Environmental Engineering Reference
In-Depth Information
Like for the Rosenstark method we have to choose a controlled source
P
inside the feedback circuit. To calculate the Return Ratio,
T,
and the Direct
Transmission Term, we can follow the same steps described in point 1)
and 2). But now, we have to change step 3) to evaluate the null return ratio.
The new point 3) is
3. Replace the critical controlled source by an independent source of
value
P
(like in the second point of the previous paragraph), without
nullifying the input source. The Null Return Ratio,
will be coincident
with the resulting controlling quantity changed in sign, assuming the
output voltage is equal to zero. It is worth noting that the input source is not
independent, but its value must guarantee the zero condition at the output.
To demonstrate point 3), set
in eq. (3.3a), yielding
and after substituting eq. (3.17) in (3.4) we get
Like the asymptotic gain, also the null return ratio gives interesting
information from a circuit/design point of view. Moreover, it helps to
identify the nature of the feedback. The ratio between the return ratio and the
null return ratio, quantifies the degree to which the local feedback
approaches global feedback [C91]. When it is the feedback is global.
Of course, both Rosenstark and Choma methods give the same results,
and comparing (3.7) with (3.15) we obtain
To evaluate the null return ratio, consider again the small-signal model of
the common Z amplifier in Fig. 3.3b. Since voltage at node X must be
assumed to be zero, this means that the current of the critical generator
P
all flows through resistances
and
Hence the null return
ratio is given by
