Homework Set #4 ENGR 264 (Electronics) 1. Following the analysis of a high-pass filter done in class analyze the low-pass filter circuit with R=1 k2 and C=0.16 µF shown below: input R C 10 output V a) Derive an expression for the transfer function G=- out also called the gain G. Vin Separate the real and imaginary part and provide a sketch of the gain in the complex plane. What is the magnitude of the gain? b) Derive an expression for the phase angle. c) Using the values for C and R, what is the breakpoint (or corner) frequency?

Homework Set #4 ENGR 264 (Electronics) 1. Following the analysis of a high-pass filter done in class analyze the low-pass filter circuit with R=1 k2 and C=0.16 µF shown below: input R C 10 output V a) Derive an expression for the transfer function G=- out also called the gain G. Vin Separate the real and imaginary part and provide a sketch of the gain in the complex plane. What is the magnitude of the gain? b) Derive an expression for the phase angle. c) Using the values for C and R, what is the breakpoint (or corner) frequency?

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

1. Following the analysis of a high-pass filter done in class analyze the low-pass filter circuit
with R=1 k2 and C=0.16 µF shown below:
O
Homework Set #4 ENGR 264 (Electronics)
R
-www
input
O
C
output
a) Derive an expression for the transfer function G
V
Vin
out also called the gain G.
Separate the real and imaginary part and provide a sketch of the gain in the complex plane.
What is the magnitude of the gain?
b) Derive an expression for the phase angle.
c) Using the values for C and R, what is the breakpoint (or corner) frequency?
d) Using Origin (available on all lab machines), plot the gain vs. frequency on a log-log plot.
Check whether your calculated corner frequency agrees with your plot.
e) Now plot the phase angle on a semi-log plot (angle linear, frequency log). What is the phase
angle at the breakpoint frequency?
2. Your low-pass filter has a resistor value of 1000 2 and you measure a Gain of 1/100 at a
frequency of 100 kHz. What is the value of the capacitor?

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