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SYSC 3501 Communication Theory Hardware Lab report
Lab Title: Frequency omain !epre"entation o# Si$nal"
%"in$ Hardware Component" Lab Section:&'
Lab ate: (uly 13 th '015
ate Completed: (uly 13th '015
+roup )ember":
Lab +rade: ,To be Filled by T&"-
Lab )ar*": . 4ame 1 &bdullah
Student . 10035'
. /rela
&lhena*i ' )ohaned &lla#
10011
3
&$atha 6on$
1 100'578
1 ' 3
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8 1007130
Introduction:
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The purpose of this lab is to be familiarized with lab equipment used to display the simulated results in the software lab previously used. This lab is consisted of analyzing the Power Density of signals using a hardware-based setup. A spectrum analyzer and an oscilloscope were used to analyze certain signals. A time varying signal was input to the spectrum analyzer and then it gave out an estimate of the Power Spectral Density PSD! the power of the signal as a function of frequency!. 7 Post-laboratory Questions 7.1 Sinusoidal input Q1: "ompare the measured PSD of the sinusoid of the #.$ %p '(z sinusoids with your theoretical predictions. )*plain any differences in the amplitudes or frequencies.
Figure 1-PSD of 10 K! sinusoid "it# a$plitude 0.%&.
+sing the theoretical derivation in the pre-lab, the theoretical PSD for the signal can be found. There are two spi'es at f # and f # and a power of A $/0. PSD 1 A$/0 1 #.$$/0 1 #.#&2 or m2. "onverting into d3m by using the following formula4 PSD 1 log ###.#&2!! 1 d3m. 2e can see that the theoretical prediction is d3m for a #.$%p 5(z sinusoid. +sing d3m as a reference spi'e at # 5(z, the measured power at - 5(z is estimated to be 6d3m. The difference in values is due calibration errors.
Q%: 2hat happens to the PSD when the amplitude of the sinusoid was increased from #.$ %p to #.7 %p and how does that compare with theory8
Figure %-PSD of 10 K! sinusoid "it# a$plitude 0.'&.
9ncreasing the amplitude from #.$%p to #.7%p, the PSD at - 5(z also increased to &:d3m. PSD 1 A$/0 1 #.7$/0 1 #.&62. "onverting to d3m using the following formula4 PSD 1 log ###.&62!! 1 $$d3m. The theoretical results indicate that for a #.7 %p '(z sinusoid, the power is $$d3m. This result is slightly higher than the measured value due to calibration errors. Q(: 2hat happens to the PSD when the frequency of the sinusoid was changed from '(z to ;# '(z, and then to $ '(z8 (ow does that compare with theory8
Figure (-PSD of )0 K! sinusoid "it# a$plitude 0.%&.
Figure *-PSD of % K! sinusoid "it# a$plitude 0.%&.
The PSD obtained at '(z is used to compare the PSD
>0. "ompare the measured PSD of the sinusoid of the #.$ %p ; '(z square wave with your theoretical predictions. )*plain any differences in the amplitudes or frequencies.
Figure 5 PSD of Square wave. 0.2V, 5kHz
The theoretical predictions can be seen in the pre-lab. To calculate PSD, the following equation is used
A square wave only outputs the odd frequencies, therefore n! will only increment by odd numbers. The function generator was set to ;'(z, pea' square output of #.$ %, and a frequency span of '(z/v. theoretical results were found to be P out 1 #.#& watt with error of ? due to calibration errors associated with the hardware devices in the lab. (armonic@ n! & B ; =
Theoretical value #.#& #.##$ #.##6 #.##B
easured value #.##:= #.##B$ #.##;& #.##$:
ectangular "a/e
>;. "ompare the measured PSD of the sinusoid of the #.$ %p ; '(z rectangular wave with $;? duty cycle with your theoretical predictions. )*plain any differences in the amplitudes or frequencies. 2hat effect does the duty cycle have on the PSD8
The function generator was set to ;'(z with pea' rectangular output of #.$%, and duty cycle of $;? using frequency span of '(z/v. Decreasing the duty cycle to $;? increases the frequency while the amplitude remains the same, and vice versa. Since the duty cycle is adCusted to $;?, for every nth harmonic that is divisible by 0, its corresponding power component will be #. riangular "a/e
>6. "ompare the measured PSD of the sinusoid of the #.$ %p ; '(z triangle wave with your theoretical predictions. )*plain any differences in the amplitudes or frequencies.
Figure ! PSD of "riangular wave. 0.2V, 5kHz.
requency span of '(z, duty cycle is off, output of #.$% with ; '(z. The magnitude decreases as the frequency gets further away from the fundamental frequency. The table below shows the differences between theoretical and measured values.
(armonic@ n! & $ B
Theoretical value #.##7$ #.##$; #.##B;
easured value #.##=& #.##$=B #.##$&
As seen above, the theoretical and the measured values are close but not the same due to the same error of calibration and the hardware devices accuracy in the lab. onclusion
The main obCective of the lab was to analyze and understand the signals using their PSD values. 9n the pre lab, many input signals and derivations were done and tested in this lab. The corresponding PSD from the e*periment for each case was analyzed and compared to the theoretical PSD from the prelab. There were differences between the theoretical and the measured PSD values, errors may occur in the calibration of the hardware devices in the lab.