# Berkeley ELENG 40 - Homework (4 pages)

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## Homework

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## Homework

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Pages:
4
School:
University of California, Berkeley
Course:
Eleng 40 - Introduction to Microelectronic Circuits
##### Introduction to Microelectronic Circuits Documents

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Fall 2009 EE40 Homework 7 Due Oct 22 Thursday 12 00 noon in Cory 240 Reading Assignments Sections 6 6 6 8 of Hambley textbook Section 6 9 on DSP will be discussed later in course Section 14 10 of Hambley active filters Problem 1 Band Pass Filter Design Hambley P6 71 Suppose that we need a filter with the Bode plot shown in Figure a below We decide to cascade a highpass circuit and a lowpass circuit as shown in Figure b So that the second i e right hand circuit looks like an approximate open circuit across the output of the first i e left hand circuit we choose R2 100 R1 a Which of the components form the highpass filter Which form the lowpass filter b Compute the capacitances needed to achieve the desired break frequencies making the approximation that the left hand circuit has an open circuit load c Write expressions that can be used to compute the exact transfer function H f Vout Vin and use the computer program of your choice to produce a Bode magnitude plot for f ranging from 1 Hz to 1 MHz The result should be a close approximation to the desired plot shown in Figure a Problem 2 Series Resonance Hambley 6 75 Consider the series resonant circuit shown in the figure below Compute the resonant frequency the bandwidth and the half power frequencies Assuming that the frequency of the source is the same as the resonant frequency find the phasor voltages across the elements and sketch a phasor diagram 20 H 14 14 1000 pF Problem 3 Another RLC Combination Hambley P6 80 Other combinations of R L and C have behaviors similar to that of the series circuit For example consider the circuit shown in the figure below a Derive an expression for the resonant frequency of this circuit We have defined the resonant frequency to be the frequency for which the impedance is purely resistive b Compute the resonant frequency given 1 mH 1000 0 25 F c Using the computer program of your choice obtain a plot of the impedance magnitude of this circuit for f ranging from 0 95 to 1 05 times the

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