Lab 10 Report
Group Six
By:
Brian Lawler, Christian Mans, Richard White
Abstract
This lab was broken down into four parts. Each part focused on the use of the oscilloscopes ability to
show a spectrum in a decibel scale. The recognition of harmonics based upon frequency, and the use of
harmonics to calculate frequency. A Quartus II project was also created to modulate two synthesizers
together to create a beat. There was also a focus placed upon the difference between Amplitude
Modulated signals and Frequency Modulated.
Introduction
The purpose of this lab is split by the four parts of the lab. The first purpose is to observe the spectrum
of sinusoidal, square, and ramp waves produced by a signal generator. The second is to produce an AM
wave by a signal generator and observe its spectrum on an oscilloscope. The third is to make
measurements on the spectrum of music originating from YouTube on the iPad. The fourth is to
produce beating of two sinusoids on your FPGA and use the CODEC to convert the discrete signal to
continuous time signal and observe the signal on the oscilloscope.
Theory
The following Equations were used:
y(f) = 20 Log10 A(f)
A1/A2 = A(f1)/A(f2)
Combining them we get:
A(f1)/A(f2) = 10^[(y(f1)-y(f2))/20]
These equations were used to find the difference in linear peak height between harmonics.
The following equations were also used:
ak = 1/jπk ; for: k=1,3,5,7,… odd harmonics
This equation was used to determine the theoretical height differences between the harmonics.
Finally this equation was used:
P(constant)*Fs/232=F
This equation was used to calculate the theoretical frequency values in experiment four.
Main Body
In Lab 10 the oscilloscope, iPad, Desktop Computer, FPGA, signal generator, and Quartus II were all used.
The first part of the lab is to generate a square wave at 1V, 1kHz, and 50% duty cycle on the signal
generator. It is then observed on the oscilloscope. After it is identified as being observed as being
correctly generated, the oscilloscope is set to display the harmonics on a 20dB scale. Then the signal
generator is changed to the ramp and sine wave to observe each of their harmonics.
Figure 1
Figure 1: shows the square wave harmonics.
Figure 2
Figure 2: The sine wave harmonics
Figure 3
Figure 3: The ramp wave harmonics
The second part of the lab is the creation of an amplitude modulated wave, and observation of this
wave. The settings for the amplitude wave are as follows, carrier frequency of 1040 Hz, 1 V peak-peak,
AM Depth 100%, AM freq 40 Hz, and Shape Sine.
Figure 4
Figure 4: is a display of the AM harmonics.
The third part of the lab is to observe the harmonics being generated from music. A music video on
YouTube was used to generate the signal, and observed on the oscilloscope. The harmonic’s peak ratio
was also measured.
Figure 5
Figure 5: shows the amplitude modulated sine harmonics.
The final part of the lab was to create a Quartus project that generates a signal that combines two
different signals from two synthesizers. The signal being generated by the FPGA is then sent to the
oscilloscope and the harmonics are observed.
Figure 6
Figure 6: The harmonics from the FPGA
Figure 7
Figure 7: Is the oscilloscopes display of the two synthesizers beating off each other.
Discussion and Suggestions
Experiment 1:
What is the frequency value of the 1st harmonic?
1kHz
Are odd harmonics present in the spectrum? Are even harmonics present in the spectrum?
If so, are the even harmonics strong compared to the strongest odd harmonics?
There were only odd harmonics observed with the square wave.
What are the frequencies of the harmonics present in the spectrum?
The following is a list of Harmonic Frequencies and their related frequency:
1st = 1kHz
3rd = 3kHz
5th = 5kHz
7th = 7kHz
9th = 9kHz
Measure the linear ratio of the peak heights between the 1st harmonic and 5th
harmonic peak. Are your results consistent with the theoretical result for the spectrum of a square
wave?
The measured difference was 13.75dBV between the 1st and the 5th harmonic. The calculated
linear ratio was 4.8697, using the equation for linear ratios given in the calculations section of
this report. The theoretical results for the linear ration were calculated to be 5. This is done by
using the Fourier Series coefficient equation for odd harmonics, also given in the calculations
portion of this report.
Sample Calculations:
A1/A5=10^[(y1-y5)/20]; where: y1=-6.25 , y5=-20.00 ; thus A1/A5=4.8697
αk= 1/(jπk) ; where: k=1,3,5,… ; Then α1/α5=5
Experiment 2:
Measure the frequency positions of the 3 peaks. Is this consistent with theoretical results of an AM
sinusoid signal?
Frequency Positions:
Peak 1=1.00kHz
Peak 2=1.04kHz
Peak 3=1.08kHz
The theoretical peak frequencies are given by the carrier frequency and the modulated
frequency. An AM signal with a carrier frequency of 1.04kHz, and Modulated frequency
of .04kHz. Will have a dominant center peak focused at 1.04kHz, and two less dominant peaks
to each side of the middle peak .04kHz away. This is exactly what is observed and measured
therefore they are accurate.
Experiment 3:
Can you observe harmonics in the signal? What harmonics are these?
Yes, but you can’t decipher what harmonics they are.
Now select any large peak near zero frequency, let us call it Peak1. Now select another dominant peak
near the frequency 3000 Hz; call it peak2. Measure the linear ratio of heights between peak1 and peak2.
Peak 1= .05kHz, -17.5dBV
Peak 2= 2.1kHz, -36.875dBV
A1/A2=10[(-17.5+36.875)/20] = 9.3057
Experiment 4:
Now observe the spectrum on the oscilloscope. How many peaks do you observe? What are their
frequencies? Do these frequencies match the frequencies calculated above?
Two peaks are observed on the oscilloscope.
Peak 1 = 9.25Hz
Peak 2 = 10.25Hz
Using the P equation listed in the calculations section a sample calculation is as follows:
939524*48000kHz/232=10.5Hz
Showing that the theoretical is very close to the experimental.
1. Describe the spectra from Experiment 1.
The spectra in experiment one displayed the harmonics of the square, ramp, and sine waves.
The harmonics are inherent to each type of wave, and change depending on the wave. The
square wave displays only odd harmonics, the sine only the first harmonic, and the ramp wave
all of the harmonics are present.
2. Explain the difference between decibel representation and linear representation.
The decibel representation is a modified version of the magnitude for the sake of more easily
comparable harmonics, and beats. It is also scaling the magnitudes relative to frequency rather
than time.
3. In Experiment 3, what does the linear ratio of Peak1 and Peak2 tell you about the bandwidth of your
music signal? Is it larger or smaller than 3kHz?
The signal seemed very garbled so it is hard to be definitive, but a linear ration showing that
peak one is 9 times larger than peak 2 would lean toward something smaller than 3kHz.
Conclusion
In conclusion the lab resulted in a close to theoretical presentation of harmonics.
Acknowledgements
Brian Lawler, Christian Mans, Richard White
References
Professor Khan’s Website.