!Reading.example

1
Chapter 1
• How are Electronic Instrumentation and related fields defined?
• How has Instrumentation evolved into Electronic Instrumentation?
• What is the internal structure of an instrument like?
• How should the quality of an instrument be specified?
• What is the smallest signal that can be measured?
• What sources of error are acting on an instrument?
1.1 Instruments for solving a measurement problem
Electronic Instrumentation is about the design, realisation and use of elec-
tronic systems for the measurement of electrical and non-electrical quantities.
Strongly related fields are measurement science and data acquisition. Each of
these disciplines has a specific function in solving a measurement problem. The
activity that is the basis of electronic instrumentation is measuring.
Measuring (performing a measurement) is formally defined as the set of
operations having the objective of determining a value of a quantity.
Measurement science provides the theoretical framework, which is used in an
initial feasibility study prior to the actual measurement to assess whether the
parameter of interest (the measurand) is measurable. Measurability can be
impaired due to a fundamental limitation or a practical constraint. For instance,
the mass and dimensions of a sculpture can be measured, but its artistic quality
for fundamental reasons cannot. For practical reasons, a certain voltage level
could prove non-measurable in cases where a high noise level is injected into the
INTRODUCTION TO
ELECTRONIC
INSTRUMENTATION

Electronic Instrumentation: R.F. Wolffenbuttel
Chapter 1: INTRODUCTION TO ELECTRONIC INSTRUMENTATION
2
input circuit by Electro-Magnetic Interference (EMI) from, for instance, a nearby
vacuum cleaner.
Measurability is analysed in terms of the requirements imposed by the measure-
ment problem (such as accuracy), the practical constraints (for instance measur-
ing at a high temperature or in water or in the case of a high noise level), and the
theoretical considerations (can the parameter be measured when considering fun-
damental constraints, such as quantisation of electric charge?). The results of this
study include, amongst others, a listing of the requirements (= problem speci-
fications) that any instrument considered for use should satisfy.
Electronic instrumentation provides the knowledge that is needed to select the
commercially available instruments if available with sufficient performance (=
instrument specifications) to do the job. Such an instrument may be availa-
ble for a routine measurement, but perhaps not in the case of a highly demanding
measurement problem. In the latter case, Electronic instrumentation also pro-
vides the required knowledge at the sub-system and component levels to design
and realise customised instruments to meet the requirements of demanding appli-
cations (= measurement problems).
Typical questions addressed in instrumentation are: what is the system structure
like?; what bandwidth is required?; where in the system structure should an
amplifier be implemented?; where are sampling and quantization implemented?
and what is the system transfer function or sensitivity? Last but not least; what is
the minimum level of the parameter of interest that can actually be measured
when using a specific instrument (or, more generally, when using a specific
instrumentation technique) when considering the practical constraints? (= what
is the detection limit?). These are questions about the basic functioning of the
system. However, it should be noted that the answers depend on issues such as
the flexibility, costs and performance of the instrument.
Data acquisition refers to a field that covers a cross-section of the disciplines
of measurement science and instrumentation with a focus on solving practical
industrial and consumer problems in measurement and control, rather than aim-
ing for the lowest possible detection limit using sophisticated instruments.
1.2 Impact of electronic instrumentation
Non-electronic instrumentation would be unthinkable with the present state-of-
the art. However, it should be noted that modern electronic instruments are the
result of microelectronic technology, which has enabled the fabrication of the
high-performance electronic components required in an instrument. The vast
majority of early instruments were based on mechanical principles and was

Section 1.2
Impact of electronic instrumentation
3
intended for the measurement of mechanical quantities (length and mass) and
also time. The measurement of electrical parameters became relevant only after
the discovery of electricity and electro-magnetism. Electronic components
emerged in the 20th century, but their potential in instrumentation was quickly
recognised. This explains the commonly used -but in historic context not obvi-
ous- combined term ‘electronic instrumentation’ for describing the field.
1.2.1 Electronic instrumentation for a structured system
The most decisive advantage of electronic instruments is the opportunity that
electronic components provide for structuring the various functions of the sys-
tem in modules, each of which is designed to form a logical entity.
Mechanical systems do not offer this flexibility. Generally the different functions
are combined. A good example is the weighing balance, which is composed of a
bar of well-defined length and attached in the middle to a supporting construc-
tion in such a way that it can rotate around the centre. The left-hand and right-
hand parts of the bar are, in the basic concept, of equal length and are referred to
as arms. The end of an arm can be loaded with an object. Loading one arm of the
balance with an object and the other arm of equal length with another object
causes the side of the balance loaded with the object of higher mass to drop. A
series of measurements enables the sorting of objects on a scale from smallest
mass to highest mass. This balance for mass measurements was already well
known in ancient times, as is e.g. demonstrated on the so-called papyrus of Ani
(Fig. 1.1).
Figure 1.1, Measurement in ancient times (1420 B.C.). The papyrus of Ani
shows a scene of the “Book of the Dead”: Anubis, god of the dead (with the
jackal head) balances the weight of the heart of the deceased person standing on
the left (Ani of Thebes) with “the feather of Maat”, which represents order, truth
and justice. The god Thoth (with the bird’s head) writes the verdict.

4
The weighing function (the imbalance) and the indicator (the angle of rotation of
the arm with respect to the vertical suspension) are structurally combined. The
instrument evolved in the 18th century to become the kind of fine mechanical
structure shown in Fig. 1.2a. Instead of a crude comparison of the mass of two
objects, the object to be weighted is attached to the tip of the measurement arm,
while the opposite arm -the compensating arm- contains a reference mass that
can be slid along the arm until balance is obtained. The value of the reference
mass in combination with the arm lengths provides a direct measurement (i.e.
measurement in an interval scale) of the mass of the object.
An electronic weighing scale has a much more modular structure. The system is
composed of a separate component for mass measurement (the sensor), elec-
tronic circuits for read-out, a microprocessor for data processing and a digital
display, as shown in Fig. 1.2b. The sensor is basically a structure which contains
strain-sensitive resistors. These are connected in a Wheatstone bridge. As is
shown in Chapter 2, this is basically the electrical equivalent of the mechanical
balance. The structured design of the electronic weighing scale offers advantages
such as: user-friendliness (reduced requirements on expertise and accuracy of the
operator), flexibility (the price per unit mass can be used as additional input to
give an indication in weight and price), objectivity of the measurement (no read-
out error), and repair (simple replacement of modules).
Figure 1.2, (a) Mechanical balance and (b) electronic weighing scale.
(a) (b)

Section 1.2
Impact of electronic instrumentation
5
1.2.2 Electronic instrumentation for miniaturisation
Traditional measurement systems are bulky, which complicates their use when
measuring small objects or measuring objects with limited access. Integration
technologies, such as Integrated Circuit (IC)-compatible Micro-Electro-Mechan-
ical System (MEMS) technologies enable the fabrication of very small measure-
ment systems on a single silicon chip, which can e.g. be implanted in the human
eye to measure eye pressure, as shown in Fig. 1.3.
Miniaturisation is not only pursued for the sake of small system dimensions, but
also for achieving improved overall system performance. The instrument is often
part of a much larger system. Embedding an instrument in such a system has
been made possible by technological breakthroughs in microelectronics and
communication technology. This aspect is very relevant in the medical applica-
tion field, where the measurement is merely a part of the entire process leading
to a diagnosis.
An example is the ElectroCardioGram (ECG), which is used for measuring heart
activity using the electrical potential differences across the human body. A prac-
tical system for actually measuring these potentials was developed by Willem
Einthoven in 1902 and was a major step forward towards the early detection of
heart failure. However, as Fig. 1.4a indicates, the system was rather cumbersome
to use. The patient had to keep his or her hands and one foot in a salt solution to
ensure sufficient electrical contact.
One century of technological progress has resulted in the hand-held system
shown in Fig. 1.4b. It can be operated by the patient at home and enables com-
munication with a central database at a hospital. Whenever a patient feels inse-
cure about his or her condition, the patient can attach the electrodes, an ECG
Figure 1.3, Eye pressure sensor (a) chip and (b) system containing sensor and
circuits for communication ready for implantation in the human eye.
transponder
chip
polyimide
foil
micro coil
(a) (b)

6
scan is made and the result can be sent to a central database, which is coupled to
an expert system. The ECG is evaluated at the medical centre connected to the
system and direct action can be taken in case of an emergency. This approach
strongly reduces the frequency of unnecessary visits to the hospital, reduces
health care costs and adds to the quality of life of the patient. The increased ben-
efits of the ECG are also brought about by the fact that electronic instrumenta-
tion is based on microelectronics, which allows a seamless integration of the
instrument in computer and telecommunication systems.
1.2.3 Electronic instrumentation for data processing
Electronic instrumentation has also benefited from advances made in signal
processing and data processing. In many measurement problems, the required
information cannot easily be extracted from measurable signals. An example is
shown in Fig. 1.5.
On June 7th 2006 a meteoroid impacted the earth’s atmosphere over northern
Norway. The effect was like a fireball followed by explosions, which were
recorded at several locations, as shown in Fig. 1.5b. The position of the impact
could be determined from the time delay experienced by the low-frequency com-
ponents of the sound while these were traveling from the location of impact
towards each of these different stations. Obviously, special signal processing
techniques (i.e. correlation) have to be applied to obtain reliable information
from a station more than 1000 km away from the location of impact.
Figure 1.4, ECG (a) in 1902 and (b) incorporated in a complete health-care
system (vitaphone-me.com).
(a) (b)

Section 1.3
Structure of the instrument
7
These are examples of electronic instrumentation as an enabling technology in
many different applications by virtue of microelectronics technology. The obvi-
ous consequence of electronic instrumentation is the need for a component for
taking the information contained in a non-electrical quantity or signal and trans-
ferring this information into an electrical quantity or signal and vice versa. This
component is usually referred to as the transducer and the associated signal
processing as transduction. The non-idealities in the transduction and the first
stage of the read-out circuits (the analog front-end) largely determine the quality
of the system and hence set the detection limit. This is a key issue in this book,
which will be more extensively introduced in Section 1.5. The transduction
determines the structure of the instrumentation system, as is discussed in the next
section.
1.3 Structure of the instrument
The measurement instrument is basically an information conveyor between a
source and a target. The source is an object (i.e. a phenomenon, process or sys-
tem of physical, chemical or physiological nature) and the value of one or more
quantities of the object is to be determined. The target defines the motive for
performing the measurement. The target could be either a human observer read-
ing the display in a measurement system (e.g. a thermometer) or an actuator that
Figure 1.5, (a) Meteoroid entering the earth’s atmosphere as a fireball over
northern Norway and (b) recording of the sound produced at different stations
(aquarid.physics.uwo.ca).
(a) (b)

8
is part of a measurement and control system (e.g. a valve in a heating system).
Three main parts of the measurement and control system can be distinguished:
• Data acquisition,
• Data processing and
• Data distribution, which are related as indicated in Fig. 1.6.
In the data acquisition sub-system, information is obtained (= acquired) on the
measurand and transferred into a measurement result (= data). The signals at the
interface between data acquisition and electronic data processing, as well as
those between the data processing and data distribution sub-systems, are by
necessity electrical and digital. This defines the data type and format directly at
the output of the data acquisition unit, hence the inclusion of a major part of the
functionality therein. Data processing involves manipulating the input data and
forwarding the result to the data distribution sub-system.
The information of interest at the source is contained in a signal domain. The sig-
nal domains are generally energetically defined; the following six signal
domains are distinguished:
• Optical (radiant),
• Thermal,
• Mechanical,
• Magnetic,
• Chemical and
• Electrical.
Transferring information from one signal domain into another requires a trans-
ducer. In electronic instrumentation one of these domains is electrical. The data
acquisition sub-system has to include an input transducer or sensor that ena-
bles the change from non-electrical carrier into the electrical domain. Similarly,
the data distribution sub-system includes an output transducer that enables the
change from the electrical domain into the actual energy domain used for display
or actuation, as shown in Fig. 1.7.
Figure 1.6, General structure of a measurement and control system.
Data-
Acquisition
Data-
Processing
Data-
Distribution
Source Target

Section 1.3
Structure of the instrument
9
Proper coupling of the signal from the sensor output into the input of the Ana-
log-to-Digital Converter (ADC) requires signal conditioning. Similarly, the
data distribution unit usually includes signal conditioning between the Digital-
to-Analog Converter (DAC) and an actuator. In the case of an instrument with
only a digital display, a direct drive from the data-processor is possible.
The signal conditioning required in the data acquisition sub-system strongly
depends on the specifications of the measurement problem and the details of the
sensor used, and may contain the following functions:
• Amplification, which matches the range of the sensor output signal to that of
the input of the AD converter,
• Impedance transformation, which enables read-out of a voltage source with
a relatively high source impedance without a scaling error (see Section 2.4.1),
• Frequency or time filtering, which optimises the Signal-to-Noise Ratio
(SNR= power of the intended signal / power of the noise signal), and
• Signal conversion within the electrical domain. Some sensor types directly
supply a voltage or current level proportional to the measurand. However,
other sensors are designed to change the value of an electrical component,
such as a resistor, capacitor or inductor in a manner that is proportional to the
non-electrical input. Read-out of these types of sensors requires circuits for
the conversion of the modulated value of the electrical component into an
electrical signal (e.g. a fixed current source to generate an output voltage pro-
portional to the change in resistance).
Figure 1.7, Structure of an electronic measurement and control system.
Sensor
Signal-
conditioning
Data-
Processor
Display,
Transmitter or
Actuator
Signal-
Conditioning
Analog-
Digital
conversion
DATA
ACQUISITION
DATA
PROCESSING
DATA
DISTRIBUTION
Digital-
Analog
conversion

10
Example 1.1
The temperature-dependent resistor in the thermostat shown in Fig. 1.8 is
specified by a resistance at 0 o
C equal to R(0 o
C)= 100 Ω and a sensitivity
α= 0.4 Ω/K (R(T)= R(0oC)+α(T- 0oC)). A fixed-value current source is used
to convert resistance value into output voltage. A second resistor, Ro, is
used to set the zero value. A differential amplifier is used to match the full-
scale temperature to the maximum input voltage of the ADC. The electrical
current supplied by the current source is limited to avoid self-heating of the
sensor by dissipation. From the figure, the following results can be derived:
Ui,ADC= I×[R(T)-Ro]G, while the dissipation can be expressed as: Pdiss=
I2
×R(T). Heat dissipation would introduce a rise in temperature equal to
∆T= gth×Pdiss, with gth [K/W] as the thermal conductivity of the resistor.
This effect adds to the measurement uncertainty, which should be lower
than the specification.
The control strategy and several parameters, such as power of the heating
element and the heat capacity of the room to be heated, are entered into the
data processor. User input, such as the desired 24-hour temperature profile,
can be entered. The data distribution sub-system is simple and is composed
of a relay to switch a heating element. Signal conditioning involves a power
amplifier to drive the relay. DA conversion is superfluous, since only the
on/off function is required. Basically the relay serves as a 1-bit DAC.
The task is to dimension the thermostat for operation between 10 o
C and 25
oC, with 10 oC as the zero level and 25 oC as the full scale. The following
additional information is available:
•The ADC operates on signals between Ui= 0 V and Ui= Uref= 1.024 V.
•The resistors are biased using I= 10 mA.
•Ro and I are temperature-independent.
Figure 1.8, Structure of a simple thermostat.
R0
U+
Uref
Ui,ADC
R(T)
I I
Gain
G
ADC
Data
processor
Temp.
Setting
Umains

Section 1.4
Error and uncertainty in an instrument
11
Solution:
Ro should be dimensioned to result in a zero differential amplifier input
voltage at 10 o
C:
Ro= R(10 oC)= R(0 oC)+ 0.4[10 oC-0 oC]= 100+ 0.4×10= 104 Ω.
Subsequently, the gain should be set to give full scale at 25 o
C. Full scale
implies code 11...112. Assume an 8-bit ADC with Uref= 1.024.
The ADC has a quantisation interval q= 1.024/28
= 4 mV.
Thus full scale is associated with Ui,ADC between 1.020 V and 1.024 V.
The gain setting required results from:
Ui,ADC= 1.024= I[R(25 o
C)-Ro]G= 10-2
[15×0.4]G. Hence G= 17.
1.4 Error and uncertainty in an instrument
An instrument basically performs a mapping of the input quantity to be meas-
ured over its full measurement range onto the available range of an output quan-
tity (e.g. the scale of a display), as shown schematically in Fig. 1.9.
A practical instrument introduces a certain amount of uncertainty (error) that
causes ambiguity about the actual value of the measurand being measured and
ultimately results in a detection limit.
Errors can be classified, according to their impact on the measurement result, as:
• Scale errors
• Additive errors
• Non-linearity errors
• Cross-sensitivity for well-defined, although undesirable, quantities
Figure 1.9, Errors and uncertainties in a measurement.
1000
100
0
output [%]
input [%]
theoretical line
actual
function
best
line
offset uncertainty
non-linearity
error
scale uncertainty

12
While all these error types need to be considered to determine the measurement
uncertainty, additive errors and cross-sensitivities are the most important in the
calculation of the detection limit. For this reason the emphasis is on additive
errors and cross-sensitivities, with multiplicative and non-linearity errors only
discussed when relevant to the detection limit in a specific application.
The sources of error enable a classification into:
• Systematic errors (= deterministic errors),
• Random errors (= stochastic errors) and
• Human errors,
which can further be divided into six categories:
1. Systematic errors that occur when the measurement activity affects the meas-
urand (source loading by the instrument). This type of error usually results
from an incorrect measurement technique or improper use of an instrument.
An example is voltage measurement across a relatively high impedance using
an instrument with a relatively low input impedance. Another example is
temperature measurement using a thermometer with a large heat capacitance.
2. Systematic errors due to the use of an improperly calibrated instrument. An
example is an amplifier that is set at the incorrect gain. If one is unaware of
this, then the deviation from the presumed gain is specified as the scale error.
3. Systematic errors due to a parasitic sensitivity to an undesired parameter (e.g.
common-mode voltage in a differential voltage measurement, or a parasitic
temperature sensitivity in a pressure sensor when operated at a temperature
not equal to the calibration temperature).
4. Random errors due to instrument noise, which could be either generated
inside the instrument or of external origin and injected into the measurement
setup (e.g. capacitive coupling).
5. Random errors due to the remaining uncertainty in the internal reference after
proper calibration. This is included in the instrument specification and is not
discussed here.
6. Human errors due to incorrect reading of a display. This type of error can be
largely avoided by an ergonomically optimised design of the instrument or by
using a fully automated measurement setup and is not considered here.
Basically, the first two classes of systematic error mentioned above are also due
to human error and are also referred to as ‘improper use of instruments’. Nev-
ertheless, these need to be considered. Loading of the source by the measurement
is undesirable, yet often unavoidable, since physical contact is often required in
order to get access to the information. In this sense it is a prerequisite for the
measurement and has to be included in the detection limit analysis. Especially in

Section 1.4
Error and uncertainty in an instrument
13
temperature measurement, source loading can be an important factor that limits
the detectivity.
The errors of the 2nd, 3rd and 4th categories are additive errors that ultimately
determine the detection limit. Depending on the application, one of these four
sources of uncertainty is usually dominant. The signal level associated with the
measurand should exceed the magnitude of these parasitics to enable a reproduc-
ible detection.
A systematic error (= deterministic error) can be avoided during the meas-
urement or corrected for at any time provided that the source of determinis-
tic error is completely described.
The key issue in this definition is the complete description of the source of
error. It is quite possible in a complex system that an experimenter is unaware of
a particular source of error at the time of a measurement. However, it can be cor-
rected for, even after completion of a measurement program, provided that:
1. this unexpected and undesirable effect is predictable in time and with temper-
ature (remains constant= repeatable, or with a known trend) and
2. the measurement procedure, the equipment used and the results obtained are
described in sufficient detail.
Having the option to correct data after gaining new insight is especially impor-
tant in the case of an expensive or dangerous experiment. This is the reason why
professionals record their findings in detail in a logbook. Moreover, in industry
each page is dated in case of a legal dispute about an infringement of a patent
that is based on a particular finding described in the logbook.
Example 1.2
A Voltmeter with an input resistance Ri= 100 kΩ is used to measure a volt-
age source, Usr, with unknown source resistance, Rsr. Measurement at 20 oC
gives: Umo= 1.961 V. The operator becomes aware of the poor quality of
the instrument at a later stage. This is a systematic error of category 1. For-
tunately, the voltage source and the instrument are still available. The
source resistance, although of unknown value, is known to be very stable.
However, it is uncertain whether the voltage has drifted in time. Two mea-
surements are performed for an ex post correction of this mistake:
(1) performing the same measurement again under identical conditions and
(2) measuring the voltage with a shunt resistor Rp= 10 kΩ connected in par-
allel to Ri. The measurement results are: Um1= 1.902 V and Um2= 1.590 V
respectively.

14
The tasks are to:
(1) determine the voltage Usr and the source resistance Rsr at the time of the
new measurements (at t= t1) and
(2) use this information to correct the original measurement for loading of
the source by the instrument, based on these additional measurements (at t=
to).
Solution:
Note that the effect of any temperature dependence can be disregarded,
because the repeated measurement is at the same temperature.
(1) Um1 = Ri ×Usr(t1)/(Ri+Rsr) = 100 kΩ/(100 kΩ+Rsr)Ubr(t1) = 1.902 V.
Um2= Ri//Rp×Usr(t1)/(Ri//Rp+Rsr)= 105
/11/(105
/11+ Rsr)Usr(t1)= 1.590 V.
Solving this set of two independent equations with two unknowns yields:
Usr= 1.938 V and Rsr= 2.002 kΩ.
(2) Usr(to)= Umo(Ri+Rsr)/Ri= 1.961×102/100= 2.000 V.
From these results it can be concluded that the voltage source has drifted
-62 mV in the time interval between the two measurements.
An essential condition for ex post correction of a systematic error (as in Example
1.2) is the reproducibility of the error: i.e. the error affects the result in a repeated
measurement in the same way. Obviously, a great deal of extra work can be
avoided in the case of an ex ante correction. However, this requires one to be
aware of the limitations of the instruments prior to the measurement.
The amplitude of a random error (= stochastic error) is described by a sta-
tistical distribution and the value cannot be predicted at every moment in
time. Therefore, this error cannot be reduced to zero by compensation or
correction.
The most prominent type of random error is noise, which is introduced in the
next sections. Although noise cannot be reduced to zero by compensation or cor-
rection, instrumentation techniques are available to minimise this type of error.
A deterministic error can in principle be reduced to zero using a perfect compen-
sation or correction. As a consequence, deterministic errors should not be a
source of uncertainty and, thus, should not be a significant factor for limiting the
detectivity. Unfortunately, in a practical instrument there is a residual determinis-
tic error signal left after correction or compensation. Since this is not expected in
the sense that measures have been implemented with the purpose of eliminating
the error, this residual should be considered a random signal.

Section 1.5
Performance of an instrument
15
This overlap between deterministic error and random error is also the reason for
the somewhat subtle difference between error and uncertainty. An error can in
principle be avoided (by eliminating human error and deterministic error),
whereas uncertainty is due to the combined effect of all the unknowns and ran-
dom properties of the setup or instrument.
As is discussed in the next section, error or uncertainty does limit the perform-
ance of an instrument, which is usually specified as the detection limit.
1.5 Performance of an instrument
The most fundamental question in Instrumentation and Measurement is:
‘What is the smallest value of the quantity of interest that can still be mea-
sured reproducibly?’
This question needs further refinement, as the fundamental (physical) limitations
need to be distinguished from the practical (instrumental) constraints. Funda-
mental limitations are due to inescapable laws of nature, whereas practical limi-
tations are imposed by shortcomings of the instrument. The fundamental type of
limitation does not change in time, whereas those of the instrument can be
relieved by an improved instrument design or by breakthroughs in technology.
Progress will bring the instrumental detection limit closer to the fundamental
(physical) limitation.
Example 1.3
Assume one would like to visualise a 10 kHz sine-wave AC-current with:
irms= 1 fA. This is an extremely small current. In fact a fundamental physi-
cal limit is exceeded. Electrical current is defined as the amount of charge
passing through a cross-section of a conductor per unit of time:
i= ∂Q/∂ t.
The amount of charge stored in a half-period is equal to:
Q= î ∫0
π sin(ωt) dt= 2î/ω = 2×10-15
/2π×104
= 3×10-20
C,
which is smaller than the unit charge. This AC-current, therefore, cannot be
displayed (basically this is a shot noise related detection limit).
After a closer look at the requirements the user realized that a mistake had
been made. The measurement of a 10 kHz square-wave AC current with î=
irms= 1 nA had been intended and not 1 fA. Therefore, the above-mentioned
fundamental limitation does not apply and the specifications of the instru-
ment can be analysed. The oscilloscope available has an extremely good
noise specification with an equivalent input current noise source over a
bandwidth of 100 kHz (to maintain shape information) equal to 300 pA.

16
This specification implies that the signal is nevertheless barely measurable
using state-of-the-art technology.
The answer to the big question raised in this section is that a practical instrument
is designed to measure the actual value of a well-defined property with given
instrument shortcomings (specifications). The lower limit that can be measured
at a specified inaccuracy level is generally referred to as the detection limit.
This is a key specification of the instrument and is the red line through this book.
The detection limit of an instrument is the minimum level of the desired
input signal that can be measured, considering parasitic signals and accu-
racy specification.
The performance of an instrument used for measuring a non-electrical quantity is
usually limited by the data acquisition unit. Any information lost or corrupted
can in principle not be retrieved by data processing, unless additional informa-
tion is included, such as redundant coding, or when prior information is available
about the signal properties.
Since the practical detection limit is due to instrument constraints, technological
advances in component manufacturing and system design may lead to a shift in
the detection limit. This progress could result in two types of progress:
(a) an instrument could become available that is able to measure a phenomenon
which has, so far, been undetectable or
(b) the costs, weight or dimensions of an instrument are reduced to such values
that a known measurement technique becomes suitable for a new application.
The first effect is the most spectacular, and the consequences of a new measure-
ment result for science have sometimes been revolutionary. One single measure-
ment that does not comply with prevailing theory could force a re-thinking of the
concepts. One example is the photo-electric effect in a vacuum tube, which was
expressed in terms of quantisation of energy and, consequently, provided another
source of experimental validation of the concept of quantum physics introduced
earlier by Planck. This concept had completely changed the understanding of
physics by the early 20th century.
The second effect is decisive for the introduction of a particular measurement
system in a consumer product. Market acceptance requires a reasonable ratio
between the costs of the added electronic feature and those of the consumer
product (e.g. the costs of a system for use in an automotive application, such as
an airbag, should at introduction not exceed €100). Obviously, the size and
weight of additional systems are also restricted. This economic constraint could

Section 1.6
Sensitivity and detection limit in an instrument
17
be bypassed by government regulations on safety or exhaust emissions. Never-
theless, the availability of cheaper, lighter and smaller systems makes new appli-
cations possible and thus does cause a shift in the detection limit, albeit related to
a particular application and not in the absolute sense.
Very powerful in this respect are approaches that combine fabrication technolo-
gies that are suitable for mass production with transduction effects in the materi-
als used. Combining a micro-electronic process with silicon sensor fabrication
has demonstrated to be successful, as it enables the high-volume production of a
combination of sensor and read-out circuits in a single chip.
1.6 Sensitivity and detection limit in an instrument
The sensitivity of an instrument can in principle be increased without constraints
by increasing the system gain. In a practical system, however, the useful gain is
limited by the detection limit.
When using or designing an instrument, it is crucial to be aware of the fact
that the smallest measurable value of the measurand is set by the detection
limit of the instrument, which is determined by system uncertainties, para-
sitic signals and interfering effects, and not primarily by the system gain.
The word ‘primarily’ refers to the fact that the system gain needs to be maxim-
ised within bounds for a low detection limit value, as is discussed in this section.
Non-perfect component performance, uncertainties in the system transfer func-
tion and interference effects can be expressed in terms of equivalent input error
sources (the term input-referred error sources is also used). The input signal
measured can be directly compared with this equivalent input error source and
conclusions with respect to measurability can be made. This concept is used in
the next chapters.
Equivalent input error sources are theoretical (calculated) quantities. These
are a set of signal sources connected to the input of an ideal system (i.e. a
system without error). The magnitudes of the signal levels of these input
sources are such, that their effect on the output of the system is identical to
that of the combined effect of all the distributed error sources of the same
kind in the actual (i.e. non-ideal) system without input signal applied.
As discussed in Chapters 3-5, the error signals could be generated inside the
measurement system (such as offset and internal noise), or could be due to a sys-
tem limitation (such as the finite rejection of a common-mode level in a differen-

18
tial measurement), or due to external noise injected into the system by its non-
zero susceptibility to that particular source of noise.
Figure 1.10a shows a simple voltage amplifier with gain G and with noise
assumed as the dominant source of error. All the distributed noise contributions
acting on the circuit are represented by the equivalent input noise source un(t), in
series with the input signal ui(t) (note that the use of only one noise source is a
simplification, which is allowed because the source voltage is assumed without
source impedance, Zg= 0 Ω -see Chapter 5). The range of the possible voltage
levels at the output of the amplifier is limited to the supply voltages (Uo,peak is in
between V+ and V-).
The maximum useful level of the gain is set by distortion due to saturation at the
output at given supply voltage levels. Figure 1.10b shows that for gain G > Gmax
the amplified input level Gui,max would result in an output voltage peak value
larger than V+. Since the amplifier cannot be driven beyond the power supply
voltage, the output voltage uo(t) is flattened at the peak values and distortion is
generated. Consequently, at a given maximum input signal level, the maximum
useful gain, Gmax, is set by the onset to saturation and thus by the maximum
acceptable output signal that satisfies the accuracy specifications due to distor-
tion.
On the other hand, the minimum measurable input signal is limited by the equiv-
alent input noise source un(t). If the level of the desired input signal, ui(t), is
lower than that of un(t), then this desirable signal can in principle not be repro-
ducibly measured. Consequently, the detection limit, ui,min(t), is defined.
Although the subsequent chapters demonstrate that it makes sense to maximise
system gain to reduce the effect of noise generated at the output, the minimum
input signal that can be detected is primarily determined by the value of the
equivalent input noise source and not by the system gain.
Figure 1.10, Dynamic range of a voltage amplifier.
+
--
uo(t)
uo(t)
ui(t)
Gmaxui,max(t)
G
t
(a) (b)
Gmaxun(t)
un(t)
V+
V--
V--
V+

Section 1.7
Procedure for determining the detection limit
19
1.7 Procedure for determining the detection limit
The analysis of the detection limit generally involves the following steps:
1. Identification of the dominating detection-limiting effect.
2. Calculation of the equivalent input error signal sources.
3. Calculation of the minimum measurable signal, while also considering the
inaccuracy or SNR specification.
An introduction to errors and uncertainties and how these limit the detection is
provided in the next section. In electrical measurements the equivalent input
error sources are voltage and current sources, whereas in, for instance, an accel-
erometer this is an equivalent acceleration. This analysis should provide the tools
for lowering the detection limit when redesigning a sub-optimum system.
In Chapter 2 the effect of a non-perfect transducer is discussed, which includes
the errors introduced by the non-selective transduction and source loading. Off-
set is the most likely detection-limiting factor when measuring the amplitude of
quasi-static signals (Chapter 3), whereas CMRR is crucial in differential systems
(Chapter 4). Noise is the limiting factor in wide band systems (Chapter 5). Cir-
cuits and signal processing techniques for improving detectivity are presented in
Chapter 6. The technique for mixed-signal domain modelling presented in Chap-
ter 7 enables the calculation of the overall system detection limit.
1.8 Exercises
1.1 Refer to Fig. 1.8, with R(T) at 0 o
C, R(0o
C) is equal to 100 Ω, and sensitivity
(TCR)= ∂R/∂T= 0.4 Ω/K. The input range of the ADC extends from 0 V to 5.12
V. The bias current sources are set to I= 10 mA. Give the values for Ro and gain
G to have the input range of the ADC covered in the case of T between 5 oC and
30 o
C. An 8-bit AD converter is used with Uref= 5.12 V.
Solution:
Ro should be dimensioned to result in a zero differential amplifier input voltage
at 5 o
C: R(5 o
C)= R(0 o
C)+ 0.4[5 o
C-0 o
C]= Ro= 102 Ω.
Subsequently, the gain should be set to give full scale at 30 o
C. Full scale implies
code 11...112. The ADC with Uref= 5.12 V has a quantisation interval: q= 5.12/
28
= 20 mV, thus full scale is associated with Ui,ADC between 5.10 V and 5.12 V.
The gain setting required results from: Ui,ADC= 5.12= I×[R(30 o
C)-Ro]G= 10-2
×
[25×0.4]G. Hence G= 51.2.
1.2 What is the maximum bias current, I, if the uncertainty in temperature due to
self-heating is limited to ∆T= 0.1 o
C. The temperature of R(T) increases 20 o
C in
the case of a dissipation of 1 W. Assume T= 0 o
C.

20
Solution:
∆Tmax=0.1 oC→ Pmax= 0.1/20= 5 mW= I2×Ro.
Hence, I= (5×10-3
/100)1/2
= 7.07 mA.
A voltage measurement on a signal source with negligible source impedance
results in a reading of 1.01400 V at 7 °C (=280 K). Long after the measurement,
the experimenter realises that this source has a parasitic temperature dependence.
Although unknown, a linear temperature dependence can be assumed. However,
the source voltage may have changed over time. To attempt an ex post recon-
struction of the temperature coefficient, two voltage measurements are per-
formed: The first is at 20 °C (= 293 K), and results in 1.0965 V. The second at 0
°C (= 273 K) yields 1.0865 V.
1.3 Calculate the temperature coefficient of the voltage source from this meas-
urement information.
1.4 How much has the voltage source drifted in time between the moment of the
initial measurement and that of the two additional measurements?
Solution:
(1) Umo (to, 280K)= 1.0140 V.
(2) Um1 (t1, 293K)= 1.0965 V= Umo(to, 280K)+ ∆U(t)+ (293−280)(∂U/∂T)→
∆U(t)+ 13(∂U/∂T)= 82.5 mV.
(3) Um2 (t1, 273K)= 1.0865 V= Umo(to, 280K)+ ∆U(t)+ (273−280)(∂U/∂T)→
∆U(t)- 7(∂U/∂T)= 72.5 mV.
(2)-(3)→ 20(∂U/∂T)= 10 mV. Hence, (∂U/∂T)= 0.5 mV/K .
(7/13)×(2)+ 1×(3)→ ∆U(t)= 76 mV.

!Reading.example

More Related Content

What's hot (20)

Viewers also liked (10)

Similar to !Reading.example (20)

Recently uploaded (20)

!Reading.example