Concept explainers
Find the Fourier series representation of the signal shown in Fig. 17.64.
Figure 17.64

Find the Fourier series representation of the signal shown in Figure 17.64.
Answer to Problem 26P
The Fourier series representation
Explanation of Solution
Given data:
Refer to Figure 17.64 in the textbook.
Formula used:
Write the expression to calculate the fundamental angular frequency.
Here,
Write the general expression to calculate trigonometric Fourier series of
Here,
Write the expression to calculate the dc component of the function
Write the expression to calculate Fourier coefficients.
Calculation:
The given waveform is drawn as Figure 1.
Refer to the Figure 1. The Fourier series function of the waveform is defined as,
The time period of the function in Figure 1 is,
Substitute
Substitute
Simplify the above equation to find
Substitute
Simplify the above equation to find
Simplify the above equation to find
Substitute
Simplify the above equation to find
Simplify the above equation to find
Substitute
Conclusion:
Thus, the Fourier series representation
Want to see more full solutions like this?
Chapter 17 Solutions
EE 98: Fundamentals of Electrical Circuits - With Connect Access
- The capacitors in the circuit shown below have no energy stored in them and then switch “S1” closes at time t=0. Assume the ideal op amp does not saturate. As stated above assume the diodes are ideal with parameters specified above. Diodes are at 0.6 Volts Show the derivations of the mathematical equations for v(t) at Locations A and B for t≥ 0arrow_forwardPhase (deg) Magnitude (dB) -20 -40 -60 -80 -100 ° -90 -180 -270 10-1 (i) ° Problem 5 Consider a unity (negative) feedback system with a proportional controller. The Bode plot of the plant transfer function G(s) is given as below. System: sys Frequency (rad/s): 1 Magnitude (dB): 13.9 System: sys Frequency (rad/s): 14.9 Magnitude (dB): 6.58 System: sys Frequency (rad/s): 1 Phase (deg): -9.76 10° System: sys Frequency (rad/s): 25.6 Magnitude (dB): -0.0703 System: sys Frequency (rad/s): 41.3 Magnitude (dB): -8.06 System: sys Frequency (rad/s): 200 Magnitude (dB): -44.4 System: sys Frequency (rad/s): 14.9 Phase (deg): -110 System: sys Frequency (rad/s): 25.6 Phase (deg): -148 System: sys Frequency (rad/s): 41.3 Phase (deg): -180 System: sys Frequency (rad/s): 200 Phase (deg): -247 101 Frequency (rad/s) 102 Find the gain crossover frequency, phase crossover frequency, gain margin and phase margin of the system. Is the closed-loop system stable? (ii) What is the steady-state error of the…arrow_forwardsolve and show in detail all calculationsarrow_forward
- solve and show in detail all calculationsarrow_forwardsolve and show in detail all calculationsarrow_forwardProblem 1 Consider the following system. In the figure, y(t) denotes the voltage across the capacitor. u(t) 1+ R W L + 0000 y(t) C Y(s) (i) Find the transfer function H(s): = of the system. U(s) Now suppose, R 10 KQ, L = 0.5 mH and C = 10 μF. (ii) Find the poles and zeros. Is the system BIBO stable? (iii) Compute settling time, rise time, peak time and % overshoot of the step response of the system. What the steady-state output for unit step input?arrow_forward
- A 3-phase, 52 H.P, 50 Hz, 6-Pole, Y- connected induction motor runs at a speed of 980 rpm.The motor is supplied from 380 V mains and it takes a rated current of 80 A at 0.8 p.f. If the total stator losses are 1.7 kW, determine: the air-gap power, rotor copper loss, friction and windage losses?arrow_forwardelectric plants do hand writingarrow_forwardplease solve quickly. thank you!arrow_forward
- Please show all stepsarrow_forward12-3) PDF, mean, & variance A random variable has the PDF shown in the figure. a) Find the numerical value of the parameter K. b) Write the numerical expression for the PDF. c) Find the probability that the random variable is negative. d) Find the mean of x, the expected value of x², and the variance of x. K Px(x) 3 Xarrow_forwardPlease show all stepsarrow_forward
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,





