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example: 12.10-2
Standard test signals such as square wave, triangular wave, sinusoidal wave, etc. are routinely used 
in electronics, communication and allied areas for a variety of purposes. It is rather easy to generate 
high quality square waves in electronic circuits. It is not so easy to make pure sinusoids. One of the 
commonly used methods to generate low power sinusoidal signals of high waveform quality is to 
generate a good square wave and pass it through a narrow band-pass filter with a large Q factor. The 
centre frequency of filter is adjusted to be equal to the frequency of square wave.
This example deals with applying a series RLC circuit for this purpose. Consider the circuit in 
Fig. 12.10-12 .
v
o
(
t
)
v
s
(
t
)
v
s
(
t
)
25.3 mH
20 
Ω
(volts)
µ
1 F
π
4
–
–
+
+
1
2 Time (ms)
π
4
–
Fig. 12.10-12 
CircuitandinputwaveformforExample:12.10-2
This circuit is used to filter the square wave shown and deliver a sine wave to the 20 
W
load 
resistance. We will accept the fact that the square wave shown can be expressed in the form of a series 
as follows.
v t
n
t
S
n
n odd
( )
=
×
=
∞
∑
1
2
10
1
3
sin
p
(a) Find and plot the steady-state output waveform expected from the circuit.
(b) If the quality factor of the inductor used was measured to be 50 at 1 kHz and the test square 
wave was obtained from a function generator which has an output resistance of 50 
W,
find and 
plot the steady-state output voltage waveform that will be observed.
Solution (a)
The circuit is the familiar series RLC circuit and the frequency-response function for resistor voltage 
in such a circuit has been shown to be
V j
V j
j
j
R
S
n
n
n
n
n
n
(
)
(
)
(
)
(
)
w
w
xww
w
w
xw w
xww
w
w
x w w
=
−
+
=
−
+
2
2
2
4
2
2
2
2 2
2
2
2
∠
∠
= −
−
−
f
f
p
xw w
w
w
R
R
n
n
where
rad
2
2
1
2
2
tan
We define x
n
=
ω ω
and express the above function as 

---

12.42


SeriesandParallel
RLC
Circuits
V j
V j
j
x
x
j
x
R
S
(
)
(
)
(
)
.
w
w
x
x
=
−
+
2
1
2
2
The input signal is a sum of sinusoids with odd multiples of 1 kHz as their frequencies. Thus, the 
separation between frequencies is large and it is quite possible that x may turn out to be quite large 
compared to 1 for many of the sinusoidal components. We calculate 
w