#### PROBLEMS

**7.1.** Determine the circuit structure, the values of resistance and capitance, the gains of any amplifiers required, and the complex-plane plot for first-order networks having the following characteristics:

**(a)** Phase lead of 60° at *ω* = 4 rad/sec, a minimum input impedance of 50,000 Ω, and an attentuation of 10 dB at dc.

**(b)** Phase lag of 60° at *ω* = 4 rad/sec, a minimum input impedance of 50,000 Ω, and a high-frequency attenuation of 10 dB.

**(c)** A phase-lag-lead network having an attenuation of 10 dB for a frequency range of *ω* = 1 to *ω* = 10 rad/sec and an input impedance of 50,000 Ω.

In all cases, limit the maximum values of resistance to 1 MΩ and capitance to 10 *μ*F. Furthermore, assume that the loads on the networks have essentially infinite impedance.

**7.2.** The system illustrated in Figure P7.2 consists of a unity-feedback loop containing a minor-rate-feedback loop.

**(a)** Without any rate feedback (*b* = 0), determine the damping ratio, undamped natural frequency, peak overshoot of the system to a unit step input, and the steady-state error resulting from a unit ramp input.

**(b)** Determine the rate-feedback constant *b* which will increase the equivalent damping ratio of the system to 0.8.

**(c)** With rate feedback and a damping ratio of 0.8, determine the maximum percent overshoot of the system to a unit step input and the steady-state error resulting from a unit ramp ...

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