 Department of Electrical & Computer Engineering
Course ECSE291
EXPERIMENT 5
Frequency Response
20032004
1
Objective:
•
To study the frequency response of simple RLC circuits.
Preparation:
1.
Determine the transfer function H(jw) = V
o
/V
i
for the circuit shown in Fig. 1.
(a)
The magnitude and phase of H(jw), viewed as functions of frequency,
together specify the frequency response of the circuit. Note particularly
that if the amplitude of the input sinusoid V, is held constant as its
frequency w is varied, in the steady state the output sinusoidal amplitude
will be linearly proportional to H(jw). In graphical presentation, the
magnitude of H(jw) is usually plotted as 20log
10
H(jw) versus log
10
w,
where the unit for 20log
10
H(jw) is the decibel (dB).
 See Section 14.2 in Ref. 1.
(b)
Find the relationship for : (i) the cutoff frequency and the time constant,
and (ii) the DC gain and the steady state of the unit step response.
(c)
If the input v
i
(t) = 0.3sin(500
Π
t +
θ
) volts, where
θ
is constant, what is
v
o
(t)?
(d)
Consider an input v
i
(t) consisting of two additive components: a sinusoidal
signal of 250 Hz and an unwanted sinusoidal component (noise) of 25
kHz. If both components have an amplitude of 0.30 volts, then
v
i
(t) = 0.30sin(500
π
t +
θ
1
)
+ 0.30sin(50 000
π
t +
θ
2
) volts
where
θ
1
and
θ
2
are constants. By using the Principal of Superposition
show that v
o
(t) is approximately equal to the lowfrequency component.
2.
Determine the transfer function H(jw) = V
o
/V
i
of the circuit shown in Fig. 2. Plot
the amplitude and phase frequency response, showing the cutoff frequency in Hz.
Find the relationship between the time constant of the circuit and the cutoff
frequency.
3.
Determine the transfer function H(jw) = V
o
/V
i
of the circuit shown in Fig. 3.
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 Winter '03
 Khazaka
 Highpass filter, Lowpass filter, Sine wave

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