ME 530.241: Electronics and Instrumentation
Lab 5: Impedance, Phasor Solution of Circuits with Sinusoidal
Excitation, and RC Circuits
Louis L. Whitcomb∗
Department of Mechanical Engineering
The Johns Hopkins University
Spring 2011
Apparatuses Multimeter, Tektronix PS280 DC Power Supply, Tektronix TDS3014B oscilloscope, Tektronix CFG 253 function generator, leads, breadboard
1
Pre-Lab Exercises
SHOW ALL YOUR WORK. No credit will be given unless your work is completely (and neatly)
presented.
1. Following the methods given in Chapter 4.4 and our Friday 3/5/2010 lecture, derive the
extression for the complex impedance of an inductor with inductance of L Henreys.
2. Exercise 4.43 of [1].
3. Exercise 4.59 of [1].
4. Exercise 4.51 of [1].
5. Exercise 4.56 of [1].
6. Frequency:
(a) Given a period p in units of seconds, what is the formula for the corresponding frequency
fHz in units of Hertz (i.e. cycles/second)?
(b) Given a frequency fHz in units of Hertz (i.e. cycles/second), derive the formula for this
frequency in units of radians/second, fRP S .
(c) Given a frequency fRP S in units of radians/second, derive the formula for this frequency
in units of Hertz (i.e. cycles/second), fHz .
(d) For periodic waveforms of the following periods, compute the frequency in (a) Hertz and
(b) radians/second.
i.
ii.
iii.
iv.
p
p
p
p
=
=
=
=
1 second.
0.1 second.
6.28 second
0.0628 second
7. Consider the first order low-pass filter circuit shown in Figure 1.
∗
c Louis L. Whitcomb — do not reproduce without permission.
Copyright 2004-2011 1
(a) Draw the the circuit shown in Figure 1 (just the circuit, omit the probe leads).
(b) Use phasor notation and impedance methods to analyze the circuit to determine the
magnitude and phase of the output voltage VC (t) for an input voltage from the signal
generator VS (t) = 1.0 cos(ωt).
i. Give an expression for the magnitude of the output as a function of frequency.
ii. Give an expression for the phase of the output as a function of frequency.
(c) Use your results from the previous question to:
i. Compute the 3dB frequency in units of Hz - i.e. the frequency at which VC (t) =
√1 VS (t). This will be f3dB for Question 6 in Section 2 of the lab.
2
A. Compute
B. Compute
ii. Compute the
iii. Compute the
f3dB in units if radians/sec.
f3dB in units if Hertz.
magnitude of the output at the 3dB frequency.
phase of the output at the 3dB frequency.
(d) Plot (using Matlab, Excel, or your favorite plotting method) the following data.
The X-axis of your plot should be frequency in Hz, with an X-axis range of 0 Hz to 10
kHz.
Later in this lab, you will measure experimentally the magnitude and phase response of
this circuit, and compare the experimentally observed magnitude and phase response to
the magnitude and phase response predicted by your analysis here.
i. Magnitude (volts) versus frequency (Hz).
ii. Phase (degrees) versus frequency (Hz).
8. Repeat Question 7 for the case where the resistor and capacitor positions are switched. The
input is VS (t) and the output of interest is VR (t). This circuit is known as a first order
high-pass filter circuit.
2
RC Low Pass Filter
In this section of the lab you will implement and test the first order low-pass filter that you
analyzed in Section 1 Question 7
Retrieve one 0.022 µ F capacitor and one 10 KΩ resistor from the supply cabinet.
Set up your oscilloscope and probes to show VC (t) (on CH2) and VS (t) (on CH1).
1. Measure and report the actual values for your capacitor and resistor.
2. Compute and report the error between the labeled values and the actual measured values for
your capacitor and resistor.
3. Using your breadboard, carefully place them in series and to the instruments as shown in the
Figure below. Set your function generator to produce a sinusoidal wave of about 1kHz at
with 1 Volt magnitude.
4. Adjust the frequency of the sine wave to high frequencies and low frequencies. What do you
observe in the response VC (t) as you vary the input frequency?
5. Using the labeled values for your capacitors and resistors, compute the 3dB frequency in
units of Hertz (cycles/second) and also in units of radians per second. Then complete the
two frequency columns in Table 1.
2
probe to channel 1
Connect Scope Probe Tips Her e
pos
Function
Generator
neg
resistor
Oscilloscope
capacitor
Connect Scope Probe Gro unds Her e
probe to channel 2
Figure 1: An RC low pass filter. Connect the input, VIN (t) to the Signal Generator, and measure
both the input and the output, VC (t), with the oscilloscope.
6. Measure the magnitude of the input and output sinusoids at the different frequencies listed
in Table 1. In each case, adjust your scope time scale to show at least one (but not more
than three) complete cycles of the sine wave. Adjust the offset of each channel so that both
signals are centered on the screen vertically.
Adjust the vertical volts / div scale so that both channels are on the same volts / div scale
and “big” on the screen.
Record the scope screen using the web interface or the printer for your records.
Use your oscilloscope to adjust the signal generator to these frequencies as accurate as possible,
and then measure and record the actual frequency.
7. For each of the above scope plots:
(a) Determine the magnitude response of the filter, i.e. the ratio of the magnitude of the
VC (t) sinusoid versus the magnitude of the VS (t) sinusoid.
(b) Determine the phase of the response of the filter, i.e. the phase of the VC (t) sinusoid
relative to the phase of the VS (t) sinusoid.
8. Plot your results and compare the experimentally observed magnitude and phase response to
the magnitude and phase response predicted by your pre-lab analysis.
(a) Plot your experimentally observed output magnitude (Volts) versus frequency (Hz) data
points (not a curve). On the same graph, plot the magnitude curve you derived in your
pre-lab analysis of this circuit.
(b) Describe briefly how the experimentally observed magnitude compares to your analysis
prediciton.
(c) Plot your experimentally observed phase (degrees) versus frequency (Hz) data points
(not a curvce). On the same graph, plot the phase curve you derived in your pre-lab
circtui analysis of this circuit.
(d) Describe briefly how the experimentally observed phase compares to your analysis prediciton.
3
4
fin = 8.0 f3dB
fin = 4.0 f3dB
fin = 2.0 f3dB
fin = f3dB
fin = 0.5 f3dB
fin = 0.25 f3dB
fin = 0.125 f3dB
Frequency
Frequency
Rad/Sec
Frequency in Hertz
(cycles/sec)
Input Magnitude
(Volts)
Output Magnitude
(Volts)
Table 1: Experimental Data for Low Pass Filter
in
Output Phase (Degrees)
3
RC High Pass Filter
In this Section you will consider the case of the first order high-pass filter that you analyzed
in Section 1 Question 8.
In this case, the input is VS (t) and the output is VR (t).
1. Using the labeled values for your capacitors and resistors, compute the 3dB frequency in
units of Hertz (cycles/second) and also in units of radians per second. Then complete the
two frequency columns in Table 2.
2. Measure the magnitude of the input and output sinusoids at the different frequencies listed
in Table 2. In each case, adjust your scope time scale to show at least one (but not more
than three) complete cycles of the sine wave. Adjust the offset of each channel so that both
signals are centered on the screen vertically.
Adjust the vertical volts / div scale so that both channels are on the same volts / div scale
and “big” on the screen.
Record the scope screen using the web interface or the printer for your records.
Use your oscilloscope to adjust the signal generator to these frequencies as accurate as possible,
and then measure and record the actual frequency.
3. For each of the above scope plots:
(a) Determine the magnitude response of the filter, i.e. the ratio of the magnitude of the
VR (t) sinusoid versus the magnitude of the VS (t) sinusoid.
(b) Determine the phase of the response of the filter, i.e. the phase of the VR (t) sinusoid
relative to the phase of the VS (t) sinusoid.
4. Plot your results and compare the experimentally observed magnitude and phase response to
the magnitude and phase response predicted by your pre-lab analysis.
(a) Plot your experimentally observed output magnitude (Volts) versus frequency (Hz) data
points (not a curve). On the same graph, plot the magnitude curve you derived in your
pre-lab analysis of this circuit.
(b) Describe briefly how the experimentally observed magnitude compares to your analysis
prediciton.
(c) Plot your experimentally observed phase (degrees) versus frequency (Hz) data points
(not a curvce). On the same graph, plot the phase curve you derived in your pre-lab
circtui analysis of this circuit.
(d) Describe briefly how the experimentally observed phase compares to your analysis prediciton.
REMEMBER
• Note your lab partner’s secret code on your lab report as well as your lab station number.
• Return all electronic test equipment and components to their proper location.
• Remember to show your work.
• Typewritten reports are not required, but messy or disorganized reports are unacceptable.
• Clean up your workstation to perfection when you are done.
• Get your station checked off by your TA.
5
6
fin = 8.0 f3dB
fin = 4.0 f3dB
fin = 2.0 f3dB
fin = f3dB
fin = 0.5 f3dB
fin = 0.25 f3dB
fin = 0.125 f3dB
Frequency
Frequency
Rad/Sec
Frequency in Hertz
(cycles/sec)
Input Magnitude
(Volts)
Output Magnitude
(Volts)
Table 2: Experimental Data for High Pass Filter
in
Output Phase (Degrees)
References
[1] Giorgio Rizzoni. Fundamentals of Electrical Engineering. McGraw Hill, New York, 2009.
7
ME 530.241 Lab 5: Impedance,
Phasor Solution of Circuits with
Sinusoidal Excitation,
and RC Circuits
My Secret Code
My Partner’s Secret Code
Lab Date
Lab Station Number
Today’s Date
:
:
:
:
:
You must have the T.A. inspect your lab station at the end of your lab session.
T.A. Signature and Date
:
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