Audio Engineering

Negative Feedback 369

One approach to appreciating NFB and its stability problems is SPICE simulation.
Some SPICE simulators have the ability to work in the Laplace or s-domain, but my
own experiences with this have been deeply unhappy. Otherwise respectable simulator
packages output complete rubbish in this mode. Quite what the issues are here I do not
know, but it does seem that s-domain methods are best avoided. The approach suggested
here instead models poles directly as poles, using RC networks to generate the time
constants. This requires minimal mathematics and is far more robust. Almost any SPICE
simulator, evaluation versions included, should be able to handle the simple circuit
used here.

Figure 12.1 shows the basic model, with SPICE node numbers. The scheme is to idealize
the situation enough to highlight the basic issues and exclude distractions such as
nonlinearities or clipping. The forward gain is simply the transconductance of the input
stage multiplied by the transadmittance of the VAS integrator. An important point is that
with correct parameter values, the current from the input stage is realistic, as are all the
voltages.

The input differential amplifi er is represented by G. This is a standard SPICE element—the
VCIS, or voltage-controlled current source. It is inherently differential, as the output
current from Node 4 is the scaled difference between the voltages at Nodes 3 and 7. The
scaling factor of 0.009 sets the input stage transconductance ( gm ) to 9 mA/V, a typical

Differential

input stage

VAS miller

integrator

3

G

4

In

Evas

1

23

Cdom 100 pF

510

Output stage

First output

stage pole

Second output

stage pole

R 1 1R 6 R 2 1R

C 1

100 nF

C 2

Eout1 100 nF Eout2

(^117) Out
Negative
feedback
network
10,000
1 1
Figure 12.1: Block diagram of system for SPICE stability testing.