Instantaneous Frequency Of An Fm Signal example essay topic

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, base band 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, etc! -).

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|fm (t) = Acos (|'E (t) ) = Acos (wet +|'Ec (t) ) where |'Ec (t) = kf!' Om (|'O) d|'Of = deviation sensitivity wc = carrier frequency The instantaneous frequency is defined as: wi (t) = d|'E (t) / F Mwi (t) = wc +km (t) equation (1.0) This form of modulation can be performed indirectly using a basic var actor diode circuit. 2 var actor diode modulator var actor 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 avar actor 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 var actor dio demodulator of Fig 1.0, the carrier is coupled via a transformer to the tank circuit in the secondary. The carrier undergoes a phase shift, |'Ec, 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, |'Ec (t) will vary at the same rate as the modulating signal so that |'Ec (t) = a (t), where a (t) = kf!' Om (|'O) d|'O (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 is 3 wi (t) = wc +km (t) which varies from wc +kf|m (t) | to wc-kf|m (t) |. Let the modulating index, m, be defined asm = kf|m (t) | / wm, where wm is m (t)!