1. (5 marks) Derive the Fourier coefficients ao, an, and bn for the input voltage function 4 - |7|-|-(1)a v(t) = ;|t| 1 on the interval [, ] with a period of T = 0.001s. This triangle wave function is the input voltage source for the rest of the assignment. v(t) 1 0 M -1 -T -T/2 0 T/2 T time Figure 1: Triangle Wave Function 2. For this question, consider the cascaded circuit diagram shown below in Figure 1. Vin(t) 10 Ω www 0000 1 mH 10 Ω w 1 μF Figure 2: Cascaded RC and RL filters with a unity gain buffer for isolation. (a) (5 marks) Make Bode plots for the magnitude and phase of the frequency response of the voltage drop across the inductor. (b) (5 marks) Make Bode plots for the magnitude and phase of the frequency response of the voltage drop across the capacitor. On your Bode plots for parts (a) and (b), indicate the locations of the first three fre- quencies of the Fourier series that have non-zero coefficients. Note that some frequencies may have coefficients that are zero, and thus do not contribute. (c) (5 marks) Using the function from question 1 as the input voltage source, plot the input voltage and the voltage drop across the capacitor as a function of time for two periods of the input signal.

1. (5 marks) Derive the Fourier coefficients ao, an, and bn for the input voltage function 4 - |7|-|-(1)a v(t) = ;|t| 1 on the interval [, ] with a period of T = 0.001s. This triangle wave function is the input voltage source for the rest of the assignment. v(t) 1 0 M -1 -T -T/2 0 T/2 T time Figure 1: Triangle Wave Function 2. For this question, consider the cascaded circuit diagram shown below in Figure 1. Vin(t) 10 Ω www 0000 1 mH 10 Ω w 1 μF Figure 2: Cascaded RC and RL filters with a unity gain buffer for isolation. (a) (5 marks) Make Bode plots for the magnitude and phase of the frequency response of the voltage drop across the inductor. (b) (5 marks) Make Bode plots for the magnitude and phase of the frequency response of the voltage drop across the capacitor. On your Bode plots for parts (a) and (b), indicate the locations of the first three fre- quencies of the Fourier series that have non-zero coefficients. Note that some frequencies may have coefficients that are zero, and thus do not contribute. (c) (5 marks) Using the function from question 1 as the input voltage source, plot the input voltage and the voltage drop across the capacitor as a function of time for two periods of the input signal.

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...

See similar textbooks

Similar questions

Fourier Expansions of Periodic Waveforms given in the Figures. Find it. Show on the amplitude-frequency axis. f=1/T 2nf=w a) b) f(t) T f(t) for -V T
it's urgent please solve asap
Write the Fourier expression for the first six non-zero sinusoidal terms for the waveform shown in the figure. Write the simplified Fourier series expression substituted value of the angular frequency and sketch the frequency domain representation of the harmonics for the waveform.
4
Fourier theory states that any sinusoidal signal may be represented or analyzed as the sum of a fundamental sine wave at the signal frequency plus odd, even, or odd plus even nonharmonic sine waves of different phases and amplitudes. True False
Please help with this question about fourier series. Show your solution and how to find time period.
If the signal has a spectrum (Fourier transform) given in Figure Q3, draw the spectrum of the sampled signal when the sampling rate is 25% higher than the Nyquist sampling rate; draw the spectrum of the sampled signal when the sampling rate is the same as the Nyquist sampling rate. Spectrum 1 -6 f (kHz) Figure Q3
i need help with part a , b , c , e thanks
Obtain the complex in Figure.. 2.8 Fourier series for the waveform shown - x() 0 A 2n
Please help find the fourier series coefficients x[k] for the three waveforms. Please use the intergration formula for x[k]. Also sketch the magnitude and phase spectra. Thank you
Itz already solved but wrong plz provide me correct solution only .other wise I vill report.
2.47 The Fourier transform of a signal is shown in Figure P-2.47. Determine and sketch the Fourier transform of the signal x1 (1) = -x(1) +x(t) cos(3000rt) + 2x(t) cos (5000rt). 500 500 Figure P-2.47