Download UNIVERSITY OF MASSACHUSETTS DARTMOUTH

UNIVERSITY OF MASSACHUSETTS DARTMOUTH
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 201
CIRCUIT THEORY I
RLC SERIES-RESONANT CIRCUIT
INTRODUCTION
A series-resonant RLC circuit is shown in Figure 1.
L
100m H
C
Rinductor
100 Ohm
0.022uF
Vsource
Rexternal
330 Ohm
10 V
1kHz
0Deg
Figure 1. A series resonant RLC circuit.
The circuit “resonates” at a single frequency determined by the expression
f 
0
1
2
1


Hz
LC 2
0
At the resonant frequency, the reactance of the capacitor and the reactance of the
inductor are equal and opposite, and, in effect, cancel each other out. This can be shown by
looking at the total series impedance of the circuit, Ztotal series at ω = ω0
Ztotal series = Rexternal + Rinductor + jω0L + 1/jω0C
Ztotal series = Rexternal + Rinductor + jω0L – jω0C since (1/j = -j)
if ω0L = ω0C
Ztotal series = Rexternal + Rinductor = R
This leaves the total “equivalent” impedance of the series circuit to be purely resistive!
PRELIMINARY DESIGN
Do your design work in your lab notebook! Submit a copy before you come into the lab!
1. Each group member will design and simulate a series RLC circuit that resonates at a
frequency equal to
f  N  2500Hz
0
where N is the last three non-zero digits of the group member’s UMD ID Number.
The formula for the resonant frequency is
f 
0
1
2
1


Hz
LC 2
0
Since there are 2 unknowns, L and C, you must choose 1 of them. For this case, each student
will use a 100 mH inductor.
The “quality factor”, Q, for the circuit is given by the expression
Q 

0
B

L
CR
2
where B = the bandwidth of the circuit in radians/sec. For this circuit, we will design for a Q = 5.
One last note. The inductor has a “built-in” resistance, RL. When you get the inductor,
measure the DC resistance with your digital multimeter. Subtract this measured value of
resistance from the series resistance necessary to obtain Q = 5.
For both the capacitor and resistor, use the standard component value that is closest to
your calculated value.
2. Once you have designed your circuit, construct it in MultiSim and run a simulation
using the Bode Plotter. Measure the resonant frequency and compare the measured value with
the desired design value. Measure both the lower and upper -3dB frequencies and calculate the
bandwidth B.
3. Calculate the value of Q and compare with the design value.
4. Make any modifications to the component values that you feel might be necessary
and simulate again until you are satisfied that your results are reasonable.
Your preliminary design and simulation results will be your
ticket into the lab!
LABORATORY PROCEDURE / RESULTS
1. Experimentally determine the resonant frequency for your circuit by measuring the
voltage across the resistor and adjusting the frequency of the function generator until that voltage
is at its maximum value.
2. Set up a table in your lab notebook to record the values of the amplitude and phase
shift of the voltage across the resistor with respect to the input voltage at frequencies of
f=0.1f0 f=0.5 f0 f=f0 f=2f0 f=10f0
Be sure to keep the input voltage constant at 1 volt peak!
3. If time permits, shut down your circuit and “exchange” the positions of the resistor and
the capacitor. Apply a 1 volt peak input voltage at the resonant frequency and measure the
voltage (amplitude and phase) across the capacitor. Compare this voltage with the input voltage
and comment on what you observed.
4. Each group member will submit Bode Plots of both the Gain and Phase of the output
voltage as a function of frequency. Compare with the Bode Plots from MultiSim7. Comment on
how well the experimentally obtained results compare with the theoretical results from MultiSim7.