CMOS Optical Preamplifier Design Using Graphical Circuit Analysis

Feedback Analysis Using Return Ratios
v s
2.4 Circuit Analysis Techniques 31
The third method of analyzing the feedback amplifier uses return ratios. The
entire solution is given in [Rosenstark,1986] 4 so only a summary is presented here.
To calculate the return ratio, the small-signal circuit is altered so that the original
voltage dependent current source is replaced by an independent source, = β , as
shown in Figure 2.15. The return ratio, determined as the negative of , is calcu-
lated to be T = 34.9 . In addition, two characteristics called the asymptotic gain,
A ∞
= 18.9 , and the direct transmission gain, Ao = 0.388 , are determined in order
to apply the Asymptotic Gain Formula to find the actual closed-loop gain:
(2.5)
The input and output resistance are obtained using Blackman’s Impedance For-
mula [Blackman,1943]. The formula states that a port impedance is given by
where
R s
A f
• T sc is the return ratio when the port in question is shorted to ground,
• T oc is the return-ratio when the port in question is open-circuited, and
• Z° is the measured port impedance when the internal feedback is disabled.
v be1
+
-
r e
4. Example 2.1, pp. 12-23.
A o
T
34.9 0.388
= A∞-------------- + -------------- = 18.9 × --------- + ------------ = 18.4
1 + T 1 + T 35.9 35.9
g m v be1
R || E R f
v c1
R 1
Z port
v port
---------- Z° 1 T + sc
= = ------------------
1 + T oc
r π
i port
x a
R f
x b
=
β
x a
R || 2 ( R f + RE) Figure 2.15 Small-signal circuit used to calculate return ratio.
x b
(2.6)
v o ′