75
4
LINEAR SIGNAL CONDITIONING TO
SIX-SIGMA CONFIDENCE
4-0 INTRODUCTION
Economic considerations are imposing increased accountability on the design of
analog I/O systems to provide performance at the required accuracy for computer-
integrated measurement and control instrumentation without the costs of overde-
sign. Within that context, this chapter provides the development of signal acquisi-
tion and conditioning circuits, and derives a unified method for representing and
upgrading the quality of instrumentation signals between sensors and data-conver-
sion systems. Low-level signal conditioning is comprehensively developed for both
coherent and random interference conditions employing sensor–amplifier–filter
structures for signal quality improvement presented in terms of detailed device and
system error budgets. Examples for dc, sinusoidal, and harmonic signals are provid-
ed, including grounding, shielding, and noise circuit considerations. A final section
explores the additional signal quality improvement available by averaging redun-
dant signal conditioning channels, including reliability enhancement. A distinction
is made between signal conditioning, which is primarily concerned with operations
for improving signal quality, and signal processing operations that assume signal
quality already at the level of interest. An overall theme is the optimization of per-
formance through the provision of methods for effective analog design.
4-1 SIGNAL CONDITIONING INPUT CONSIDERATIONS
The designer of high-performance instrumentation systems has the responsibility of
defining criteria for determining preferred options from among available alterna-
tives. Figure 4-1 illustrates a cause-and-effect outline of comprehensive methods
that are developed in this chapter, whose application aids the realization of effective
signal conditioning circuits. In this fishbone chart, grouped system and device op-
Multisensor Instrumentation 6
␴
Design. By Patrick H. Garrett

magnetic shielding are usually implemented by the installation of signal cables in
steel conduit of the necessary wall thickness. Additional magnetic field attenuation
is furnished by periodic transposition of twisted-pair signal cable, provided no sig-
nal returns are on the shield, where low-capacitance cabling is preferable. Mutual
coupling between computer data acquisition system elements, for example from fi-
nite ground impedances shared among different circuits, also can be significant,
with noise amplitudes equivalent to 50 mV at signal inputs. Such coupling is mini-
mized by separating analog and digital circuit grounds into separate returns to a
common low-impedance chassis star-point termination, as illustrated in Figure 4-3.
The goal of shield ground placement in all cases is to provide a barrier between
signal cables and external interference from sensors to their amplifier inputs. Signal
cable shields also are grounded at a single point, below 1 MHz signal bandwidths,
and ideally at the source of greatest interference, where provision of the lowest im-
pedance ground is most beneficial. One instance in which a shield is not grounded
is when driven by an amplifier guard. Guarding neutralizes cable-to-shield capaci-
tance imbalance by driving the shield with common-mode interference appearing
on the signal leads; this also is known as active shielding.
The components of total input noise may be divided into external contributions
associated with the sensor circuit, and internal amplifier noise sources referred to its
input. We shall consider the combination of these noise components in the context
of band-limited sensor–amplifier signal acquisition circuits. Phenomena associated
with the measurement of a quantity frequently involve energy–matter interactions
that result in additive noise. Thermal noise V
t
is present in all elements containing
resistance above absolute zero temperature. Equation (4-1) defines thermal noise
voltage proportional to the square root of the product of the source resistance and its
temperature. This equation is also known as the Johnson formula, which is typically
evaluated at room temperature or 293°K and represented as a voltage generator in
series with a noiseless source resistance.

tivity effects. This noise component has a unique characteristic that varies as the re-
ciprocal of signal frequency 1/f, but is directly proportional to the value of dc cur-
4-1 SIGNAL CONDITIONING INPUT CONSIDERATIONS
77
rent. The behavior of this fluctuation with respect to a sensor loop source resistance
is to produce a contact noise voltage whose magnitude may be estimated at a signal
frequency of interest by the empirical relationship of equation (4-2). An important
conclusion is that dc current flow should be minimized in the excitation of sensor
circuits, especially for low signal frequencies.
V
c
= (0.57 × 10
–9
) R
s
Ί
๶
V
rms
/
͙
H
ෆ
z
ෆ
(4-2)
I
dc
= average dc current (A)
f = signal frequency (Hz)

c
2
+ V
n
2
)( f
hi
)]
1/2
(4-3)
4-2 SIGNAL QUALITY EVALUATION AND IMPROVEMENT
The acquisition of a low-level analog signal that represents some measurand, as in
Table 4-2, in the presence of appreciable interference is a frequent requirement. Of
concern is achieving a signal amplitude measurement A or phase angle
␾
at the ac-
curacy of interest through upgrading the quality of the signal by means of appropri-
ate signal conditioning circuits. Closed-form expressions are available for deter-
mining the error of a signal corrupted by random Gaussian noise or coherent
sinusoidal interference. These are expressed in terms of signal-to-noise ratios
(SNR) by equations (4-4) through (4-9). SNR is a dimensionless ratio of watts of
signal to watts of noise, and frequently is expressed as rms signal-to-interference
I
dc
ᎏ
f
78
LINEAR SIGNAL CONDITIONING TO SIX-SIGMA CONFIDENCE
amplitude squared. These equations are exact for sinusoidal signals, which are typi-
cal for excitation encountered with instrumentation sources.

ᎏᎏ
͙
S
ෆ
N
ෆ
R
ෆ
␧
%FS
ᎏ
100%
1
ᎏ
2
⌬A
ᎏ
A
1
ᎏ
2
4-2 SIGNAL QUALITY EVALUATION AND IMPROVEMENT
79
FIGURE 4-2. Sensor–amplifier noise sources.
P(⌬
␾
;
␾
) = erf
΂

· 100%
= of full scale
␧
coh phase
= degrees (4-9)
The probability that a signal corrupted by random Gaussian noise is within a
specified ⌬ region centered on its true amplitude A or phase
␾
values is defined by
equations (4-4) and (4-6). Table 4-1 presents a tabulation from substitution into
these equations for amplitude and phase errors at a 68% (1
␴
) confidence in their
measurement for specific SNR values. One sigma is an acceptable confidence level
100
ᎏ
2
͙
S
ෆ
N
ෆ
R
ෆ
100%
ᎏ
͙
S
ෆ
N

ᎏ
57.3
0
/rad
1
ᎏ
2
⌬
␾
ᎏ
␾
1
ᎏ
2
80
LINEAR SIGNAL CONDITIONING TO SIX-SIGMA CONFIDENCE
TABLE 4-1. SNR Versus Amplitude and Phase Errors
Amplitude Error Phase Error Amplitude Error
SNR Random
␧
%FS
Random
␧
␾
deg
Coherent
␧
%FS
10
1

0.00044 0.0002 0.00031
10
12
0.00014 0.00007 0.00009
for many applications. For 95% (2
␴
) confidence, the error values are doubled for
the same SNR. These amplitude and phase errors are closely approximated by the
simplifications of equations (4-5) and (4-7), and are more readily evaluated than by
equations (4-4) and (4-6). For coherent interference, equations (4-8) and (4-9) ap-
proximate amplitude and phase errors where ⌬A is directly proportional to V
coh
, as
the true value of A is to V
FS
. Errors due to coherent interference are seen to be less
than those due to random interference by the ͙2
ෆ
for identical SNR values. Further,
the accuracy of these analytical expressions requires minimum SNR values of one
or greater. This is usually readily achieved in practice by the associated signal con-
ditioning circuits illustrated in the examples that follow. Ideal matched filter signal
conditioning makes use of both amplitude and phase information in upgrading sig-
nal quality, and is implied in these SNR relationships for amplitude and phase error
in the case of random interference.
For practical applications the SNR requirements ascribed to amplitude and phase
error must be mathematically related to conventional amplifier and linear filter sig-
nal conditioning circuits. Figure 4-3 describes the basic signal conditioning struc-
ture, including a preconditioning amplifier and postconditioning filter and their
bandwidths. Earlier work by Fano [1] showed that under high-input SNR condi-

Signal Bandwidth (Hz)
dc dV
s
/
␲
V
FS
dt
Sinusoidal 1/period T
Harmonic 10/period T
Single event 2/width
␶
82
FIGURE 4-3. Signal acquisition system interfaces.