ANADOLU UNIVERSITY
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
EEM 102 INTRODUCTION TO ELECTRICAL ENGINEERING
EXPERIMENT 8:
RLC CIRCUITS
Prepared by Prof.Dr. Atila BARKANA
EXPERIMENT 8
RLC CIRCUITS
OBJECTIVE:
To observe the response of RLC circuits.
PRELIMINARY WORK:
Calculate the resonant frequency w0, and the half power frequencies w1 and w2, where the
magnitude of the output voltage becomes
Vm
, of the parallel RLC circuit in part B and the
2
series RLC circuit in part C assuming the inductance is 200 H.
INTRODUCTION:
An inductor and a capacitor in series or in parallel show an interesting behavior.
Fig. 1. Parallel RLC circuit.
Y1 
1
1 1
1 

 jwC    j wC 

jwL
R R
wL 

Z eq  Ra 
1
Y1
The frequency at which Zeq becomes real is called the resonance frequency wo. Then the
circuit is said to be at resonance. For the circuit in Fig.1 in order Zeq to be real
wo C 
1
0
wo L
wo 
1
LC
 resonance frequency
Then
Y1 ( wo ) 
1
R
Z eq  Ra  R and Vo 
R
Vs
Ra  R
Note that at w  wo ,
Z L  jwo L
,
ZC   j
1
wo C
and their parallel equivalent
1
L
L
)
wo C
C
Zp 

 C 
1
1
0
jwo L.  j
j ( wo L. 
)
wo C
wo C
jwo L.( j
Hence these two elements act like an open circuit at w  wo .
At any other frequency
1
1
Y1
1
1
 j ( wC 
)
R
wL
Vo ( w) 
Vs ( w) 
Vs ( w)
1
1
Ra 
Ra 
1
1
Y1
 j ( wC 
)
R
wL
=
1
1 
1
Ra   j ( wC 
) 1
wL 
R
Vs ( w)
That is, the output voltage is maximum at w  wo , since the magnitude of the denominator is
minimum at this frequency.
Fig. 2. Series RLC circuit.
Z eq  Ra  Ro  jwL  j
1
wC
Again for the imaginary part to be zero,
( wL 
wo 
1
)= 0
wC
1
LC
In this case
Vo ( w) 
Ro
Vs ( wo )
Ra  Ro
Note that, at w  wo , the series combination of L and C results in
Z s  jwo L  j
1
0 
wC
Hence these two elements act like a short circuit at w  wo .
At any other frequency
Vo 
Ro
1
( Ra  Ro )  j ( wL 
)
wC
Vs
and
Ro
Vo ( w) 
( Ra  Ro  ( wL 
2
1 2
)
wC
Vs ( w) 
Ro
Vs ( wo )
Ra  Ro
That is, the output voltage is maximum at w  wo .
Since
Vo ( w) 
Ro
Vs ( wo )
Ra  Ro
the input and the output are at the same phase at resonance.
PROCEDURE:
A.1. Winding an Inductor:
Using the ferrite core and the laminated wire given to you, wind an inductor with the
number of turns N. Make sure the windings are tight and close to each other. Tape the
windings so they will not come loose. Make the following measurements:
1. D = The diameter of the coil.
2. l = The length of the coil in meters.
3. N = The number of turns.
Calculate the inductance of the coil using
L
N 2 A
l
(H )
where  air  4 *10 7 H / m,
A   r2 , r 
A   r2 
D
, r in meters.
2
2. Measure the inductance of your coil using the RLC meter.
B. Parallel Resonance:
1. Set up the circuit in Fig. 1. Use Ra =100 ohms, R=2200 ohms, C= 220 nF and the
inductor you wound.
2. Connect CH.1 of the oscilloscope between A and B to observe input signal.
3. Connect CH.2 to observe output signal.
4. Adjust the maximum (peak) value of Vs to Vp = 2 V
5. Starting at 1 KHz, increase the frequency until you find maximum output, and the
input and the output voltages are in phase.
6. Read the period of the source and calculate fo and wo, and the peak voltage of the
output Vm.
7. Calculate wo 
1
LC
.
Vm
8. Decrease the frequency slowly until the peak voltage of the output is equal to
,
2
and measure the period of the signal, T1. Calculate the half power frequency f1.
9. Increase the frequency slowly until the peak voltage of the output is equal to
Vm
and measure the period of the signal, T2. Calculate the half power frequency f2.
C. Series Resonance:
1. Set up the circuit in Fig. 2. Use R0=220 ohms, C = 1 nF and your inductor.
2. Repeat B-2 to B-9.
D. Effect of the Core on the Inductance:
1. Take out the ferrite core carefully from the coil. Measure the inductance now.
2. Put the iron core into the coil and measure the inductance.
2
,
EXPERIMENT 8
RLC CIRCUITS
Name: …………………………..
No :…………………………......
Table No:……………………….
REPORT
A. 1. Winding on Inductor:
D = ……………. meters,
r = ……………. meters
l = ……………. meters,
N = …………… turns
Calculate the following.
A   r 2 = ……………… meter2
L
N 2 A
l
( H ) = ………………….Henry
2. Lmeasured = ………………….Henry
B . 6. T = ……………. s
fo = ……………Hz
wo,measured = ……….. rad/s
Vm = …….. Volts.
1
7. wo,calculated 
 ……………………… rad/s
LC
8. T1= ……… s, f1= ………….KHz.
9. T2= ……… s, f2= ………….KHz
Bandwidth = BW = ………… Hz
Compare wo,measured and wo,calculated and explain the difference.
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
C. 2.
T = ……………. s
fo = …………… Hz
wo,measured = ……….. rad/s
wo,calculated 
1
LC
 ……………………… rad/s
Compare wo,measured and wo,calculated and explain the difference.
…………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
T1= ……… s, f1= ………….KHz.
T2= ……… s, f2= ………….KHz
Bandwidth = BW = ………… Hz
D. 1. Inductance without the core
Lair = …………….. Henry
2. Inductance with the iron core
Liron = …………….. Henry
Compare Lferrite, Lair, and Liron.
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Date:
Table No:
Name:
No:
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