Course Notes #9
USC Viterbi School of Engineering
- 271 -
All electronic circuits are nonlinear networks because the active devices embedded
within them have inherently nonlinear static volt-ampere characteristics and nonlinear intrinsic
energy storage parasitics.
When these inherently nonlinear circuits are earmarked for linear sig-
nal processing applications, design care must be exercised to bias relevant active devices well
within their nominally linear volt-ampere domains.
Moreover, additional care must be taken to
ensure that the perturbations in quiescent operating points incurred in active elements by all input
signals applied to these networks are sufficiently small to sustain device operation in their
approximately linear regimes.
With suitable biasing implemented and applied signals constrained to sufficiently small
amplitudes, the response,
, to a signal excitation,
, applied to an electronic circuit can be
described to first order by the linear time domain relationship,
In this expression, the constant,
, is determined by network biasing considerations, which ac-
count for targeted power dissipation constraints.
, along with such other linear
performance metrics as impedance levels, bandwidth, phase and delay responses, phase and gain
margins, rise, fall, and settling times, and the like derive from analyses executed on a small sig-
nal model of the network undergoing study.
is identically the small signal input -to-
output (I/O) gain of the considered circuit.
Since (1) pertains to time domain analytical
investigations, the constants,
, are necessarily real numbers.
However, these numbers
can be positive or negative.