Chapter 11, Problem 29P

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jan G(f) f Sketch the spectrum of g(t), which has a maximum frequency of 5 kHz, if it is sampled at the following sampling frequencies: 7 kHz, 10 kHz and 15 kHz. Indicate if and how the signal can be recovered at each sampling frequency.

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A single tone is modulated using FM transmitter. The SNR, at the input of the demodulator 20 dB. If the maximum frequency of the modulating signal is 4 kHz, and the maximum equency deviation is 12 kHz, find the SNR, and the bandwidth (using Carson rule) at the ollowing conditions: . For the given values of fm and Af. !. If the amplitude of the modulating signal is increased by 80%. 3. If the amplitude of the modulating signal is decreased by 50%, and frequency of modulating signal is increased by 50%.

The circuit shown below on the left has the following parameters: V₁ = 5 V. R₁ = 40, R₂ = 40, α = 0.1. This circuit can be replaced by an equivalent circuit shown below on the right such that the voltage and current received by an arbitrary load resistor RL, are identical when connected to either circuits. Determine the value of the resistor R (in ) in the equivalent circuit. R₁ Rx R2 R₁ Vx R₁ Vi απ. b

1. Consider the following a unity feedback control system. R(s) + E(s) 500(s+2)(s+5)(s+6) s(s+8)(s+10)(s+12) -Y(s) Find the followings: a) Type of the system b) Static position error constant Kp, Static velocity error constant Ry and Static acceleration error constant Ka c) Find the steady-state error of the system for (i) step input 1(t), (ii) ramp input t 1(t), (iii) parabolic input t² 1(t). 2. Repeat the above problem for the following system. R(s) + E(s) 500(s + 2)(s + 5) (s+8)(s+ 10)(s+12) Y(s) 3. Repeat the above problem for the following system. R(s) + E(s) 500(s+2)(s+4)(s+5)(s+6)(s+7) s²(s+8)(s+10)(s+12) Y(s)

4. Consider a unity (negative) feedback control system whose open-loop transfer function is given by the following. 2 G(s) = s³ (s + 2) Find the steady-state error of the system for each of the following inputs. = a) u(t) (t²+8t+5) 1(t) b) u(t) = 3t³ 1(t) c) u(t) (t+5t² - 1) 1(t) =

1 2. For the following closed-loop system, G(s) = and H(s) = ½ (s+4)(s+6) a. Please draw the root locus by hand and mark the root locus with arrows. Calculate the origin and angle for asymptotes. b. Use Matlab to draw the root locus to verify your sketch. Input R(s) Output C(s) KG(s) H(s)

5. Consider following feedback system. R(s) + 100 S+4 +1 Find the steady-state error for (i) step input and (ii) ramp input.