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Lab 4 AC Lab

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Lab 4 AC Lab
1
Ve215
Lab 4 AC Lab
I. Goals
1. Learn how to define, calculate, and measure the amplitude of a sinusoidal
signal
2. Learn how to define, calculate, and measure the Rise Time and Fall Time of a
signal
3. Learn how to observe FFT spectra of signal and measure their parameters with
cursors

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Lab 4 AC Lab
1
Ve215
Lab 4 AC Lab
I. Goals
1. Learn how to define, calculate, and measure the amplitude of a sinusoidal
signal
2. Learn how to define, calculate, and measure the Rise Time and Fall Time of a
signal
3. Learn how to observe FFT spectra of signal and measure their parameters with
cursors
4. Measure the waveforms and FFT spectra of various signals
5. Compare your theoretical results obtained in the Pre-Lab with your In-Lab
data.
II. Introduction
1. High-Z mode
Here I want to introduce you what is the High-Z mode we have kept emphasizing
during the previous Labs.
You have already learnt Thevenin equivalent of a circuit. You can think the
function generator in terms of its Thevenin equivalent circuit, which includes the
voltage source and VS and the equivalent resistance of 50

as shown below.
When the load RL is 50
 , according to voltage division, we know that the VL
measured will be 0.5VS. In this case, we use the 50 OHM mode, in which the
function generator produces voltage VS but displays voltage 0.5VS. In that way, if
you set 2Vppk for the function generator, the actual VS will be 4Vppk to make sure
the load get a voltage of 2Vppk.
Lab 4 AC Lab
2
In our lab measurements, the load resistance RL is very high—the input resistance
of the oscilloscope is about 1
M
. The VL measured across RL practically equals
VS. So we use High Z mode, in which the function generator produce voltage VS
and displays VS.
2. The Rise Time and Fall Time of signals
The Rise time is the interval between the moment of the time when the signal
reaches its 10% level and the moment of time when the signal reaches its 90%.
We have already used this concept in our Lab3.
The above two figures illustrate the rise time of a sinusoidal like wave and a
saw-tooth wave. If you do not know what is Vppk, you can refer to part 4 of this
section.
Take the sinusoid wave as an example to calculate the rise time.
sin(2 )
2
Vppk
y   ft
Lab 4 AC Lab
3
,
2 2
ppk ppk
min max
V V
V V
 
 
1 1 0.9 0.1
sin ( ) sin ( )
0.5 0.5
2
min ppk min ppk
ppk ppk RiseTime
V V V V
V V
 f
 
 


3. Fourier Series Representation of a Signal
Here I am going to give you a general idea of Fourier Series to help you
understand some parts of this lab. You will learn Fourier Series in details in your
math course this semester.
Fourier series is a way to represent a wave-like function as a combination of
simply sine waves. It decomposed and period function into the sum of a (possibly
infinite) set of simple oscillation functions.
Let
xt()
be a periodic signal with fundamental period
T0
. It can be represent by the
following synthesis equation,
0
0
0
( ) , where jk t 2
k
k
x t c e
T
 



  
The coefficients
k
c
in the above equation can be calculated by the analysis
equation,
0
0
0
0
1
( ) , 0, 1,…
T
jk t
k
c x t e dt
T
k
 
  
Plot[Sum[(−1)^(((? + 1)) ⁄ 2) ∗ 2 ⁄ ((? ∗ Pi) ) Cos[? ∗ Pi ∗ (? +
0.5)], {?, 1,100,2}], {?, −4,4}]
You can use the above Mathematic code to get the feeling of how a series of
sinusoidal waves can form a square wave (actually, any waveform). You can
change the value in the red box, and the larger the value is, the more accurate the
result will be. Here we thank the Vv286 TA for FA2014 Gao Yuan for offering us the source
code.
For value 3, we can get the following result.
Lab 4 AC Lab
4
For value 20, we can get the following result,
And for value 100, we get,
4. Four ways to measure the amplitude of a sinusoid
a) Vpeak=Vp=Vpk=V0 is the peak amplitude of the sinusoid measured in V or mV.
b) Vpeak-to-peak=Vppk=Vmax-Vmin=2V0 is the value we often use in the lab to
determine the overall size of the waveform. We have used it many times in the
4 2 2 4
0.6
0.4
0.2
0.2
0.4
0.6
4 2 2 4
0.6
0.4
0.2
0.2
0.4
0.6
4 2 2 4
0.6
0.4
0.2
0.2
0.4
0.6
Lab 4 AC Lab
5
previous Labs.
c) VRMS is the Root-Mean-Square, or RMS amplitude of the sinusoid. The
sinusoidal voltage
0 V V sin( )   t 
dissipates as much power in the load resistor
as does the DC voltage equals to VRMS
For any periodic function f(t) that has period T, the RMS amplitude is defined as
0
0
2
, ( 1
( ))
t T
t
Amplitude RMS f t dt
T

 
In the case of sinusoid
0
f t V t ( )   sin( ),
0
2 2 2 2
peak ppk
RMS
V V V
V   
d) The above three ways all study the signal in time domain, plotted as voltage vs.
time. In this Lab, we also need to study the frequency domain, when you measure
their spectra displayed as amplitude vs. frequency. In frequency domain, the
oscilloscope measures the amplitude of on a logarithmic scale, using decibels.
10 (dBV) 20 ( log )
1
RMS
RMS
Amp Amplitude i litude in decibe n V
V
ls 
Decibels are used to calculate ratios of two amplitudes on a logarithmic scale.
10 , (dB) #2, 20 log
#1,
( ) Amplitudeo Ratio in decibels
Amplitude of signal
f signal RMS
RMS

III. Pre-Lab Assignment
1. Consider a sinusoidal signal at 3Vppk and 10 kHz. Calculate its amplitude in
Vpk, RMS, and dBV.
2. Consider a square wave at 3Vppk and 10 kHz. Calculate the amplitude of its
frequency components—fundamental and harmonics up to the 5th
–in Vpk, VRMS,
and in dBV. Fill the following table.
Lab 4 AC Lab
6
Column 1 2 3 4
Frequency
component
Frequency,
kHz
Amplitude in
dBV
Amplitude in
VRMS
Amplitude in
Vpk
Fundamental
1
nd harmonic
2
nd harmonic
3
nd harmonic
4
nd harmonic
5
nd harmonic
3. Consider a sinusoidal signal at 3Vppk and 1kHz, calculate the rise time of this
signal.
IV. In-Lab Procedure
Part I
1. On the function generator, set a sine wave at 1 [kHz] and keep its amplitude
at 3 [Vpp]. The load must be High-Z mode.
2. Record the parameters on the datasheet. Fill the table with the data set on the
function generator and displayed on the oscilloscope.
3. Repeat the Step 2 with a sine wave at 1.5 [kHz] and 5 [Vpp] on the function
generator. The load should remain High-Z mode.
4. In post-report, calculate the rise time in theory and compare it with the values
displayed on the oscilloscope.
5. Reminder:
Part II
1. First, we set a sine wave and a square wave, respectively. The frequency is 1
[kHz] and the amplitude is 3 [Vpp].
2. On the oscilloscope, set 1 [V/div] and 5 [ms/div].
3. Push the “MATH” button and select “FFT” function.
4. Push the “cursor” button and select “trace” mode to trace the spectrum.
5. When the cursor reach a peak of the spectrum, record the Frequency in [kHz]
and the Amplitude in [dBV].
6. Set another sine wave and a square wave. The frequency is 2 [kHz] and the
amplitude is 6 [Vpp]. Repeat the steps above.
7. In post-report, you need to calculate the theoretical amplitude of sine wave in
[dBV]. Besides, you need to calculate the Vpeak of each square wave
measured in Part II. You should give a brief conclusion on what you learn
from this lab.
Lab 4 AC Lab
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8. Reminder: for sine wave.
9. Reminder: for square wave.
V. Reference
Circuits make sense A new Lab Book for introductory Course In Electric Circuits.
Fifth edition. Alexander Ganago.