ECE360 HOMEWORK #1 DUE: FRIDAY, SEPTEMBER 7, 2007
Problem 1.1
o
1R2
v1v2
C1C2
+
−
R
i
+
−
v (t)v (t)
Derive a state-space model for the above electric circuit in the form:
"˙v1
˙v2#="a11 a12
a21 a22 #" v1
v2#+"b1
b2#vi(t)
vo=hc1c2i"v1
v2#+ [d]vi(t)
Problem 1.2
Using the results of Problem 1.1, derive the input-output differential equation of the circuit in the
form:
d2vo
dt2+αdvo
dt +βvo=γvi(t)
Problem 1.3
(a) Apply the definition of the Laplace transform and show that:
Lne−ato=1
s+a
(b) Use the linearity property of the Laplace transform and show that:
L {cosh at}=s
s2−a2
L {sinh at}=a
s2−a2
Problem 1.4 (Problem B-2-4)