Section 10.9 Applications

10.89 The op amp circuit in Fig. 10.131 is called an inductance simulator. Show that the input impedance is given by

\mathbf{Z}_{in} = \frac{\mathbf{V}_{in}}{\mathbf{I}_{in}} = j\omega L_{eq}

where

L_{\text{eq}} = \frac{R_1 R_3 R_4}{R_2 C}

Figure 10.131 For Prob. 10.89.

10.91 Consider the oscillator in Fig. 10.133.
- (a) Determine the oscillation frequency.
- (b) Obtain the minimum value of R for which oscillation takes place.

Figure 10.133 For Prob. 10.91.

10.87 Determine V1, V2, and V3 in the circuit of Fig. 10.129 using PSpice or MultiSim.

10.92 The oscillator circuit in Fig. 10.134 uses an ideal op amp.
- (a) Calculate the minimum value of Ro that will cause oscillation to occur.
- (b) Find the frequency of oscillation.

Figure 10.134

10.93 Figure 10.135 shows a Colpitts oscillator. Show that the oscillation frequency is

f_o = \frac{1}{2\pi\sqrt{LC_T}}

where CT = C1C2∕(C1 + C2). Assume Ri ≫ XC² .

A Colpitts oscillator; for Prob. 10.93.

(Hint: Set the imaginary part of the impedance in the feedback circuit equal to zero.)

10.94 Design a Colpitts oscillator that will operate at 50 kHz.

10.95 Figure 10.136 shows a Hartley oscillator. Show that the frequency of oscillation is

10.96 Refer to the oscillator in Fig. 10.137.

(a) Show that

\mathbf{v} \text{ that}

\frac{\mathbf{V}_2}{\mathbf{V}_o} = \frac{1}{3 + j(oL/R - R/oL)}

(b) Determine the oscillation frequency fo.
(c) Obtain the relationship between R1 and R2 in order for oscillation to occur.

Figure 10.137 For Prob. 10.96.

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