EE  401 / E01 Fall 2002
Introductory Communications Theory
Professor: Conner
Submitted By:
Andrew Buettner
Lab #1: Spectral Analysis and Filtering
Table Of Contents
1) Cover Page 1
2) Table of Contents 2
3) Objective 3
4) Components Used 3
5) Procedures 3
6)
Lab Data / Results 3
1) Table 1 3
2) Table 2 3
3) Table 3 4
4) Table 4 4
5) Table 5 4
6) Diagram 1 5
7) Conclusions 5
8) Attachments 5
Objective
The objective of this lab is to become more familiar with the HP 3585A Spectrum Analyzer. This will be accomplished by making several spectral measurements and then making calculations based on those measurements.
Components Used
1) HP 3585A Spectrum Analyzer #1939
2) Function Generator #1512
3) Trainer #1517
4) Oscilloscope #10875
Procedures
1) Set the spectrum analyzer to use the 1MW input, have f_{c} of 1MHz and have a frequency span of 500KHz.
2) Use the generator to generate a 1KHz sinewave.
3) Measure the total harmonic distortion over the first five harmonics.
4) Repeat step 3 for a 10KHz signal.
5) Calculate the Fourrier series of both a square wave and a triangle wave
6) Generate a 10KHz square wave and compare the spectrum with the calculated one.
7) Repeat step 6 using a triangle wave.
8) Design a low pass filter with a cutoff frequency of 20KHz.
9) Calculate the spectrum of a 10KHz square wave passed through this filter.
10) Construct the filter and observe the actual spectrum of a 10KHz square wave.
11) Compare the two spectra.
12) Repeat steps 9  11 for a triangle wave.
Lab Data / Results
1) Table 1: Harmonic Distortions Observed From a 1KHz Sine Wave:

Fundamental 
1^{st} Harmonic 
3^{rd} Harmonic 
5^{th} Harmonic 
Total 

Voltage: 
1V 
8.6mV 
436mV 
1.51mV 
10.54mV 
dBm: 
13dBm 
28.5dBm 
57.0dBm 
43.4dBm 
26.5dBm 
2) Table 2: Harmonic Distortions Observed From a 10KHz Sine Wave:

Fund. 
1^{st} 
2^{nd} 
3^{rd} 
4^{th} 
5^{th} 
6^{th} 
Total 

Voltage: 
956mV 
2.09mV 
7.68mV 
506mV 
402mV 
0 
1.44mV 
12.12mV 
dBm: 
12.6dBm 
40.1dBm 
29.3dBm 
53.3dBm 
55.3dBm 
'dBm 
43.7dBm 
25.3dBm 
3) Table 3: Harmonic Distortions Observed From a 10KHz Square Wave:

Fund: 
1^{st} 
3^{rd} 
5^{th} 
Total: 

Expected: 
1.31V 
437mV 
262mV 
187mV 
0 
Observed: 
1.31V 
430mV 
256mV 
182mV 
0 
Difference: 
0 
7mV 
6mV 
5mV 
18mV 
4) Table 4: Harmonic Distortions Observed From a 10KHz Triangle Wave:

Fund: 
1^{st} 
3^{rd} 
5^{th} 
Total: 

Expected: 
776mV 
86.2mV 
31.0mV 
15.8mV 
0 
Observed: 
776mV 
86.0mV 
31.2mV 
16.4mV 
0 
Difference: 
0 
.2mV 
.2mV 
.6mV 
1mV 
5) Table 5: Harmonics of a 10KHz Square Wave Passed Through a Low  Pass Filter with a Critical Frequency of 20KHz.

Observed: 
Expected: 
Difference: 
% Error: 

Fundamental: 
7.96V 
7.96V 
0 
0 
1^{st} 
1.43V 
1.05V 
380mV 
36.2% 
3^{rd} 
556mV 
449mv 
107mV 
23.8% 
5^{th} 
294mV 
249mV 
45mV 
18.1% 
7^{th} 
180mV 
158mV 
22mV 
13.9% 
9^{th} 
121mV 
110mV 
11mV 
10.0% 
11^{th} 
86.0mV 
80.4mV 
5.6mV 
6.97% 
13^{th} 
66.0mV 
61.5mV 
4.5mV 
7.32% 
15^{th} 
50.6mV 
48.5mV 
2.1mV 
4.33% 
17^{th} 
40.6mV 
39.3mV 
1.3mV 
3.31% 
Total: 
0 
0 
578.5mV 
7.27% 
6) Diagram 1: Resistor  Capacitor Network used:
Answers to Lab Questions
1) Q: What is the total harmonic distortion of the following wave: .5cosw_{o}t + .3cos3w_{o}t + .04cos4w_{o}t?
A: .34V
2) Q: If the wave in Q1 was passed through a low pass filter with a cutoff frequency of w_{o}, what would the total harmonic distortion be?
A: f_{H2} = .00754, f_{H3} = .000159 T_{HD} = .0077
Conclusions
This lab has demonstrated the basic functionality of the HP3585A spectrum analyzer. I am fairly confident in the results. Even though the % error was high on the last phase I believe that it was due to the accuracy of the capacitor. Also, the calculations were not based on the harmonic distortions found in the square wave which could have contributed significantly. Also, I have found that the spectrum it's self has a significant amount of inaccuracy associated with it. Also, I am not sure of the total harmonic distortion calculations are entirely accurate. I believe that there may be errors. My method, which was just summing the individual overtone errors, I do not believe is correct. Other than that, most of the data in this lab should be fairly accurate.
Attachments
Original lab handout
Original lab data
Calculations