LABORATORY 3:
FREQUENCY MODULATION AND DETECTION
EEE 186: COMMUNICATIONS SYSTEMS LABORATORY
Department of Electrical & Electronic Engineering
College of Engineering & Computer Science
California State University, Sacramento
FALL 2015
Frequency Modulation and Detection
Frequency modulation (FM) is more complex than Amplitude Modulation (AM), since it involves changing the carrier frequency, rather than the carrier amplitude. It was proposed first by Armstrong [1], who had to fight an uphill battle, with intense opposition from the AM industry. Even then, it was accepted only after his lifetime. Basically, FM can be defined by the following equation:
(1)
where the terms in the equation are defined as:
A: Carrier amplitude, Volts
fc: Carrier frequency, Hz
kf: FM constant, Hz/Volts
m(t): message signal, Volts
Defining the modulation index as:
we can rewrite eqn.(1) as follows:
(2)
The bandwidth of FM is inherently larger compared to the bandwidth of AM, hence accounting for its higher fidelity and quality of audio and music. However, the lower bandwidth of AM is useful in video, which occupies the MHz range, as compared to audio, which occupies lower KHz range. A classic application of AM and FM is in television, which uses FM for audio and AM for video.
Part I. Simulation of Frequency Modulation using Simulink
The simulation of FM basically involves the implementation of eqn. (2) given above. The process involves addition, integration and cosine function to generate the frequency modulated signal.
(a)Simulate the FM system as shown below in Figure 1, using Simulink software.
Figure 1. Block diagram of Frequency Modulation (FM) System
(b)Obtain the time domain plot and power spectrum plot of the FM signal.
(c)Note down the frequency and amplitude of the carrier and first four sidebands.
Part II. Fabrication and Testing of FM transistor circuit
The simple FM circuit is shown below in Figure 2, and is built using the general purpose 2N3904 transistor. The carrier frequency is determined by the tank or oscillator circuit, comprising of the inductor L1 and variable capacitor VC1 connected in parallel. The frequency of oscillation is determined by the equation:
Assuming L1 = 0.1 H and VC1 = 50pF, we obtain fc ~ 50 MHz. The variable capacitor can be tuned to get exactly 50 MHz as the unmodulated carrier.
Figure 2. FM Modulation circuit
(Courtesy:
Fabricate the circuit shown in Figure 2 above. Measure the carrier signal, audio signal and the modulated FM signal in both time and frequency domains. Note the frequencies and amplitudes of the carrier and first four sidebands.
Part III. Comparison of Simulated and Measured data
(a) Compare the measured and computed power spectrum of the carrier and four sidebands in mW, after normalizing the peak values of the fundamental to 1 mW (0 dBm).
(b) Compute the % error between the computed and measured power spectrum (mW).
The % error is defined as:
|Pcn, comp - Pcn, meas|
% error = ------
Pcn, comp