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Unformatted text preview: 5-1YEDITEPE UNIVERSITY ENGINEERING FACULTY COMMUNICATION SYSTEMS LABORATORY EE 351 – COMMUNICATION SYSTEMS I EXPERIMENT 5: ANALYSIS OF THE FM SPECTRUM Objective: Understanding the nature of phase modulated (PM)and frequency modulated (FM)signals and the action of a synchronous demodulator on FM signal. Equipment: ¾Audio Oscillator Module ¾Buffer Amplifier Module ¾VCO Module ¾Oscilloscope General Information: Angle Modulation: The defining equation for both PM and FM can be written in the form: ( ) ( )ttEtyμβωsincos.+=βcan be chosen to represent either PM or FM as: for PM φβΔ=, the peak phase deviation for FM μφβ/Δ=the parameter βis often called the deviation. Both PM and FM fall into a class known as angle modulatedsignals. Phase Modulation (PM) A signal can be phase modulated by the message tAμcos., if: total phase = tktμωcos.1+and provided k1is linearly proportional to A, the message amplitude. Hence: ( )tktEPMμωcoscos.1+=is a phase modulated signal. Note that, for PM: instantaneous frequency = tkμμωsin..1−5-2Although the frequency is also varying with the message, the variation is not directly proportional to the message amplitude alone. Hence, by definition, this is not frequency modulation. Frequency Modulation (FM) A signal can be phase modulated by the message tAμcos., if: instantaneous frequency = tkμωcos.2+and provided k2is linearly proportional to A, the message amplitude. The total phase is obtained by integration of the instantaneous frequency, and thus the signal itself must be: ⎟⎟⎠⎞⎜⎜⎝⎛+=tktEFMμμωsincos.1Although the phase is also varying with the message, the variation is not directly proportional to the message amplitude alone. Hence, by definition, this is not phase modulation. Spectrum Analysis The spectrum of an angle modulated signal can be obtained by trigonometrical expansions and be found in the compact form as: ( ) ( ) ( )∑∞=−∞=+=nnntnJEtyμωβcos..Here Jn(β) is a Bessel function of the first kind, argument β, and order n. Despite the apparent complexity of this equation, which describes the spectrum of the signal, it is easy to make and remember many general observations about the nature of this spectrum using the nature of the Bessel functions shown in Figure 5.1....
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This note was uploaded on 10/18/2009 for the course EE ee353 taught by Professor Ee during the Spring '05 term at Istanbul Technical University.
- Spring '05