ECE 232 Homework I
Due date: 10-April-2015
Q1) For the circuit second order circuit below the resistance value R = 3 Ohm,
the capacitance value C = 0.5 Farad and the inductance value L = 1 Henry.
L
R
IL(t)
+
Vin(t)
Vc(t)
C
-
For the following cases use Laplace transformation to find the results
a) Assume Vin(t) = Sin(t) Volt when t>0 and the initial conditions for the
capacitor voltage VC(0) = 0 Volt and inductor current IL(0) = 0 Ampere.
Find VC(t) when t>0.
b) Assume Vin(t) = u(t) Volt (unit step function) when t>0 and the initial
conditions for the capacitor voltage VC(0) = 0 Volt and inductor current
IL(0) = 0 Ampere. Find VC(t) when t>0.
c) Assume Vin(t) = δ(t) Volt (impulse function) when t>0 and the initial
conditions for the capacitor voltage VC(0) = 0 Volt and inductor current
IL(0) = 0 Ampere. Find VC(t) when t>0.
d) Assume Vin(t) = 0 Volt when t>0 and the initial conditions for the
capacitor voltage VC(0) = 3 Volt and inductor current IL(0) = 1 Ampere.
Find VC(t) when t>0.
Q2) For the circuit second order circuit below the resistance value R = 1 Ohm,
the capacitance value C = 0.5 Farad and the inductance value L = 0.5 Henry.
L
IL(t)
V1(t)
R
+
Vc(t)
C
V2(t)
-
For the following cases use Phasor transformation to find the results:
a) Assume V1(t) = Cos(2t) Volt and V2(t) = Sin(2t) Volt when t>0. Find VC(t)
and power dissipated over the resistor R when sinusoidal steady state
conditions are reached.
b) Assume V1(t) = Cos(2t) Volt and V2(t) = Sin(t) Volt when t>0. Find VC(t)
and power dissipated over the resistor R when sinusoidal steady state
conditions are reached.
100(s + 2)
.
(s +10)(s + 20)
Find the magnitude characteristics of the frequency response of H(jw).
Find the phase characteristics of the frequency response of H(jw).
Draw the approximate magnitude response in dB (decibel) in logarithmic
scale. While obtaining the approximate magnitude response show all the
approximations and in your plot show all the important points and details.
Draw the approximate phase response in dB in logarithmic scale. While
obtaining the approximate phase response show all the approximations
and in your plot show all the important points and details.
Q3) For the transfer function H (s) =
a)
b)
c)
d)
100s
.
s +100s +100 2
Find the magnitude characteristics of the frequency response of H(jw)
Find the phase characteristics of the frequency response of H(jw)
Find the resonant angular frequency.
Find the damping ratio.
Find the corner frequencies.
Draw the magnitude response in linear scale. While obtaining the
magnitude response show all the important points and details.
Draw the phase response linear scale. While obtaining the phase response
show all the important points and details.
Q4) For the transfer function H (s) =
a)
b)
c)
d)
e)
f)
g)
2