.
Every Sunday, however, Maze continued to dine with the family, but
it was no longer pleasant to spend the evenings with them, albeit no
serious difference had arisen; and this strange embarrassment
increased from week to week. One evening, just after Maze had
gone, Cachelin cried with an air of annoyance: "That fellow is
beginning to weary me to death!"
Lesable replied: "The fact is, he does not improve on acquaintance."
Cora lowered her eyes. She did not give her opinion. She always
seemed embarrassed in the presence of the handsome Maze, who,
on his side, appeared almost ashamed when he found himself near
her. He no longer smiled on looking at her as formerly, no longer
asked her and her husband to accompany him to the theatre, and
the intimacy, which till lately had been so cordial, seemed to have
become but an irksome burden.
One Thursday, when her husband came home to dinner, Cora kissed
him with more coquetry than usual and whispered in his ear:
"Perhaps you are going to scold me now?"
"Why should I?" he inquired.

"Well, because—M. Maze came to see me a little while ago, and, as I
do not wish to be gossiped about on his account, I begged him
never to come when you were not at home. He seemed a little hurt."
Lesable, very much surprised, demanded:
"Very well, what did he say to that?"
"Oh! he did not say much, but it did not please me all the same, and
then I asked him to cease his visits entirely. You know very well that
it is you and papa who brought him here—I was not consulted at all
about it—and I feared you would be displeased because I had
dismissed him."
A grateful joy beamed from the face of her husband.
"You did right, perfectly right, and I even thank you for it."
She went on, in order to establish the understanding between the
two men, which she had arranged in advance: "At the office you
must conduct yourself as though nothing had happened, and speak
to him as you have been in the habit of doing; but he is not to come
here any more."
Taking his wife tenderly in his arms, Lesable impressed long kisses
on her eyelids and on her cheeks. "You are an angel! You are an
angel!" he repeated, and he felt pressing against his stomach the
already lusty child.
VIII
Nothing of importance happened up to the date of Cora's
confinement, which occurred on the last day of September. The
child, being a daughter, was called Désirée. As they wished to make
the christening an imposing event, it was decided to postpone the
ceremony until they were settled in the new country house which
they were going to buy.
They chose a beautiful estate at Asnières, on the hills that overlook
the Seine. Great changes had taken place during the winter. As soon

as the legacy was secured, Cachelin asked for his pension, which
was granted, and he left the office. He employed his leisure
moments in cutting, with the aid of a little scroll-saw, the covers of
cigar-boxes. He made clocks, caskets, jardinières, and all sorts of
odd little pieces of furniture. He had a passion for this work, the
taste for which had come to him on seeing a peripatetic merchant
working thus with sheets of wood on the Avenue de l'Opéra; and
each day he obliged everybody to admire some new design both
complicated and puerile. He was amazed at his own work, and kept
on saying: "It is astonishing what one can accomplish!"
The assistant-chief, M. Rabot, being dead at last, Lesable fulfilled the
duties of his place, although he did not receive the title, for sufficient
time had not elapsed since his last promotion.
Cora had become a wholly different woman, more refined, more
elegant, instinctively divining all the transformations that wealth
imposes. On New Year's Day she made a visit to the wife of her
husband's chief, a commonplace person, who remained a provincial,
notwithstanding a residence of thirty-five years in Paris, and she put
so much grace and seductiveness into her prayer that Mme
Torchebeuf should stand godmother to her child that the good
woman consented. Grandpapa Cachelin was the godfather.
The ceremony took place on a brilliant Sunday in June. All the
employees of the office were invited to witness it, except the
handsome Maze, who was seen no more in the Cachelin circle.
At nine o'clock Lesable waited at the railway station for the train
from Paris, while a groom, in livery covered with great gilt buttons,
held by the bridle a plump pony hitched to a brand-new phaeton.
The engine whistled, then appeared, dragging its train of cars, which
soon discharged their freight of passengers.
M. Torchebeuf descended from a first-class carriage with his wife, in
a magnificent toilette, while Pitolet and Boissel got out of a second-
class carriage. They had not dared to invite old Savon, but it was

understood that they were to meet him by chance in the afternoon
and bring him to dinner with the consent of the chief.
Lesable hurried to meet his superior, who advanced slowly, the lapel
of his frock-coat ornamented with a decoration that resembled a full-
blown red rose. His enormous head, surmounted by a large hat that
seemed to crush his small body, gave him the appearance of a
phenomenon, and his wife, if she had stood on tiptoe, could have
looked over his head without any trouble.
Léopold, radiant, bowed and thanked his guests. He seated them in
the phaeton, then running toward his two colleagues, who were
walking modestly behind, he pressed their hands, regretting that his
phaeton was too small to accommodate them also. "Follow the
quay," he directed, "and you will reach my door—'Villa Désirée,' the
fourth one after the turn. Make haste!"
And mounting the phaeton, he took the reins and drove off, while
the groom leaped lightly to the little seat behind.
The ceremony was very brilliant, and afterwards they returned for
luncheon. Each one found under his napkin a present proportioned
to his station. The godmother received a bracelet of solid gold, her
husband a scarf-pin of rubies, Boissel a pocket book of Russian
leather, and Pitolet a superb meerschaum pipe. "It was Désirée,"
they said, "who offered these presents to her new friends."
Mme Torchebeuf, blushing with confusion and pleasure, placed on
her fat arm the brilliant circle, and, as the chief wore a narrow black
cravat, which would not receive the pin, he stuck the jewel in the
lapel of his frock-coat, under the Legion of Honour, as if it had been
another decoration of an inferior order.
Outside the window the shining band of the river was seen, curving
toward Suresnes, its banks shaded with trees. The sun fell in a rain
on the water, making it seems a river of fire. The beginning of the
repast was rather solemn, being made formal by the presence of M.
and Mme Torchebeuf. After a while, however, things began to go
better. Cachelin threw out some heavy jokes, which he felt would be

permitted him since he was rich, and everyone laughed at them. If
Pitolet or Boissel had uttered them, the guests would certainly have
been shocked.
At dessert, the infant was brought in and received a kiss from each
of the company. Smothered in a cloud of snowy lace, the baby
looked at the guests with its blue eyes void of intelligence or
expression, and rolled its bald head from side to side with an air of
newly awakened interest.
Pitolet, amid the confusion of voices, whispered in the ear of Boissel:
"It looks like a little Mazette."
The joke went round the Ministry next day.
At two o'clock the health of the newly christened baby was drunk,
and Cachelin proposed to show his guests over the property, and
then to take them for a walk on the banks of the Seine.
They moved in a slow procession from room to room, from the cellar
to the garret; then they examined the garden tree by tree, plant by
plant; after which, separating into two parties, they set out for a
walk.
Cachelin, who did not feel at home in the company of ladies, drew
Boissel and Pitolet into a café on the bank of the river, while
Mesdames Torchebeuf and Lesable, with their husbands, walked in
the opposite direction, these refined ladies not being able to mingle
with the common Sunday herd.
They walked slowly along the path, followed by the two men, who
talked gravely of the affairs of the office. On the river the boats were
continually passing, propelled by long strokes of the oars in the
hands of jolly fellows, the muscles of whose bare arms rolled under
the sunburned skin. Women, reclining on black or white fur rugs,
managed the tillers, drowsing under the hot sun, holding open over
their heads, like enormous flowers floating on the surface of the
water, umbrellas of red, yellow, and blue silk. Cries from one boat to
the other, calls, and shouts, and a remote murmur of human voices

lower down, confused and continuous, indicated where the
swarming crowds were enjoying a holiday.
Long files of fishermen stood motionless all along the river, while the
swimmers, almost naked, standing in heavy fishing boats, plunged in
headforemost, climbed back upon the boats and leaped into the
water again.
Mme Torchebeuf looked on in surprise.
Cora said to her: "It is like this every Sunday; it spoils this charming
country for me."
A canoe moved softly by. Two women rowed, while two men were
stretched in the bottom of the boat. One of the women, turning her
head towards the shore, cried:
"Hello! hello! you respectable women! I have a man for sale, very
cheap! Do you want him?"
Cora turned away contemptuously and taking the arm of her
companion said: "We cannot remain here; let us go. What infamous
creatures!"
They moved away as M. Torchebeuf was saying to Lesable: "It is
settled for the first of January. The head of the Department has
positively promised me."
"I don't know how to thank you, dear master," Lesable replied.
When they reached home they found Cachelin, Pitolet, and Boissel
laughing immoderately and almost carrying old Savon, whom they
jokingly declared they had found on the beach in the company of a
girl.
The frightened old man was crying: "It is not true, no, it is not true.
It is not right to say that, M. Cachelin, it is not kind."
And Cachelin, choking with laughter, cried: "Ah, you old rogue, did
you not call her your 'sweet goose quill'? We caught you, you
rascal!"

Then the ladies, too, began to laugh at the dismay of the poor old
man.
Cachelin continued: "With M. Torchebeuf's permission, we will keep
him prisoner as a punishment and make him dine with us."
The chief good-humouredly consented, and they continued to laugh
about the lady abandoned by the old man, who protested all the
time, annoyed at this mischievous farce.
The subject was the occasion of inexhaustible wit throughout the
evening, which sometimes even bordered on the obscene.
Cora and Mme Torchebeuf, seated under a tent on the lawn,
watched the reflections of the setting sun, which threw upon the
leaves a purple glow.
Not a breath stirred the branches, a serene and infinite peace fell
from the calm and flaming heavens.
Some boats still passed, more slowly, drifting with the tide.
Cora remarked: "It appears that poor M. Savon married a bad
woman."
Mme Torchebeuf, who was familiar with everything of the office,
replied:
"Yes, she was an orphan, very much too young for him, and
deceived him with a worthless fellow, and she ended in running
away with him."
Then the fat lady added: "I say he was a worthless fellow, but I
know nothing about it. It is reported that they loved one another
very much. In any case, old Savon is not very seductive."
Mme Lesable replied gravely:
"That is no excuse; the poor man is much to be pitied. Our next
door neighbour, M. Barbou, has had the same experience. His wife
fell in love with a sort of painter who passed his summers here, and
she has gone abroad with him. I do not understand how women can

fall so low. To my mind it seems a special chastisement should be
meted out to those wicked creatures who bring shame upon their
families."
At the end of the alley the nurse appeared, carrying the little Désirée
wrapped in her laces. The child, all rosy in the red gold of the
evening light, was coming towards the two women. She stared at
the fiery sky with the same pale and astonished eyes with which she
regarded their faces.
All the men who were talking at a distance drew near, and Cachelin,
seizing his little granddaughter, tossed her aloft in his arms as if he
would carry her to the skies. Her figure was outlined against the
brilliant line of the horizon, while her long white robe almost touched
the ground; and the grand-father cried: "Look! isn't this the best
thing in the world, after all, father Savon?"
But the old man made no reply, having nothing to say, or perhaps
thinking too many things.
A servant opened the door and announced: "Madame is served!"

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