EE42/100 Problem Set 7
Assigned Tuesday October 18, 2005
Due at 12:00 noon Thursday October 27 in box in 240 Cory Hall.
Note: Midterm 2 will be in class Tuesday November 8
Problem 1. (10 points) Hambley P14.8 (resistive op-amp circuit)
Problem 2 (25 points) Hambley P14.17 (various ideal op-amp circuits)
Problem 3 (25 points) (Orcad/PSpice: RC filters put in series)
Suppose you put several RC filters in series – how will that affect the filter
characteristics?
a. (Review from Lab 5) What is the break-point (the frequency at which the output
voltage is 3 dB below the input voltage) for a highpass RC filter having R = 10
k and C = 0.1 F? Draw the circuit and find the break-point frequency.
b. Now put this filter in series with another RC filter. If you try to analyze the
output of this series combination, you’ll find that you get a difficult algebraic
tangle – so let’s simulate it. Enter using Orcad the series combination of an input
1-volt rms AC voltage source; RC lowpass filter #1 having R = 10 k and C =
0.1 F connected to the voltage source; and followed by a highpass RC filter #2
having R = 20 k and C = 0.1 F connected to the output of the lowpass filter.
c. Draw the circuit and simulate in PSpice the output voltage as a function of
frequency. Print and hand in your circuit and plot (use logarithmic frequency and
voltage scales).
d. Now use the same source and filters but between the two filters assume that
there’s an ideal op-amp voltage follower (or buffer) – an active circuit having an
infinite input impedance and an output voltage that exactly equals its input
voltage (see p. 643 of Hambley for the op-amp circuit that does this). This has the
effect of making the characteristics of the first (lowpass) filter independent of the
circuit that follows it (the highpass filter).
Unfortunately, PSpice does not contain an ideal op-amp so you can’t easily
simulate the voltage follower. Instead, work algebraically, using the opencircuited transfer functions of the lowpass and highpass filters, assume that they
don’t change when the filters are coupled with a voltage follower, and find the
transfer function of the combination. Plot the approximate output versus
frequency (use logarithmic scales and straight-line approximations where
appropriate).
Problem 4 (10 points) (Current source)
Show that the ideal op-amp circuit below produces a current I = Vin/R through the load,
and therefore approximates a current source that is controlled by the input voltage Vin.
(Note: the problem with this current source is that the load is “floating” -- neither
terminal of it is at ground potential, which is often what is desired.)
Vi n
LOAD
R
I
Problem 5 (20 points) (First-order active lowpass filter)
The figure on the left below shows one type of first-order active filter that employs an
ideal op-amp. The components selected for Zi and Zf determine whether the filter is
lowpass or highpass, but one of the components must be reactive. The transfer function
for the filter, denoted by the complex quantity H(), is
H() = Vo/Vi = -Zf/Zi
The figure on the right shows a corresponding lowpass active filter. Find an expression
for the transfer function for this filter, in terms of  and the passive components shown.
What is the DC gain of the filter? What is the break frequency of the filter? Sketch the
magnitude of the transfer function as a function of frequency, using log scales. How does
this filter differ from the simple passive RC lowpass filter that you studied in the lab?
Cf
Zf
Rf
Zi
+
Vi
-
+
+
Vo
-
Vi
-
Ri
+
Vo
-