ECE 201 Lab 5

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Oscilloscope , Wave Function Generator (WFG)
and AC series RC circuits. ECE201 - LAB 7 2 of
final grade
Projects and Notes prepared by Dr. Gabriele
Formicone
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OUTLINE
A Brief Introduction to AC signals, AC signal
generators, and AC signal measurements. Circuit
1 Series RC with grounded
capacitor. Circuit 2 Series RC with
grounded resistor.
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INTRODUCTION
The wave function generator (WFG) supplies
(generates) a variety of time-varying voltages
(sine-wave, square-wave, saw-tooth-wave, ) at
its output terminals. The oscilloscope (OS)
measures and plots the signal versus time on its
monitor.
Connect the WFG (Wave Function Generator) output
up to the input of channel 1 of the scope.
Push the auto-scale button. Turn the trigger
knob until a pretty sine wave is displayed.
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Peak to peak means this
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Reading the scope display
The horizontal axis is time. The display will
tell you how much time is represented by 1
division of the screen. This is done along the
top of the display. The vertical axis is voltage.
The volts per division is displayed in the
upper left corner.
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Computing the rms or Root Mean Square of a time
varying signal.
You do the s first, the m second and the r last.
That is, proceed through rms from right to
left. square x(t) to get x2(t). Take its time
average or mean. You do this by integrating
x2(t) over time from time t to time tT. Then,
divide the result by T. Take the square root of
the result.
The usual rule is that the rms value of Asin(wt)
is 0.707A.
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Practice
Generate the following functions on the WFG and
use the scope to measure their period, their peak
to peak amplitude and their rms amplitude sine
wave of 1 kHz, 0.1 volt amplitude sine wave of 10
kHz, 0.1 volt amplitude sine wave of 1 kHz, 0.3
volt amplitude
Does the rms value depend on the frequency? Does
the rms value depend on the amplitude?
The oscilloscope measures the amplitude of a
signal. The voltmeter set to AC measures the rms
of a signal.
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Practice
Generate a square wave with a 0.1 volt amplitude
using the wave function generator and test to
see if its rms value is 0.707 times its
amplitude. Generate a saw-tooth wave with a 0.1
volt amplitude using the wave function generator
and test to see if its rms value is 0.707 times
its amplitude.
In general, is the rms value always equal to
0.707 times the amplitude?
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A closer look at what an oscilloscope really is!
It is a device which uses a Cathode Ray Tube
(CRT) to display a time-varying voltage or
current. (see next slide)
How does a CRT work?
An electron gun generates a beam of electrons
which are accelerated toward the part of the
display we see. When the electrons hit the
screen, they excite a material which generates
light when hit by electrons. We see the light.
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What types of voltages are used?
Typically, several thousand volts are used in
these devices. We, however, plug the scope into
110V AC outlet, so where do we get several
thousand volts? Such voltages are generated by
using transformers, a device discussed by Irwin
in Chapter 8, a chapter we will not cover in ECE
201.
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Few guidelines for measurements with AC circuits
Because a WFG is not an ideal voltage source, the
voltage across its terminal will likely change
when you change the load impedance connected to
its terminals. Whenever you change the frequency
of the AC signal through capacitors and
inductors, the load impedance changes.
Therefore always adjust the WFG source voltage
amplitude when you change the Frequency between
measurements.
Because of the grounding effect, when measuring
voltages with the oscilloscope, only the voltage
across a grounded element is a correct reading!
This is due to the fact that an oscilloscope is a
grounded device. For comparison, a multi-meter is
NOT a grounded device. Therefore When using
the oscilloscope to measure a voltage across a
capacitor, the capacitor MUST be connected to
ground. When using the oscilloscope to measure a
voltage across a resistor, the resistor MUST be
connected to ground. when using the oscilloscope
to measure a voltage across an inductor, the
inductor MUST be connected to ground.
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Series RC Circuit 1
i(t)
Build this RC series circuit with grounded
capacitor
vR
R
vS(t) vS sin(2pf t)
vC
C
For a given value of R, C and VS, measure the
voltage vC(t) versus the frequency f. Sweep the
frequency f from about 50Hz to 200KHz. You can
measure either rms value or amplitude.
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Series RC Circuit 2
i
Build this RC series circuit with grounded
resistor
vC
C
vS(t) vS sin(2pf t)
vR
R
For a given value of R, C and VS, measure the
voltage vR(t) versus the frequency f. Sweep the
frequency f from about 50Hz to 200KHz. You can
measure either rms value or amplitude.
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SOLVE the circuit using KVL in phasor
notation. Calculate the current i and the
voltages vC and vR versus frequency from 50Hz to
200KHz.
VS VR VC
where
VR R I VC I / (j wC)
Therefore
VS I R 1/(jwC)
w 2 p f
I VS / R 1/(jwC)
or
VR VS R / R 1/(jwC) j VS w RC / 1 j
w RC VC VS / (j wC) 1/R 1/(jwC) VS /
1 j w RC
It follows
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In terms of magnitude (amplitude), we have
mag(I) mag(VS) / vR2 1/(wC)2 mag(VS) wC /
v1(wRC)2
mag(VR) mag(VS) w RC / v1(wRC)2
mag(VC) mag(VS) / v1(wRC)2
mag(IR) mag(VR) / R mag(IC) mag(VC) (wC)
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Plot the magnitude or rms value of the calculated
currents iC and iR versus frequency, and the
theoretical i obtained from KVL in phasor
notation. How are they related to each other?
Why? Explain. On another graph, plot the
magnitude or rms value of the voltages vS, vR and
vC versus frequency, and the values obtained from
KVL in phasor notation. On this same graph, also
plot the quantity vT v(vR2 vC2). How is
it related to vS? Explain why.
Follow the example in the next slides for your
report. Use similar but different values for your
resistor R, capacitor C and source voltage vS.
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Example Measurement R 10 kW, C 1 nF, vS 5V
(vSpp 10V, vSRMS 3.535 V). Measured vSRMS
3.57 V
Measured and Theoretical Data
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Voltage vs. Frequency
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Current vs. Frequency
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LAB REPORT
Write a clearly legible Technical Report using
the guidelines suggested in the next slide.
Describe the measurements your team made on
the RC circuit used as template. See Lab 1 for
Report Guidelines!