CHAP. 5]

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS

99

5.34

In the circuit of Fig. 5-13, Vcc ¼ 10 V, R1 ¼ 2 k and v1 ¼ 1 V. Find the maximum value of R2 before the op amp is saturated. Ans: R2 ¼ 20 k

5.35

Let the summing circuit of Fig. 5-14 have two inputs with v1 ¼ 1 and v2 ¼ sin t (V). Let R1 ¼ 3 k, R2 ¼ 5 k, and Rf ¼ 8 k. Apply superposition to ﬁnd vo . Ans: vo ¼ ð83 þ 85 sin tÞ

5.36

In Fig. 5-17 let R1 ¼ 4 k and R2 ¼ 8 k. Ans: vo ¼ v1 þ v2 þ v3

5.37

Find the input resistance seen by vf in Fig. 5-19.

5.38

Use superposition to ﬁnd vo in Fig. 5-20 for R1 ¼ 2, R2 ¼ 7, R3 ¼ 10, R4 ¼ 5, all values in k. Ans: vo ¼ 1:5v2  3:5v1

5.39

In the circuit of Fig. 5-20 ﬁnd (a) v0 for R1 ¼ 1, R2 ¼ 3, R3 ¼ 2, and R4 ¼ 2, all values in k; (b) the input resistance R2 in seen by v2 ; (c) i1 as a function of v1 and v2 and show that v1 sees a variable load which depends on v2 . Ans: ðaÞ vo ¼ 2v2  3v1 ; ðbÞ R2 in ¼ 4 k; ðcÞ i1 ¼ v1  v2 =2

5.40

Using a single op amp, design an ampliﬁer with a gain of v2 =v1 ¼ 3=4, input resistance of 8 k, and zero output resistance. Ans: See Fig. 5-53.

Apply superposition to ﬁnd vo in terms of the input voltages.

Ans:

Rin ¼ 2R1

Fig. 5-53

5.41

Show that, given R1 ¼ 1 and R2 ¼ 0, the noninverting op amp circuit of Fig. 5-15 and (12) is reduced to a voltage follower.

5.42

In the circuit of Fig. 5-22 let Rs ¼ 10 k. Discuss. Ans: ðaÞ 40 k; ðbÞ yes

5.43

The input to the circuit of Fig. 5-23 with RC ¼ 1 is v1 ¼ sin !t. Ans: v2 ¼ ð1=!Þ cos !t þ C

5.44

Show that the output v2 in Fig. 5.54 is the same as the output of the integrator in Fig. 5-23.

(a) Find Rf such that is ¼ 0.

Fig. 5-54

(b) Is Rf independent of Rs ?

Write KCL at node B and solve for v2 .

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An