Passive Electronic Components and Circuits
Laboratory 10
Time response of the RC circuits
Objective:
o Study the transient response of a RC circuit and understand the time constant concept
using pulse waveforms.
Equipment:
o
o
o
o
Digilent Electronics Explorer Board,
Digital Multimeter,
Resistors,
Capacitors.
Theoretical support:
o Lecture 7 (Microsoft Power Point Support).
Prelab:
1. Describe the transient behavior of a RC circuit: charging and discharging a capacitor.
2. Describe the meaning of the time constant.
Problems:
1. The following circuit is given:
vo
Fig.1. RC circuit.
For R=1kΩ, C=1nF and for the input signal describe by the waveform from Fig.2:
1
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Passive Electronic Components and Circuits
1.0V
0.8V
0.6V
0.4V
0.2V
0V
0s
2ms
4ms
V(V1:+)
6ms
8ms
10ms
Time
Fig.2.
a.
b.
c.
d.
e.
Determine the signal period,
Compute the value of the time constant,
Compute the voltage across the resistor. Plot the signal.
Compute the voltage across the capacitor. Plot the signal.
Discuss the situation when the pulse width tp≅5τ.
For R=1kΩ, C=1nF and for the input signal describe by the waveform from Fig.3:
1.0V
0.8V
0.6V
0.4V
0.2V
0V
0s
10ms 20ms
V(V1:+)
40ms
60ms
80ms
Time
Fig.3.
a.
b.
c.
d.
e.
Determine the signal period,
Compute the value of the time constant,
Compute the voltage across the resistor. Plot the signal.
Compute the voltage across the capacitor. Plot the signal.
Discuss the situation when the pulse width tp≫5τ.
For R=1kΩ, C=1nF and for the input signal describe by the waveform from Fig.4:
1.0V
0.8V
0.6V
0.4V
0.2V
0V
0s 0.1ms
0.3ms
V(V1:+)
0.5ms
0.7ms
0.9ms
Time
Fig.4
2
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Passive Electronic Components and Circuits
a.
b.
c.
d.
e.
Determine the signal period,
Compute the value of the time constant,
Compute the voltage across the resistor. Plot the signal.
Compute the voltage across the capacitor. Plot the signal.
Discuss the situation when the pulse width tp≪5τ.
Lab work:
1. Set up the circuit shown in the Fig.1 with the component values R=1kΩ and C=1µF.
Switch on the Digilent Electronics Board Power Supply.
2. Open the application “Arbitrary Waveform Generator” from the Waveform Generator
Menu and apply a 1V peak-to-peak square wave as input voltage to the circuit.
3. Open the application “Scope” from the Waveform Generator menu. Make sure the input
signal is read on channel 1 of the Scope module, the output signal on channel 2, and the
“Base” Time and “Range” are properly set. Also, using Kirchhoff’s laws, determine the
mathematical equation that describe the signal vR(t). Using this relationship, plot on the
Mathematical channel this signal.
4. Observe the response of the circuit for the following three cases record the results.
a. tp≅5τ: Set the frequency of the input signal such that tp =5τ. Since the pulse
width is exactly 5τ, the capacitor should just be able to fully charge and discharge
during each pulse cycle (See the waveform from Fig.2). From the Fig.2 determine
the time constant.
b. tp≫5τ: Set the frequency of the input signal such that the capacitor has enough
time to fully charge and discharge during each cycle of the square wave. An
approximately value of this frequency is presented in Fig.3. Determine the time
constant from the waveforms obtained on the Oscilloscope.
c. tp≪5τ: Set the frequency of the input signal such that the capacitor does not have
time to charge significantly before it is switched to discharge, and charge again.
Set the frequency accordingly with the frequency of the signal from Fig.4.
5. Repeat the steps using other values for the capacitance of the capacitors and for the
resistance of the resistors. Compute the time constant in each case and determine the
period of the square waveform for the three cases presented above.
Questions for Lab Report:
1. Discuss the effects of changing component values.
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