Homework Assignment #8 Filter Problems

Homework Assignment #8 Filter Problems
Homework Assignment #8
Filter Problems
Circuits as Systems
ECEN 2260, Spring 2014
University of Colorado, Boulder
Prof. Robert Erickson
1. (50 points) You are given the R–L–C filter circuit of Fig. 1.
L
V1
+
–
+
R2
C1
R1
C2
Zout
V2
–
Figure 1 Filter circuit of Problem 1
The element values are:
•
•
•
•
•
R1 = 100 Ω
R2 = 10 Ω
L = 25 µH
C1 = 6.8 µF
C2 = 150 µF
(a) (20 points) Use the graphical construction method to construct the approximate magnitude asymptotes of k Z(s) k.
(b) (20 points) Use the graphical construction method to construct the approximate magnitude asymptotes of k G(s) k, where G(s) = V2 (s)/V1 (s).
(c) (10 points) Write an analytical expression for the approximate G(s) that corresponds to
the magnitude asymptotes you constructed in part (b). On semilog axes, construct the
phase asymptotes for this G(s), and label all break frequencies and asymptote slopes.
For both of the above magnitude plots:
• Construct the magnitude asymptotes on semilog paper, to scale
• Give analytical expressions (in terms of L, R1 , R2 , etc.) for each asymptote, corner
frequency, and Q–factor as appropriate
• Give numerical values for each asymptote slope, corner frequency, and for the Q–factor
2. (50 points) An op-amp filter design.
+ 20 dB
20 Hz
500 Hz
– 20 dB/dec
+ 20 dB/dec
5 kHz
20 kHz
– 20 dB/dec
Figure 2 Filter circuit of Problem 2
Design an op-amp inverting amplifier circuit having the Bode plot magnitude asymptotes
shown in Fig. 2. You should specify realizations of the impedances in the standard inverting amplifier circuit, using only resistors and capacitors. Specify all resistor and capacitor
values in your circuit, and sketch the complete schematic of your design. To facilitate grading,
choose the smallest resistor value in your design to be equal to 1 kΩ.
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