University of California, Berkeley
Fall 2010
EE 42/100
Prof. A. Niknejad
Problem Set 6 [rev A]
Due Friday (5pm), October 22, 2010
1. We are given a black box with input and output terminals. All we know about it is
that (a) it is a linear timeinvariant system, (b) the step response is the waveform
shown below.
V
in
V
out
Mysterious
Box
Step Input
Step Response
t
V
1
t
V
Input Waveform
t
V
1
1
2
1
Draw the output waveform that would result from the input waveform above. Hint:
First, break the input waveform into several timeshifted step functions. Then apply
linearity/superposition.
(Note: It would be pretty tough to build a LTI system that behaves this way. But
the triangular step response makes the drawing easier. When you’re done with your
drawing, imagine what it would look like if the step response were an exponential
decay, like most RC circuits).
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2. A RC circuit is stimulated by a 1 V step voltage at time
t
= 0.
R
1
= 200 kΩ and
C
1
= 100 nF.
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 Fall '07
 Boser
 LTI system theory, RC circuit, Impulse response, Exponential decay

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