EE - 401 / E01 Fall 2002

Introductory Communications Theory

Professor: Conner

Submitted By:

Andrew Buettner

Lab #3: Frequency Modulation

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 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 Multi-Meter #1367

7) Various components from the EE-301 / 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_mof 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