Page 109 - Schaum's Outline of Theory and Problems of Electric Circuits

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS
98
The rate of change of G with respect to A is [CHAP. 5

dG 1 dA
¼ from which dG ¼
dA ð1 þ AÞ 2 ð1 þ AÞ 2
The percentage change produced in G is 100ðdG=GÞ.

dG dA 1 þ A 1 dA
¼ ¼
G ð1 þ AÞ 2 A 1 þ A A
and the sensitivity is
dG=G 1
s ¼ ¼
dA=A 1 þ A
The percentage change in G depends on A. Samples of dG=dA and s are shown in Table 5-8.

Table 5-8
A G ¼ v 2 =v 1 dG=dA s
10 0.909 0.008 0.091
11 0.917 0.007 0.083
100 0.990 0.0001 0.01
1000 0.999 0 0

For high values of A, the gain G is not sensitive to changes in A.

Supplementary Problems

5.30 Repeat Problem 5.3 by replacing the circuit to the left of node B (including v s , R 1 , and R i ) by its The ´ venin
equivalent (see Fig. 5-33) Solve the problem by applying the results of Example 5.4.

5.31 Find the The ´ venin equivalent of the circuit to the left of nodes A-B in Fig. 5-52 with k ¼ 10 for (a) R 2 ¼1
and (b) R 2 ¼ 50 k
. Ans: ðaÞ v Th ¼ 100 V; R Th ¼ 100
; (bÞ v Th ¼ 31:22 V; R Th ¼ 37:48

Fig. 5-52

5.32 Repeat Problem 5.31 for R 2 ¼ 50 k
and k ¼ 100. Ans: v Th ¼ 47:16 V; R Th ¼ 5:66

5.33 Determine the relationship between R, R 1 , and R 2 in Fig. 5-41 such that the circuit has a gain of
6
v 2 =i 1 ¼ 10 V/A. Ans: RR 2 =R 1 ¼ 10 6