Verify that Eqs. (15.46) and (15.57) describe the operation of the circuits in Fig. 15.12.

## The circuit shown in Fig. P14.26 is a model for a tunnel diode. We wish to simul

The circuit shown in Fig. P14.26 is a model for a tunnel diode. We wish to simulate this circuit for an experiment using the concepts of Section 14.6. It is specified that the simulation circuit must not contain inductors nor, of course, negative resistors. Find an equivalent circuit meeting these specifications and having the same Zin.

## The circuit in Fig. P 13.16 is the LC ladder impknicntation of a bandpass filter

The circuit in Fig. P 13.16 is the LC ladder impknicntation of a bandpass filter with a I.7-dB equal-ripple passband in 10 kHz. The stop hand attenuation Realize the circuit with the operational simulation method and test your design.

## A poorly packaged and badly wound inductor of value L. = 0.34 His found to have

A poorly packaged and badly wound inductor of value L. = 0.34 His found to have a self-resonance frequency of only This implies that the parasitic capacitor that appears in parallel to L is approximately 600 pF. Since the inductor cannot be changed. it is proposed to reduce the parasitic capacitor so that the self-resonance frequency is at least equal to 200 kHz. Design and test an appropriate circuit to accomplish this goal.

## Design a filter that has a bandpass characteristic by the operational-simulation

Design a filter that has a bandpass characteristic by the operational-simulation (leapfrog) method. For this problem. the prototype is the third-order Chebyshev filter with a 0.541B ripple width obtained from Table 13.3. Design for the center frequency of rap = 3000 J.-AA. with a 0.5-dB bandwidth of 500 Hz. Use the method of Section 15.3. practical component values. and LM74 I opamps. Test your design.

## What passive circuit has the same input impedance as the circuit given in Fig. P

What passive circuit has the same input impedance as the circuit given in Fig. P14.24?

## Repeat Problem 15.9 with the prototype changed to a fifth-order Chebyshev filter

Repeat Problem 15.9 with the prototype changed to a fifth-order Chebyshev filter with a 0.1-dB ripple width as obtained from Table 13.3. Problem 15.9 This problem requires the design of a bandpass filter making use of the operational simulation method. The prototype lowpass is a third-order Butterworth litter. The two half-power frequencies of the band-pass filter arc 1960 and 2040 Hz. Source and load resistors are Consider whether the simplified circuitry in Section 15.3 can he used. Use LM741 opamps. practical element values, and test your de-sign.

## To optimize the performance of some equipment, the loss of an inductor L. modele

To optimize the performance of some equipment, the loss of an inductor L. modeled as a series loss-resistor a must be eliminated. For the operation it is very important that the effective inductor is “lossless” over as wide a frequency range as possible. The equipment must be very inexpensive: LM74I opamps should be used. Using the information in Section 14.6, the student engineer assigned to the task designs a negative resistor to be placed in series with L. Making use of Eq. (14.44), optimize the negative-resistor circuit so that the finite opamp w, has as little effect as possible.

## Scale the normalized LC ladder of Fig. 13.14h such that passband corner and sour

Scale the normalized LC ladder of Fig. 13.14h such that passband corner and source and load terminations are (2. Realize the circuit as a gm-C ladder and test the designs with EWB. (a) Use element replacement. (b) Use operational simulation. (c) Compare the two designs. The circuits should be the same.

## The OTA of Problem 16.1 with gm adjusted to the value 195 AS is used to implemen

The OTA of Problem 16.1 with gm adjusted to the value 195 AS is used to implement a resistor in the circuit of Fig. P16.3. (a) What is the gain of the circuit at 100 kHz? (b) What is the expected 3-dB frequency? (c) The 3-dB frequency must be increased substantially but no additional OTA is available on the IC to make the divider frequency independent as suggested in Recommend a method that would achieve the desired in-creased bandwidth. (d) Implement the circuit and test your design EWB. Problem 1 A gm-C integrator must be designed for a unity-gain frequency of 9 MHz. The available transconductor is known to have the parameters The de gain must be at least 68 (a) Determine the required load capacitor. (b) Determine the minimum value of output resistance r„ the OTA must have. (c) What is the phase at the unity-gain frequency? (d) What arc the 3-dB frequency and the phase at the 3-dB frequency? (e) What is the highest unity-gain frequency that an integrator with this OTA can have? (f) Implement the circuit in single-ended and differential form and test your designs with Electronics Workbench (EWB).