EE - 401 / E01 Fall 2002

Introductory Communications Theory

Professor: Conner

Submitted By:

Andrew Buettner

Lab #1: Spectral Analysis and Filtering

Thursday, March 06, 2003

1) Cover Page 1

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 fc 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

1st Harmonic

3rd Harmonic

5th 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.

1st

2nd

3rd

4th

5th

6th

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:

1st

3rd

5th

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:

1st

3rd

5th

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

1st

1.43V

1.05V

380mV

36.2%

3rd

556mV

449mv

107mV

23.8%

5th

294mV

249mV

45mV

18.1%

7th

180mV

158mV

22mV

13.9%

9th

121mV

110mV

11mV

10.0%

11th

86.0mV

80.4mV

5.6mV

6.97%

13th

66.0mV

61.5mV

4.5mV

7.32%

15th

50.6mV

48.5mV

2.1mV

4.33%

17th

40.6mV

39.3mV

1.3mV

3.31%

Total:

0

0

578.5mV

7.27%

6) Diagram 1: Resistor - Capacitor Network used:

1) Q: What is the total harmonic distortion of the following wave: .5coswot + .3cos3wot + .04cos4wot?

A: .34V

2) Q: If the wave in Q1 was passed through a low pass filter with a cutoff frequency of wo, what would the total harmonic distortion be?

A: fH2 = .00754, fH3 = .000159 THD = .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

1. Original lab handout

2. Original lab data

3. Calculations