Explanation Given data: The input voltage is, v i ( t ) = 2 t e − t u ( t ) V The given diagram is shown in Figure 1. Calculation: Mark the loop current i in the given figure. The required diagram is shown in Figure 2. The expression for output voltage using KVL is given by, 2.5 i + 5 d i d t = v i ( t ) Substitute 2 t e − t u ( t ) for v i ( t ) in the above expression. 2.5 i + 5 d i d t = 2 t e − t u ( t ) Apply Fourier transform to the above expression. 2.5 I ( j ω ) + 5 j ω I ( j ω ) = F [ 2 t e − t u ( t ) ] (1) The expression for the property of Fourier transform is given by, t f ( t ) = j d d ω F ( j ω ) The Fourier transform of 2 t e − t u ( t ) using the above property is given by, F [ 2 t e − t u ( t ) ] = j [ d d ω ( 2 1 + j ω ) ] = j ( − 2 ( 1 + j ω ) 2 ) j = ( 2 ( 1 + j ω ) 2 ) Substitute ( 2 ( 1 + j ω ) 2 ) for F [ 2 t e − t u ( t ) ] in equation (1). 2.5 I ( j ω ) + 5 j ω I ( j ω ) = ( 2 ( 1 + j ω ) 2 ) I ( j ω ) [ 2.5 + 5 j ω ] = ( 2 ( 1 + j ω ) 2 ) I ( j ω ) = 2 ( 2.5 + 5 j ω ) ( 1 + j ω ) 2 I ( j ω ) = 0.4 ( 0.5 + j ω ) ( 1 + j ω ) 2 Apply partial fraction rule in the above expression. 0.4 ( 0.5 + j ω ) ( 1 + j ω ) 2 = A ( 0.5 + j ω ) + B ( 1 + j ω ) + C ( 1 + j ω ) 2 (2) Substitute − 1 for j ω in the above expression to find the value of A . 0.4 = A ( 1 − 0.5 ) 2 0.4 = A ( 0.5 ) 2 A = 1.6 Further solve the equation (2) to find the value of A and B . 0.4 ( 0.5 + j ω ) ( 1 + j ω ) 2 = A ( 1 + j ω ) 2 + B ( 0.5 + j ω ) ( 1 + j ω ) + C ( 0.5 + j ω ) ( 0.5 + j ω ) ( 1 + j ω ) 2 0.4 = A ( 1 + j ω ) 2 + B ( 0.5 + j ω ) ( 1 + j ω ) + C ( 0.5 + j ω ) 0.4 = A ( 1 + ( j ω ) 2 + 2 j ω ) + B ( 0.5 + 1.5 j ω + ( j ω ) 2 ) + C ( 0.5 + j ω ) Equate the second order terms to find the value of B . A + B = 0 B = − A Substitute 1.6 for A in the above equation

9th Edition

ISBN: 9781260540666

Author: Hayt

Publisher: MCG CUSTOM

See similar textbooks

Question

Chapter 17, Problem 58E

To determine

The value of output voltage v0(t).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17, Problem 57E

Chapter 17, Problem 59E

Students have asked these similar questions

Homework Help

Could you help me with this one please, thank you.

2. Represent the following as a Cosine Fourier integral. x) = { 8² 0 f(x) = 0 a

Chapter 17 Solutions

ENGINEERING CIRCUIT...(LL)>CUSTOM PKG.<

Ch. 17.1 - Let a third-harmonic voltage be added to the...Ch. 17.1 - A periodic waveform f(t) is described as follows:...Ch. 17.2 - Prob. 3P Ch. 17.2 - Prob. 4P Ch. 17.3 - Prob. 5P Ch. 17.3 - Prob. 6P Ch. 17.4 - Prob. 7P Ch. 17.5 - Prob. 8P Ch. 17.5 - Prob. 9P Ch. 17.6 - Prob. 10P

Ch. 17.6 - Prob. 11P Ch. 17.7 - Prob. 12P Ch. 17.7 - Prob. 13P Ch. 17.8 - Find (a) F5sin23t); (b) FAsin20t); (c)...Ch. 17.9 - Prob. 15P Ch. 17.10 - Prob. 16P Ch. 17 - Determine the fundamental frequency, fundamental...Ch. 17 - Plot multiple periods of the first, third, and...Ch. 17 - Calculate a0 for the following: (a) 4 sin 4t; (b)...Ch. 17 - Prob. 4E Ch. 17 - Prob. 5E Ch. 17 - Prob. 6E Ch. 17 - Prob. 7E Ch. 17 - With respect to the periodic waveform sketched in...Ch. 17 - Prob. 9E Ch. 17 - Prob. 10E Ch. 17 - A half-sinusoidal waveform is shown in Fig. 17.31,...Ch. 17 - Plot the line spectrum (limited to the six largest...Ch. 17 - Prob. 13E Ch. 17 - Prob. 14E Ch. 17 - Prob. 15E Ch. 17 - Prob. 16E Ch. 17 - Prob. 17E Ch. 17 - Prob. 18E Ch. 17 - The nonperiodic waveform g(t) is defined in Fig....Ch. 17 - Prob. 20E Ch. 17 - Prob. 21E Ch. 17 - Prob. 22E Ch. 17 - Prob. 23E Ch. 17 - Prob. 24E Ch. 17 - Prob. 25E Ch. 17 - Prob. 26E Ch. 17 - Prob. 27E Ch. 17 - Prob. 28E Ch. 17 - Prob. 29E Ch. 17 - Prob. 30E Ch. 17 - Prob. 31E Ch. 17 - Prob. 32E Ch. 17 - Prob. 33E Ch. 17 - Prob. 34E Ch. 17 - Prob. 35E Ch. 17 - Prob. 36E Ch. 17 - Use the Fourier transform to obtain and plot the...Ch. 17 - Prob. 38E Ch. 17 - Prob. 39E Ch. 17 - Prob. 40E Ch. 17 - For g(t) = 3etu(t), calculate (a) G(j); (b) ().Ch. 17 - Prob. 42E Ch. 17 - Prob. 43E Ch. 17 - Prob. 44E Ch. 17 - Prob. 45E Ch. 17 - Prob. 46E Ch. 17 - Find F(j) if f(t) is given by (a) 2 cos 10t; (b)...Ch. 17 - Prob. 48E Ch. 17 - Prob. 49E Ch. 17 - Prob. 50E Ch. 17 - Prob. 51E Ch. 17 - Prob. 52E Ch. 17 - Prob. 53E Ch. 17 - If a system is described by transfer function h(t)...Ch. 17 - Prob. 55E Ch. 17 - (a) Design a noninverting amplifier having a gain...Ch. 17 - Prob. 57E Ch. 17 - Prob. 58E Ch. 17 - Prob. 59E Ch. 17 - Prob. 60E Ch. 17 - Prob. 61E Ch. 17 - Prob. 62E Ch. 17 - Design an audio amplifier with gain of 10, using...

Knowledge Booster

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,