1. The Nyquist plot of a transfer function G(s) is shown in Figure 1. (a) Suppose G has two unstable open loop poles. When G(s) is placed in a unity feedback loop, is the closed loop system stable or unstable? Explain. (b) Suppose G has one unstable open loop pole. When G(s) is placed in a unity feedback loop, is the closed loop system stable or unstable? Explain. Imaginary Axis 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 1 Nyquist Diagram -1 -2 -1.5 -0.5 0 0.5 Real Axis Figure 1: Nyquist plot for Problem 1.

Discuss the difference between the current series negative feedback amplifier and voltage shunt feedback amplifier in terms of output impedance, input impedance, voltage gain, bandwidth, distortion and noise.

1) Explain the concept of positive and negative feedback And derive the formula of closed loop voltage gain? Please don't write by hand

a) Two feedback configurations are shown in Figures Q1.a(i) and Q1.a(ii). Derive the closed-loop gain Af in each case. V₁. V₁. A1 B1 Figure Q1.a(i) A₁ B₁ Figure Q1.a(ii) A₂ A₂ B₂ ܘܢ -V

Draw a feedback circuit and Explain the concept of feedback and how it contributes to the stability and performance of amplifiers.

1) Explain the concept of positive and negative feedback And derive the formula of closed loop voltage gain. Note: Please do not handwritten. Also, write a lot of information by your own words. Thank you

(A) Draw and clearly label the circuit diagram of an op-amp configured as a practical inverting differentiator circuit. (B) For the op-amp in part (A), explain how the DC-offset volatge is reduced at the output? (C) Calculate the feedback resistance Rf and the input reistance R, in a practical diffrentiator if fo =1 kHz and a high-frequency gain of 15 is required. Choose a capacitor of 1µF.

For the unity feedback system given below, the damping ratio of the closed looppoles is given by a) 1.5 b) 1 c) 0.5 d) 0.25

Q2) Consider the following feedback system outlined in Figure Q2 Plant R(s) + 10 1 C(s) S+ 1 K, Figure Q2 a) Derive the closed loop transfer function GRC (S). b} Calculate the value of Ky that will result in the closed loop system to have a maximum overshoot of 35% and a peak time of approximately 1 second. c) For the following systems assume zero initial conditions. Determine i) The peak overshoots. ii) Corresponding peak times iii) Decay rate characteristics. Produce a sketch of the unit step response using the above values calculated.

Question 2: For the Feedback Control system given in the figure. (a) Find the closed-loop transfer function, C(s)/R(s). (b) Determine the system's stability range for gain Kusing Routh-Hurwitz criterion. (c) What is the type of the system? (You need to convert the system to a simple unity feedback.) (d) Sketch the root-locus in Matlab (you need to use the open-loop transfer function with K= 1) and validate the stability region you found in (b). (e) Plot the step response up to 10 seconds for the input of 1.5u(t) and the gain value that makes the system marginally stable. for (f) Find the steady-state error for an input step of 1.5u(t) for K= 22 and plot this response together with the input up to 10 seconds in order to display the steady-state error you computed. (g) Find the steady-state error for an input ramp of 1.5tu(t) for K= 22 and plot this response together with the input up to 10 seconds in order to indicate the steady-state error you computed. R(s) K 1 s(s+2)(s+5) C(s)