MEMORIAL UNIVERSITY OF NEWFOUNDLAND
Faculty of Engineering and Applied Science
Eng. 3821 Circuit Analysis
Exp. 3821-2 Step Response of RL, RC and RLC Circuits
Instructor: E. Gill
PURPOSE
1.
To study the response of RC, RL and RLC circuits when energized by an independent
voltage source.
INTRODUCTION
Many phenomena that occur in electric circuits involve or produce time-dependent variables.
When a RC, RL, or RLC circuit is suddenly energized or de-energized, a transient phenomenon,
which dies out as the circuit approaches it steady-state operation, occurs. This is because of the
way in which inductors and capacitors store energy and resistors dissipate it. The exact nature of
the transients depends on the values of R, L and C as well as on how they are combined in a
circuit. As you progress in your study of circuits you will meet instances where particular
transient responses are beneficial and desired and, likewise, instances where such responses are
detrimental to desired circuit behaviour.
The steady state response of the circuit, which is determined by the external source, is reached
only after a transient time interval. It has also been discussed in the class notes, that the response
of RLC circuits may be under damped, critically damped or over damped.
PRELAB
1. Study Section 4 of the PSpice Tutorial. It contains many ideas relevant to this prelab.
2. The circuit of Figure 1 is excited by a square wave voltage of 4V (peak to peak) and which
has a frequency of 100 Hz. In PSpice, use VPULSE to create this voltage waveform by
setting V1 to 0 and V2 to 4. Use a pulse width of 5ms. (What is the pulse period here?) Use
PSpice to determine the transient response (voltage across the capacitor) of the circuit. Limit
your transient response plot to one cycle of the source voltage. This may be done by setting
the "Run to time" parameter in the "Edit Simulation" window to be of the same length as the
period of the VPULSE. Obtain the response for the following two RC combinations:
R=3.3 kΩ ; C=0.1 µF;
R=3.3 kΩ ; C=0.22 µF
1
Calculate the time constants using the circuit parameters. Also, determine them from the plots.
Remember the response changes by a factor of 1/e during one time constant.
R
V1
C
Figure 1 RC circuit with square wave input.
3. The circuit of Figure 2 is excited by a square wave voltage of 4V (peak) having a frequency 5
kHz. Again, create the waveform so that the pulse width is half the period. Use PSpice to
determine the step response (voltage across the resistor) of the circuit. Limit your transient
response plot to one cycle of the source voltage. Obtain the response for the following two
RL combinations using Rbreak:
R=100 Ω ; L=1.0 mH;
1
L
R=220 Ω ; L=1.0 mH
2
V1
R
Figure 2 RL circuit with square wave input.
4. The circuit of Figure 3 is excited by a symmetrical square wave voltage of 4V (peak) and
frequency 500Hz. Using PSpice obtain the plot of the variation of the voltage across the
capacitor. Assume zero initial conditions. Limit the response to two cycles only. Do your
simulations for the following two combinations.
R=10Ω, L=2.2 mH, C=0.1µF;
R=100Ω, L=2.2 mH, C=0.1µF;
2
R
1
L
2
C
V
Figure 3 RLC circuit with square wave input.
Find the frequency of the oscillations using the circuit parameters. Also, determine them from
the plot.
EXPERIMENT
Preliminaries: Setting up the Equipment
Set the controls on the function generator to output a square wave with an amplitude of 4V and a
frequency of 100 Hz. Connect the output of the function generator to channel 1 of the scope.
Adjust the scope to auto trigger and to use internal triggering off channel 1. Why do we trigger
the scope with the function generator output instead of triggering off the voltage across one of
the circuit elements? There may be a trigger slope button on the scope; you can use this to view
a different portion of the voltage trace.
Use the time base and amplitude controls to adjust the scope display. Likewise the vertical and
horizontal positioning may be adjusted to move the curve. Don't forget to check the ground level
of the scope to make sure amplitude measurements are accurate.
1.1
Construct the circuit of Figure 1. Adjust the function generator to provide 4 V (peak),
100Hz symmetrical square wave. Note that the use of this signal enables you to simulate the
effect of repeatedly energizing the RC circuit and the waveform in the oscilloscope may be
considered similar to the step response of this circuit. Sketch to scale the first half of the input
square wave and voltage across the capacitor. Determine the time constant of the circuit by
observing the waveform. Repeat the measurement for the second half of the input signal. Do
your experiment for the following two combinations:
R=3.3kΩ ; C=0.1µF
R=3.3kΩ ; C=0.22µF
2.1
Construct the circuit of Figure 2. Adjust the function generator to provide 4 V (peak),
5KHz symmetrical square wave. Sketch to scale the first half of the input square wave and the
voltage across the resistor. Determine the time constant of the circuit. Do your experiment for
the two combinations of R and L as in prelab.
3
3.1
Construct the circuit of Figure 3. Adjust the function generator to provide 4 V (peak),
500Hz symmetrical square wave. Note that the use of this signal enables you to simulate the
effect of repeatedly energizing the RLC circuit and the waveform in the oscilloscope may be
considered similar to the step response of this circuit. Sketch to scale one half of the input
square wave and the voltage across the capacitor. Do your experiment for the two combinations
of the circuit elements as in prelab. For the response which is more oscillatory, try to estimate the
frequency of oscillation.
REPORT
General
Present all results in a clear and coherent manner. Use tables, graphs and diagrams as
appropriate in addressing the particulars of the lab requirements listed below. Also, summarize
your findings in a brief conclusion.
Analysis
1.
Based on your experiments with the two RC circuits, discuss the effect of change in R, C
on the nature of the response and final value of the capacitor voltage. Compare the experimental
plot with that obtained using PSpice (PreLab) and comment on the discrepancies.
2.
Using your experiment with the RL circuits, discuss the effect of change in R, L on the
nature of the response, final value of the resistor voltage and final value of the current in the
circuit. Compare the experimentally determined time constant with that obtained using PSpice
(Prelab) and comment on the discrepancies.
3.
Compare the response of the RLC circuits obtained from the experiment with the PSpice
simulation. Discuss the differences between the types of response for the two circuits. Compare
the experimentally determined frequency of oscillation with the theoretical value.
4