3. What should be gain margin and phase margin for acceptable transicnt response? Determine both for a system with $$ \mathrm{GH}(j \omega)=\frac{1}{(j \omega+1)^{3}} $$
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op-amp & capacitorplease solve this problem6. 76 Given the network in Fig. \(\mathrm{P} 6.76 .\)(a) Determine the equation for the closed-loop gain \(|\mathrm{G}|=\left|\frac{v_{0}}{v_{i}}\right|\)(b) Sketch the magnitude of the closed-loop gain as a function of frequency if \(R_{1}=1 \mathrm{k} \Omega, R_{2}=10 \mathrm{k} \Omega\), and \(C=2 \mu \mathrm{F}\).
A unity feedback control system has the open loop TF as: \(G(s)=\frac{K(s+a+1)(s+b)}{s(s+a)(s+a+2)}\)a) Find analytical expressions for the magnitude and phase response for \(\mathrm{G}(\mathrm{s}) .\left[K=K_{1}\right]\)b) Make a plot of the log-magnitude and the phase, using log-frequency in rad/s as the ordinate. \(\left[K=K_{1}\right]\)c) Sketch the Bode asymptotic magnitude and asymptotic phase plots. \(\left[K=K_{1}\right]\)d) Compare the results from \((a),(b)\), and \((c) .\left[K=K_{1}\right]\)e) Using the Nyquist criterion, find out if system is stable. Show your steps. \(\left[K=K_{1}\right]\)f) Using the Nyquist criterion, find the range...
10 GH = 60 B) For the system shown in 6A calculate the magnitude and phase of response for a unit input with an operating speed of w=1.0 rad/sec. C) Identify the system's bandwidth, phase and gain margin as applicable directly on the asymptotic Bode plot drawn in 6A. D) Based on the phase and gain margin values found in 6C is the system stable?Yes / No) E) Apply gain compensation and solve for a new value of K for...
A servomechanism has an open loop transfer function of G(s) = 10 / s (1+0.5s) (1+0.1s) Draw the Bode plot and determine the phase and gain margin. A networks having the transfer function (1+0.23s)/(1+0.023s) is now introduced in tandem. Determine the new gain and phase margins. Comment upon the improvement in system response caused by the network
consider a feedback control system shown in Fig.1, where Problem 3 Consider a feedback control system shown in Fig. 1, where s2 +s+4 1. Is the system open-loop stable? 2. Determine the value of the proportional gain K such that the phase margin is Ap 3. What is the gain margin with this gain K? 50
For the differential amplifier shown in Figure (2),assume \(\mathrm{VCC}=12 \mathrm{~V}, \mathrm{VEE}=-12 \mathrm{~V}, \mathrm{Rc}=2 \mathrm{k} \Omega\), and \(\beta=100\) for all transistors.For the current source circuit (Transistor \(\left.Q_{3}\right): R_{1}=4 k \Omega, R_{2}=4 k \Omega, R_{3}=3 \mathrm{k} \Omega\), and \(r_{0}=100 \mathrm{k} \Omega\).a) In differential amplifier circuits, what do "well-matched transistors" mean?b) Why it is important to use well-matched transistors in differential amplifier circuits?c) What are the operating \(Q\) point values \(\left(I_{c Q}\right.\) and \(\left.V_{C Q}\right)\) for the transistors \(Q_{1}\) and \(Q_{2}\) ?d) Draw...
Find the Equivalent ResistanceFour resistors are connected as shown in figure (a), below. (Let R=3.00 Ω.)The original network of resistors is reduced to a single equivalent resistance.(a) Find the equivalent resistance between points \(a\) and \(\mathrm{c}\).solutionConceptualize Imagine charges flowing into and through this combination from the left. All charges must pass from a to \(b\) through the first two resistors, but the charges split at \(b\) into Categorize Because of the simple nature of the combination of resistors in the...
3. The open loop transfer function of a unity feedback system is given by \(G(S)=\frac{K}{S(1+S T)}\) Where Tand \(\mathrm{K}\) are constants having positive values. By what factor the amplifier gain be reduced so that (a) peak overshoot of unit step response of the system is reduced from \(75 \%\) to \(25 \% .\) b) The damping ratio increases from \(0.1\) to \(0.6\).
A discrete-time LTI system has the system function \(H(z)\) given below:$$ H(z)=\frac{z^{2}}{z^{2}-\frac{1}{4}} $$(a) Sketch the pole-zero plot for this system. How many possible regions of convergence (ROCs) are there for \(H(z)\). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to.(b) Which ROC (or ROCs) correspond to a stable system? Why?(c) Which ROC (or ROCs) correspond to a causal system? Why?(d) Write a difference equation that relates the input to the output of...
Construct the bode plot on a semilog Graph-paper for a unity feedback system whose open looptransfer function is given by \(G(S)=\frac{100}{S(S+1)(2+S)} .\) From the bode plot determinea) Gain and phase crossover frequencies.b) Gain and Phase margin, andc) Stability of the closed loop system