EE  401 / E01 Fall 2002
Introductory Communications Theory
Professor: Conner
Submitted By:
Andrew Buettner
Lab #3: Frequency Modulation
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 4
1) Diagram 1 4
2) Table 1 4
3) Table 2 4
4) Diagram 2 5
5) Diagram 3 5
6) Table 3 6
7) Diagram 4 6
8) Table 4 6
9) Table 5 7
10) Diagram 5 7
11) Table 6 7
12) Table 7 8
13) Diagram 6 8
14) Diagram 7 9
7 Answers to Lab Questions 9
7) Conclusions 9
8) Attachments 10
Objective
The objective of this lab is to gain a better understanding of FM bandwidth by generating an FM wave and comparing it's spectrum to an expected one. Additionally, to compare the significant signal bandwidth to the predicted bandwidth calculated by Carson's Rule.
Components Used
1) FM Function Generator #1512
2) Voltage Regulated Power Supply #1517
3) Spectrum Analyzer #1939
4) Modulation Function Generator #1310
5) Oscilloscope #10875
6) Digital MultiMeter #1367
7) Various components from the EE301 / EE  401 lab kit
Procedures
1) Set the FM function generator to a frequency of 1MHz.
2) Connect the output to the oscilloscope and the spectrum analyzer.
3) Apply a DC voltage of 1V to the input of the modulator.
4) Adjust the modulation gain of the modulator until the frequency deviation is 20KHz.
5) Apply a voltages of .5V, 1V, 2V, and 4V to the modulator and record the deviation.
6) Graph the results.
7) Disconnect the DC power source and connect the modulator to the input of the FM generator.
8) Adjust the modulator to have an 1V_{p} output and f_{m }of 20KHz.
9) Record the output.
10) By adjusting the frequency of the modulator, generate a modulation index of .25.
11) Record the output.
12) Calculate the expected spectrum.
13) Measure the spectrum on the spectrum analyzer and compare the results.
14) Compute the bandwidth using Carson's Rule and compare with the observed bandwidth.
15) Repeat steps 10 through 14 using modulation indices of .5, 1, 2, and 4.
Lab Data / Results
1) Diagram 1: Graph of Voltage vs. Deviation for FM Modulator:
2) Table 1: Voltage vs. Deviation Data:

.5V 
1.0V 
2.0V 
4.0V 

Deviation: 
10KHz 
20KHz 
40KHz 
72KHz 
3) Table 2: Expected vs. Observed Data at m_{f} of .25:

Carrier: 
1^{st} 
2^{nd} 
3^{rd} 
4^{th} 
Bandwidth 

Expected: 
6.20V 
760mV 
0 
0 
0 
200KHz 
Observed: 
6.20V 
506mV 
22.9mV 
24.5mV 
4.22mV 
160KHz 
Difference: 
0 
254mV 
22.9mV 
24.5mV 
4.22mV 
40KHz 
4) Diagram 2: Frequency Modulation with m_{f} of .25:
5) Diagram 3: Frequency Modulation with m_{f} of .50:
6) Table
3: Expected vs. Observed Data at m_{f} of .50:

Carrier: 
1^{st} 
2^{nd} 
3^{rd} 
4^{th} 
Bandwidth 

Expected: 
5.80V 
1.48V 
185mV 
0 
0 
120KHz 
Observed: 
5.80V 
1.43V 
155mV 
28.8mV 
4.22mV 
160KHz 
Difference: 
0 
50mV 
30mV 
28.8mV 
4.22mV 
40KHz 
7) Diagram 4: Frequency Modulation with m_{f} of 1.0:
8) Table 4: Expected vs. Observed Data at m_{f} of 1.0:

Carrier: 
1^{st} 
2^{nd} 
3^{rd} 
4^{th} 
Bandwidth 

Expected: 
5.02V 
2.87V 
717mV 
130mV 
0 
80KHz 
Observed: 
5.02V 
2.56V 
580mV 
91.2m 
12.0mV 
120KHz 
Difference: 
0 
310mV 
137mV 
38.8mV 
12.0mV 
40KHz 
9) Table 5: Expected vs. Observed Data at m_{f} of 2.0:

Carrier: 
1^{st} 
2^{nd} 
3^{rd} 
4^{th} 
5^{th} 
Bandwidth 

Expected: 
2.02V 
5.32V 
3.21v 
1.19V 
275mV 
0 
60KHz 
Observed: 
2.02V 
3.64V 
1.97V 
632mV 
155mv 
29.8mV 
100KHz 
Difference: 
0 
2.68V 
1.24V 
558mV 
120mV 
29.8mV 
40KHz 
10) Diagram 5: Frequency Modulation with m_{f} of 2.0:
11) Table 6: Modulation Index vs. Frequency:
Modulation Index: 
0.25 
0.50 
1.0 
2.0 
4.0 

Frequency: 
80KHz 
40KHz 
20KHz 
10KHz 
5KHz 
Deviation: 
20KHz 
20KHz 
20KHz 
20KHz 
20KHz 
12) Table 7: Expected vs. Observed Data at m_{f} of 2.0:

Expected: 
Observed: 
J_{x} 
O_{x} 
Difference: 

Carrier: 
2.40V 
2.40V 
.40 
.40 
0 
1^{st} Side Band: 
420mV 
472mV 
.07 
.079 
52mV 
2^{nd} Side Band: 
2.16V 
2.72V 
.36 
.45 
560mV 
3^{rd} Side Band: 
2.58V 
2.51V 
.43 
.42 
70mV 
4^{th} Side Band: 
1.68V 
1.41V 
.28 
.24 
270mV 
5^{th} Side Band: 
780mV 
580mV 
.13 
.10 
200mV 
6^{th} Side Band: 
300mV 
202mV 
.05 
.033 
98mV 
7^{th} Side Band: 
120mV 
60.0mV 
.02 
.01 
60mV 
8^{th} Side Band: 
0 
13.1mV 
0 
0 
13.1mV 
Bandwidth: 
70KHz 
50KHz 
0 
0 
20KHz 
13) Diagram 6: Frequency Modulation with m_{f} of 2.0:
14) Diagram 7: Schematic of Helper Circuitry:
Answers to Lab Questions
1) Q: What modulation index yielded a bandwidth closest to that of AM, and why?
A: m_{f} = .25 because the signal has only one set of side bands that are very low.
2) Q: If there was an FM signal that had an fc of 10MHz and deviated between 10.004MHz and 9.996MHz at a rate of 100Hz, what would the f_{m} and m_{f} be?
A: m_{f} = 40, f_{m} = 100Hz
3) Q: Given the same information in question 2, except the signal deviates form 10.005MHz to 9.996MHz, what is the modulation index, modulation freqency, and what type of wave would cause this?
A: m_{f} = 45, f_{m} = 100Hz; The signal is sinusoidal with a slight DC offset.
Conclusions
This lab has demonstrated that the bandwidth of an FM signal can be predicted in multiple ways. The ways are by predicting the size of the side bands or by using Carson's rule. Interestingly enough, the difference in bandwidths were identical throughout most of the trials. I believe that this is because Carson's Rule is based on 1% power and my method is based on 1% voltage. The FCC generally wants signal overtones attenuated between 40dB and 60dB from their useful counterparts, therefore, I believe that my method (BW = 2 * n_{sidebands} * f_{mpk)} is much more accurate. It should be noted that, in order to obtain a 20KHz deviation at a 2V_{pp} signal, a pre amplifier was required. The 1Vp signal was applied to the input of the operational amplifier preamplifier input signal. All fm calculations were based off of this input. Because of some of the operational amplifiers limitations, I believe that many of the inaccuracies in this lab can be attributed to that. However, the lab was fairly accurate. I do believe that the carrier calculation for m_{f} = 2.0 was incorrect and let that set of results to be somewhat inaccurate. It is also possible that the signal generator was not accurate and therefore the signal was not truly 2.0. For the voltage offsets, the signal from the 1KW pot was sent to the input of the preamplifier. I believe that some of the inaccuracies of the last reading of 72KHz was possible skewed by this as well. I calculated and figured that with an amplification of approximately 5.8 and a Vi of 4V, compounded with the face that the power supply was not truly balanced, the op  amp was attempting to put out a voltage beyond it's capabilities and therefore caused skewed results. I am satisfied with the results of the lab due to the circumstances that it was run under. For a schematic diagram of the assist circuit, please refer to item #14, Diagram 7.
Attachments
Original lab handout
Original lab data
Calculations