Villanova University
ECE 2055 Electrical Engineering II Lab
C. McKeough
Spring 2012
Experiment 8 – Frequency and Phase of Series RLC Circuit
Introduction
This experiment continues with the frequency characteristics introduced in the previous experiment.
The circuit introduced this week is the series RLC shown in Fig. 1. A PSpice simulation of this circuit was
executed, and a plot of VR versus ω, and a plot of arg(VR) versus ω is shown in Figure A1 in the Appendix.
A
B
2
R
FG
L
1
C
C
0
Figure 1
An important frequency parameter for the series RLC circuit is the resonant frequency, denoted ωo.
The resonant frequency for the series RLC is defined as ωo = 1/LC. If the input source frequency ω is
set to ωo then the phase of the source current relative to the phase of the source voltage, is 0 degrees.
Also, the magnitude of the source current is at a peak.
A simplified derivation, for the series RLC circuit, says, that if VL =  VC at the frequency ωo, where VC
is the phasor voltage across the capacitor, and VL is the phasor voltage across the inductor, then
Kirchhoff’s voltage around the loop says
Vs = VR + VL + VC = VR  VC + VC = VR
Vs = VR =R I
Thus the current I is in phase with the source voltage Vs.
Also, if if VL =  VC, then
XC =1/ωoC = XL = ωoL
Thus
ωo = 1/LC
Exercise 1: Series RLC Circuit –Resistor Voltage
1. Design a series RLC circuit with an ωo of 20 krad/s + 5 krad/s and an input impedance magnitude
Zin of 100 Ω + 10 Ω.
2. Wire the circuit as shown in Fig. 2 on the next page. Refer to Appendix 1 for setting the FG.
3. Display vS(t) and vR(t) on the scope. Vary the source frequency and measure:
- the resistor voltage amplitude
- the resistor voltage phase
Do this for the following cyclical frequencies:
200, 500, 1k, 2k, 3k, 5k, 10 k, 20 kHz
(The source phase is assumed zero degrees.)
4. Sketch in your notebook the resultant magnitude characteristic and phase characteristic for the
resistor voltage.
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Villanova University
ECE 2055 Electrical Engineering II Lab
C. McKeough
Spring 2012
5. Examine your magnitude plot. Find the frequency where the magnitude has a peak value. What
frequency is it?
6. Adjust the source frequency until the phase between the source voltage and the resistor voltage
equals exactly 0 degrees. Record the frequency as f0(meas) in Hz. The value should be close to the
predicted resonant frequency f0 = (1/2)ωo.
7. Examine your phase plot. Find the frequency where the phase is 0. Again, record the
frequency.
ZL
1
Vs
2
1 cos w t
1 V peak
ZC
0 V dc offset
ZR
VR
0
The following is the symbol for the scope probe.
Scope channel
Vc
Figure 2
8. From step 6, calculate the quantity VR / R, at the resonant frequency. The quantity is I, the
magnitude of the current. Now, divide this value of I into 1 volt – the result is the magnitude of
the circuit impedance of the circuit. Is it close to 100 ?
9. Comment on any significant differences between it and the desired value.
Exercise 2: Series RLC Circuit – Capacitor Voltage
1. Reconfigure the circuit from Exercise 1 so the circuit looks like that in Fig. 3.
2. The scope measures source voltage vs(t) and capacitor voltage vC(t).
ZR
1
Vs
ZL
2
Vc
1 cos w t
1 V peak
ZC
0 V dc offset
0
Figure 3
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Villanova University
ECE 2055 Electrical Engineering II Lab
C. McKeough
Spring 2012
3. Vary the source frequency as done previously and measure the capacitor voltage amplitude and
the capacitor voltage phase (the source phase is assumed zero degrees).
4. Sketch in your notebook the resultant magnitude characteristic and phase characteristic for the
capacitor voltage.
5. Adjust the source frequency until the phase between the source voltage and the capacitor
voltage equals exactly 90 degrees. Again, record the frequency – it should be close to the
measured resonant frequency f0(meas).
6. Comment on any significant differences between it and the desired value.
Report
Exercise 1 – Circuit Impedance
a) From the recorded data of VS, VR, and (VR) compute the source current magnitude, Iin, from VR
and R. Make a table, with the following headings, and place the results in it. Note: Zin is the
magnitude of the input impedance of the circuit, and equals VS divided by Iin.
Table 1. Measured Voltage Data and Computed Impedance Data
f
Measured VR
Iin
Zin
(Zin)
(Hz)
(V)
(mA)
(Ω)
(deg)
200
b) Run a PSpice simulation on the circuit. From the simulation, plot (1) VR versus frequency in Hz,
and (2) phase of VR versus frequency in Hz.
c) Place your measured data, as prominently marked data points, on the above two graphs.
d) Next, from the PSpice simulation, plot (1) Zin versus frequency in Hz, and (2) phase of Zin versus
frequency in Hz.
e) Place your above computed data, as prominently marked data points, on these two graphs.
f) Using your calculator, compute the complex impedance, Zin, of the circuit at these frequencies:
200, 500, 1k, 2k, 3k, 5k, 10 k, 20 kHz.
Put the calculated results into polar form, i.e., Zin = ZinZin and place the results in table form
such as:
Table 2. Theoretical Values of Impedance
f
Zin
Zin
(Hz)
(Ω)
(deg)
200
g) Comment on any significant discrepancies.
Exercise 2 – Capacitor Voltage
a) Run a PSpice simulation, plotting (i) VC versus frequency in Hz, and (ii) phase of VC versus
frequency in Hz.
b) Place your measured data, as prominently marked data points, on the above two graphs.
c) Comment on any significant discrepancies.
d) Derive the equation for phasor VC in terms of R, L, C, , and VS. Note: This is an algebraic
equation – no numbers.
Parts List
Resistors: all 5%, ¼ W
Capacitors: 0.005 F to 0.1 F Inductors: 30 mH to 50 mH
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Villanova University
ECE 2055 Electrical Engineering II Lab
C. McKeough
Spring 2012
Appendix 1 FG settings
For the remainder of the semester reset the FG default display as follows.
Enter the following commands on the front panel of the FG. The readout will be the actual peakto-peak value.
Keys to Press
Shift Menu
On/Off
→ → →
↓
↓
→
Enter
What is in the Display
A: MOD MENU
D: SYS MENU
1: OUT TERM
50 OHM
HIGH Z
ENTERED
Appendix 2 Current and Phase Characteristics for Series RLC
The netlist is:
Series RLC Frequency Response
Vs 1 0 AC 1
R 1 2 150ohms
L 2 3 25mH
C 3 0 0.01uF
.AC DEC 100 1000Hz 100kHz
.Probe
.end
The probe plots below are the magnitude of the resistor voltage versus frequency and phase versus
frequency in Hz.
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Villanova University
ECE 2055 Electrical Engineering II Lab
C. McKeough
Spring 2012
Figure A1
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