Fm Receivers

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

Frequency modulation (FM) was invented in 1936 by an American electrical engineer/

inventor named Edwin H. Armstrong. Possessing numerous advantages over the existing

AM broadcasting system, as will be discussed later, in combination with relatively low

cost of implementation, resulted in its rapid growth. In the years following World War

Two, there were 600 licensed stations broadcasting in the U.S. By 1980, the number grew

to 4000. On another historical note, in 1961 stations began broadcasting in stereo.

The basic receiver design consists of the following components. An antenna is used to

convert electro-magnetic waves into electrical oscillations. Amplifiers are used

throughout the receiver to boost signal power at radio, baseband and intermediate

frequencies. The core of the FM receiver, the discriminator, comes in various circuit

forms and is used in detection and demodulation. Basically, its role is to extract the

intelligence or message from the carrier wave. Another component, essential in most

electronic circuits, is the power supply (DC or AC converted to DC). Finally, a

transducer (speaker in the case of Radio) is needed to convert the message signal into its

final form (audio, mechanical, etcÐŽ­). Other components more specific to FM receivers

are mixers combined with local oscillators used for frequency manipulation, limiters to

control amplitude, de-emphasis and other filter circuits.

2

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(¦Ð˜(t)) = Acos(wct +¦Ð˜c(t))

where ¦Ð˜c(t)= kf ЎТm(¦Ð£)d¦Ð£

kf = deviation sensitivity

wc = carrier frequency

The instantaneous frequency is defined as:

wi(t)=d¦Ð˜(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

3

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, ∆¦Ð˜c, 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, ¦Ð˜c(t) will vary at the same rate as

the modulating signal so that ¦Ð˜c(t)= a(t), where a(t) = kf ЎТm(¦Ð£)d¦Ð£ (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 wc-kf|m(t)|. Let the modulating index, m, be defined as

m = kf|m(t)| / wm , where wm is m(t)ЎЇs frequency.

It can be demonstrated the bandwidth of an FM signal is theoretically infinite. This

would pose a serious problem in the signalЎЇs reception. However, for narrowband FM (m

is small), the effective bandwidth can be approximated to be that of m(t), centered at wc.

For wideband FM (m large) the bandwidth depends mostly on the magnitude of m(t) and

can be approximated by 2kf|m(t)|. In practice, FM broadcasting