370 Chapter 12
fi gure for a bipolar input with some local feedback. Stability in an amplifi er depends on the
amount of NFB available at 20 kHz. This is set at the design stage by choosing the input
gm and Cdom , which are the only two factors affecting the open-loop gain. In simulation it
would be equally valid to change gm instead; however, in real life it is easier to alter Cdom
as the only other parameter this affects is slew rate. Changing input stage transconductance
is likely to mean altering the standing current and the amount of local feedback, which will
in turn impact input stage linearity.
The VAS with its dominant pole is modeled by the integrator Evas , which is given a high
but fi nite open-loop gain, so there really is a dominant pole P 1 created when the gain
demanded becomes equal to that available. With Cdom 100 pF, this is below 1 Hz.
With infi nite (or as near-infi nite as SPICE allows) open-loop gain, the stage would be a
perfect integrator. As explained elsewhere, the amount of open-loop gain available in real
versions of this stage is not a well-controlled quantity, and P 1 is liable to wander about in
the 1- to 100-Hz region; fortunately, this has no effect at all on HF stability. Cdom is the
Miller capacitor that defi nes the transadmittance, and since the input stage has a realistic
transconductance,Cdom can be set to 100 pF, its usual real-life value. Even with this
simple model we have a nested feedback loop. This apparent complication here has little
effect, as long as the open-loop gain of the VAS is kept high.
The output stage is modeled as a unity-gain buffer, to which we add extra poles modeled by
R 1 , C 1 and R 2 , C 2. Eout1 is a unity-gain buffer internal to the output stage model, added so
that the second pole does not load the fi rst. The second buffer Eout2 is not strictly necessary
as no real loads are being driven, but it is convenient if extra complications are introduced
later. Both are shown here as a part of the output stage but the fi rst pole could equally well
be due to input stage limitations instead; the order in which the poles are connected makes
no difference to the fi nal output. Strictly speaking, it would be more accurate to give the
output stage a gain of 0.95, but this is so small a factor that it can be ignored.
The component values here are of course completely unrealistic and chosen purely to
make the math simple. It is easy to appreciate that 1 Ω and 1 μ F make up a 1- μ s time
constant. This is a pole at 159 kHz. Remember that the voltages in the latter half of the
circuit are realistic, but the currents most certainly are not.
The feedback network is represented simply by scaling the output as it is fed back to the
input stage. The closed-loop gain is set to 23 times, which is representative of most power
amplifi ers.