EE - 401 / E01 Fall 2002

Introductory Communications Theory

Professor: Conner

Submitted By:

Andrew Buettner

Lab #1: Spectral Analysis and Filtering

Thursday, March 06, 2003

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_ot + .3cos3w_ot + .04cos4w_ot?

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