Consider a causal LTI system implemented as the RL circuit shown below. In this circuit,v(t) is the input voltage. The current i(t) is considered the system output.i(t)Rlellllv(t)(a) Find the differential equation relating v(t) and i(t).(b) Determine the frequency response of this system (H(jw)).(c) Determine the output i(t) if v(t) = sin(t) , R=10 and L=1.(d) Sketch Bode plot of H(jw) for R=10 and L=1.(e) Determine if the system is a lowpass filter, highpass filter, or none.

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Answered: Consider a causal LTI system…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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For the circuit shown below, the initial conditions are zero, Idc is a current source continuous and switch S is open at t = 0.a)Determine the equivalent impedance to the right of points a and b of the circuit, Z(s).b)Obtain the voltage between points a and b of the circuit in the frequency domain, V(s). Employ the initial and final value properties and calculate the values of v(0) and v(∞).c)Find the expression for v(t). Check that the values of v(0) and v(∞) agree with those calculated in the previous item.d)Obtain currents i1(t) and i2(t).
If ? = 50Ω, L = 1.5H, what value of C will cause a sourceless series RLC circuit to be a) overdamped ?, b) critically damped ?, c) underdamped?
The attatched image shows the position of two complex poles in the s-plane. The poles represent an underdamped second order system. The Figure shows that there is an angle of 40 degrees between the horizontal axis and the line drawn to the upper pole. It also shows that the poles are positioned horizontally with a position of -3.6, and vertically with an imaginary value of +3j and -3j. What is the value of the damping coefficient? & What is the value of the natural frequency?
100 y(t)+ y (t) = X(t) for a system defined by a first-order differential equation:a. Draw the log magnitude(dB)-log frequency graph of H (jw) (phase graph is not requested. it is expected that the frequency axis will also be logarithmic when plotting the log magnitude graph).b. If the magnitude of H(jw) is -40 dB, it is assumed that the input is suppressed. it is given that the signal X (t) = coswat is suppressed by this system. What is the smallest wa value in this case?
Calculate the range of values K will take for the steady-state error to be ??? ≤ 0.04 when the input of the system is ?(?) = ?. Calculate the range of values K will take for the damping ratio to be 1>ξ ≥(1/2√6). Calculate the damping rate ξ and the undamped natural frequency ?? so that ? = 0.5
Solve All parts or will dislike answer A. Find the open-loop transfer function . Y(S) / R(S)B. Find ?(?) when the input ?(?) is a step function (use expansion of partial fractions).C. State the damping factor ?.D. Indicate whether the system is overdamped, underdamped, or critically damped.E. Indicate the natural frequency of the system ??.F. Indicate the poles and zeros of the system.G. Use the end theorem to find the steady-state value.H. Find ?(?) (use inverse Laplace transform).I. Plot the time response of the system.
I need help with the question below Consider a causal LTI continuous system described by the differential equation y′′(t) + 3y′(t) + 2y(t) = x(t) where y(t) is the system output and x(t) is the input.1. Find the transfer function H(s) of the system.2. Find its poles and zeros. From its poles and zeros, determine if the system is BIBO stable or not.3. If x(t) = u(t) and initial conditions are zero, determine the steady-state response yss(t)4. If the initial conditions were not zero, would you get the same steady state?. Explain
Difference equation of a discrete-time causal (right-sided) LTI system, y(n) = 2 x(n) – x(n-1) -1/4 y(n-1) + 1/8 y(n-2) is given as. a) Give the system function H(z). b) Indicate zero, poles and ROC in the Z-plane. Is the system stable? Please explain. c) Find the impulse response of the system. d) If the system is left-sided, repeat (b) and (c).
For the circuit of Fig., let C = 15.0 nF, L = 22 mH, and R = 75.0 Ω. (a) Calculate the oscillation frequency of the circuit once the capacitor has been charged and the switch has been connected to point a. (b) How long will it take for the amplitude of the oscillation to decay to 10.0% of its original value? (c) What value of R would result in a critically damped circuit?
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A continuous time signal, x(t) = sin(20πt) + cos(40πt), is sampled uniformly at intervals of T to obtaina discrete time signal,x(n) = sin(πn/5) + cos(2πn/5).a) What is the value of T assuming no aliasing has occurred?b) Assume both frequency components have been aliased. In this case, is your choice of T unique? If not,specify some choices of T consistent with the information given
: If F(s) = s 4+ 5s3+20s 2 + 40s + 50 , Investigate the stability of this system

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