ELEC1000 – Introduction to Electrical Engineering
Laboratory Experiment 7
Phasors & Complex Impedances
Work in Groups of two
Equipment
Adjustable Power Supply
Function Generator
Oscilloscope.
Prototyping Board + Patch Wires
Patch Leads and Coax cables
Components:
Resistors: 100 1k
Capacitor: 0.1µF (marked as 104K)
Inductor: 22mH (marked as 223K or 226C)
Aim of the experiment:
This experiment continues information learned in Lab 4 – Introduction to Oscilloscopes. Please
review if necessary. In this experiment you will calculate theoretical values for phasors then
construct a circuit and compare measured values to your theoretical values. Your theoretical values
are first drawn on a graph, then after gathering experimental values, a second graph is drawn for
comparison.
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Parts 1 – 2 cover RC circuits
Parts 3 – 4 cover RL circuits
Parts 5 – 6 cover LC circuits
You will use a function generator to supply an AC input signal, whilst observing and measuring the
output on an oscilloscope. A multimeter will also be used to measure RMS signals. These results
will then be used to draw a phasor from your measurements.
Capacitors
Inductors
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Part 1. RC Circuit
(a) Wire up the following circuit using the function generator, oscilloscope, prototyping board and
components:
(b) Measure VS on CH1 and VC on CH2.
(c) You can use the MATH function (see Lab 4 – Intro to Oscilloscopes) to view and measure VR.
Assume the voltage source has a phase angle of 0, ie. VS = 2 volts = 2 + j0 volts
(d) Solve for phasor IRC and hence calculate phasors VR and VC.
(e) Sketch a phasor diagram showing VS = VR + VC
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Here is a sketch of what the voltages look like plotted against time:
(a) Wire up the circuit, set the function generator to sinusoidal output, Display VS(t) on CH1 of
the oscilloscope and adjust amplitude and frequency, and adjust the horizontal position so
that VS has zero phase, ie, peak voltage is on the Y axis (t=0).
(b) Now display VC(t) on CH2 and measure the amplitude and phase.
(c) Now display VR(t) using MATH function CH1- CH2 and measure the amplitude and phase.
(d) Also measure the voltages using the AC scale of your multimeter (note that this will
measure RMS voltage)
Voltage
RMS voltage on
Multimeter
VS
VC
VR
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Amplitude on
Oscilloscope
Sketch the oscilloscope display:
(e) Draw a phasor diagram of the measured voltages:
(f) Compare to the estimated phasors.
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Part 2. RC Circuit
(a) Repeat the previous calculations and measurements, with the same circuit, but this time at a
different frequency:
(b) Assume the voltage source has a phase angle of 0, ie. VS = 2 volts = 2 + j0 volts
(c) Solve for phasor IRC and hence calculate phasors.
(d) Sketch a phasor diagram showing VS = VR + VC.
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(e) Measure voltages using multimeter and oscilloscope.
Voltage
VS
VC
VR
Multimeter RMS
Amplitude on O’scope
(f) Sketch the oscilloscope display:
(g) Draw a phasor diagram of the measured voltages:
(h) Compare to the estimated phasors.
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Phase
Part 3. RL Circuit
Repeat the previous calculations and measurements, this time with an inductor and a resistor. Note
the required frequency and amplitude.
(a) Note that the wire-wound inductor has quite a high series resistance of approximately 75
ohms, which must be taken into account, and which appears as RL in the circuit below.
(b) Measure VS on CH1 and VL on CH2.
(c) Use your multimeter to measure the resistance of your particular inductor, and use this value
in your calculations.
Assume the voltage source has a phase angle of 0, ie. VS = 1 volts = 1+ j0 volts
(d) Solve for phasor IRL and hence calculate phasors.
(e) Sketch a phasor diagram showing VS = VR + VL.
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(f) Measure voltages using multimeter and oscilloscope.
Voltage
VS
VL
VR
Multimeter RMS
(g) Sketch the oscilloscope display:
(h) Draw a phasor diagram of the measured voltages:
(i) Compare to the estimated phasors.
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Amplitude on O’scope
Part 4. RL Circuit
Repeat the previous calculations and measurements, this time with a different frequency and
amplitude. Measure VS on CH1 and VL on CH2.
Assume the voltage source has a phase angle of 0, ie. VS = 1 volts = 1 + j0 volts
(a) Solve for phasor IRL and hence calculate phasors.
(b) Sketch a phasor diagram showing VS = VR + VL
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(c) Measure voltages using multimeter and oscilloscope.
Voltage
VS
VL
VR
Multimeter RMS
(d) Sketch the oscilloscope display:
(e) Draw a phasor diagram of the measured voltages:
(f) Compare to the estimated phasors.
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Amplitude on O’scope
Part 5. LC Circuit
This circuit contains a capacitor and inductor, plus the series resistance of the inductor
Measure VS on CH1 and VC on CH2. Now display VL(t) using MATH function CH1- CH2 and
measure the amplitude and phase.
Assume the voltage source has a phase angle of 0, ie. VS = 1 volts = 1 + j0 volts
(a) Solve for phasor ILC and hence calculate phasors.
(b) Sketch a phasor diagram showing VS = VL + VC
(c) Measure voltages using multimeter and oscilloscope.
Voltage
VS
VC
VL
Multimeter RMS
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Amplitude on Oscilloscope
(d) Sketch the oscilloscope display:
(e) Draw a phasor diagram of the measured voltages:
(f) Compare to the estimated phasors.
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Part 6. LC Circuit as a Filter
This circuit uses the same circuit as part 5, but varies the frequency across a range of values.
We can calculate the relative amplitudes of VC and VS as a function of frequency
(a) Measure VC / VS (we call this the transfer function) at the following frequencies:
Use the oscilloscope to do the measurements – multimeters are not designed for high frequency AC
measurements.
Freq
(Hz)
VS
VC
100
300
1000
3000
1
1
1
1
Max
3393
1
3800
1
10000 30000 100000
1
1
1
VC /
VS
(b) You could use a spreadsheet to help you calculate the theoretical values for |Vc|/|Vs|. Setup
a column which contains a vertical list of the frequencies from 100Hz to 100 000 Hz, then
make a separate column for each of the bracketed equations in the denominator of the
equation above, where ω = 2 π f. A 4th column could hold the sum of the terms (which will
show some interesting values), a 5th could hold the square root of column 4, and finally,
column 6 would hold the inverse of column 5, giving you the ratio of |Vc|/|Vs| for each
frequency. If you plot this in your spreadsheet, you will see the theoretical shape of your
filter response, which you can confirm against your measured results.
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(c) Plot a graph of VC / VS versus frequency.
Note that the horizontal scale is logarithmic:
Such a circuit is called a bandpass filter, and is used, for example, to select a particular station at a
particular frequency in a simple AM radio.
END OF EXPERIMENT
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