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There are many good references that discuss methods of characterizing, specifying, and implementing
frequency-selective analog filters. See Van Valkenburg (1960) for design of passive filters; for the design
of active-RC filters, see Sedra and Brackett (1978) and Stephenson (1985).

47.2 Nonlinear Operations

There is a wide variety of nonlinear operations useful to signal-conditioning tasks. Listed below are some
typical nonlinear blocks along with brief descriptions. Most of the blocks are available as ICs.
1. Comparator. A comparator is a two-input device whose output voltage, V o , takes on one of two
stable values, V o0 and V o1 , as follows:

 V o0 , if V 2 < V 1
V o = 
 V o1 , otherwise

where V 1 and V 2 are the voltages at the two inputs.
2. Schmitt trigger. A Schmitt trigger is a comparator with hysteresis. It can be constructed from a
comparator by applying positive feedback.
3. Multiplier. A two-input multiplier supplies an output voltage that is proportional to the product
of its input voltages.
4. Divider. A two-input divider has as its output a voltage proportional to the ratio of its input
voltages. The functions of multiplication and division are usually combined within a single device.
5. Squarer. A squarer has as its output a voltage proportional to the square of its input. Squarers can
be constructed by a number of means: from multipliers, based on diode-resistor networks, based
on FETs, and so forth.
6. Square-rooter. A square-rooter has as its output a voltage proportional to the square root of its
input. A square-rooter can be built most easily from either a divider or a log/antilog amplifier.
7. Logarithmic/antilogarithmic amplifier. A log/antilog amplifier produces an output voltage propor-
tional to the logarithm or the antilogarithm of its input voltage.
8. True RMS-to-DC converter. A true RMS-to-DC converter computes the square root of the average,
over some interval of time, of the instantaneous square of the input signal. The averaging operation
is generally accomplished via a simple low-pass filter whose capacitor is selected to give the desired
interval.
9. Trigonometric function generator. Generators are available in IC form that produce as their outputs
any of the standard trigonometric functions or their inverses, taken as functions of the differential
voltage at the generator’s inputs.
10. Sample-and-hold and track-and-hold amplifiers. A sample-and-hold amplifier (SHA) is a device
that samples the signal at its input and holds the instantaneous value whenever commanded by
a logic control signal. A track-and-hold amplifier is identical to an SHA but is used in applications
where it spends most of its time tracking the input signal (i.e., in “sample” or “track” mode), in
contrast to the SHA, which spends most of its time in “hold” mode.
11. Precision diode-based circuits. Circuits such as precision half-wave rectifiers, absolute-value circuits,
precision peak detectors, and precision limiters are relatively easy to design and implement based on
diodes and op amps. See Horowitz and Hill (1989), Stout and Kaufman (1976), and Graeme (1977).
A detailed description of these and other nonlinear circuit blocks can be found in Sheingold (1976).
Example
We provide briefly an example of a device that has embedded within it several signal-conditioning circuits.
Figure 47.1 shows the basic block diagram of a therapeutic ultrasound unit, which finds widespread use
in physical medicine.

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