Topics: Amplitude modulation, Radio, Frequency modulation Pages: 6 (1874 words) Published: April 14, 2005
Abstract
This paper will discuss the design of an FM receiver. It will begin with a brief historical backdrop of FM broadcasting and its use in society. It will continue by providing the necessary mathematical background of the modulation process. Furthermore, it will enumerate some of the advantages of FM over other forms of modulation, namely AM. Finally, the paper will discuss the design of a basic FM receiver as well as introduce some circuits and circuit components which the reader may not be familiar with. Introduction

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Mathematics of FM
Unlike amplitude modulation (AM) where the message or modulating signal, call it m(t), is used to modulate the amplitude of the carrier signal, frequency modulation, as the name implies, uses m(t) to transform the frequency of the carrier. The amplitude of an FM signal should remain constant during the modulating process; an important property of FM. A general FM signal can be described by the following:1 ¦µFM(t) = Acos(¦È(t)) = Acos(wct +¦Èc(t))

where ¦Èc(t)= kf ¡Òm(¦Ó)d¦Ó
kf = deviation sensitivity
wc = carrier frequency
The instantaneous frequency is defined as:
wi(t)=d¦È(t)/dt
for FM
wi(t) = wc +kfm(t) equation(1.0)
This form of modulation can be performed indirectly using a basic varactor diode circuit.2 varactor diode modulator varactor diode model
1 Derivation/Definition from Signals & Systems 2nd Edition
2 Circuit Diagram from Analog Communications for technology
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When the diode is placed in reverse bias, the depletion region of the pn junction increases. Charge builds up on both sides of the junction implying a capacitance Cj. In a varactor diode, Cj is a function of the reverse bias voltage. During this application, the diode is biased such that this relationship is approximately linear. In the varactor diode modulator of Fig1.0, the carrier is coupled via a transformer to the tank circuit in the secondary. The carrier undergoes a phase shift, ∆¦Èc, due to the complex impedance of the tank. The modulating signal changes the biasing point and consequently Cj of the diode. This in turn changes the resonant frequency of the tank circuit and consequently, the phase shift of the incoming signal. If design properly, ¦Èc(t) will vary at the same rate as the modulating signal so that ¦Èc(t)= a(t), where a(t) = kf ¡Òm(¦Ó)d¦Ó (i.e. an integrator, not shown in figure, is used beforehand to generate a(t)).

Properties of FM Signals
As defined in equation (1.0), the instantaneous frequency of an FM signal is3 wi(t) = wc +kfm(t)
which varies from wc +kf|m(t)| to...