ANGLE MODULATION CHAPTER 3 ANGLE MODULATION Part 1

ANGLE MODULATION CHAPTER 3

ANGLE MODULATION Part 1 n. Introduction

Introduction n Angle modulation is the process by which the angle (frequency or phase) of the carrier signal is changed in accordance with the instantaneous amplitude of modulating or message signal.

Cont’d… n classification into two types such as n n n Frequency modulation (FM) Phase modulation (PM) Used for : n n n Commercial radio broadcasting Television sound transmission Two way mobile radio Cellular radio Microwave and satellite communication system

Cont’d… Advantages over AM: Ø Ø Ø freedom from interference: all natural and external noise consist of amplitude variations, thus the AM receiver usually cannot distinguish between amplitude of noise or desired signal. AM is noisier than FM. operate in very high frequency band (VHF) and above; (commercial FM broadcast band): 88 M-108 MHz Can transmit musical programs with higher degree of fidelity.

FREQUENCY MODULATION PRINCIPLES n n In FM the carrier amplitude remains constant, the carrier frequency varies with the amplitude of modulating signal. The amount of change in carrier frequency produced by the modulating signal is known as frequency deviation.

Carrier Resting fc Increasing fc Decreasing fc Increasing fc Resting fc Modulating signal FM

Comparison of AM and FM

n n The process by which changing the phase of Phase carrier signal inmodulation(PM) accordance with the instantaneous of message signal. The amplitude remains constant after the modulation process. Mathematical analysis: Let message signal: And carrier signal:

PM(cont’d) n n Where = phase angle of carrier signal. It is changed in accordance with the amplitude of the message signal ; After phase modulation the instantaneous voltage will be where ; modulation index of phase modulation K is a constant and called deviation sensitivities of the phase. Unit in rad/V or deg/V.

FREQUENCY MODULATION(FM) n n A process where the frequency of the carrier wave varies with the magnitude variations of the modulating or audio signal. The amplitude of the carrier wave is kept constant.

Differences between FM and PM Waveforms Carrier Modulating signal FM PM

FM(cont’d) n Mathematical analysis: Let message signal: n And carrier signal: n

n During the process of frequency modulations the frequency of carrier signal is changed in accordance with the instantaneous amplitude of message signal. Therefore the frequency of carrier after modulation is written as FM (cont’d) n To find the instantaneous phase angle of modulated signal, integrate equation above with respect to t where K 1 is the deviation sensitivity constant for FM, unit in or Hz/V.

FM(cont’d) n Thus, we get the FM wave as: where modulation index for FM is given by

FM(cont’d) n Frequency deviation: ∆f is the relative displacement of carrier frequency (Hz) w. r. t its unmodulated value. Given as:

FM(cont’d) n where is the modulation index for FM. Therefore:

Equations for Phase and Frequency Modulated Carriers Equations for Phase- and Frequency-Modulated Carriers Tomasi Electronic Communications Systems, 5 e Copyright © 2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Bessel Function n The expression of a carrier that either being phase or frequency modulated by a single frequency modulating signal can be written in a general form as, ----- (1) where deviation. is the instantaneous phase

Bessel function (cont’d) n BF is used to analyze angle-mod. wave by a singlefreq. sinusoidal produces a peak phase deviation of m radians, where m is the modulation index. BF identity states, ----(2) Jn(m) is the Bessel Function of the First Kind of nth order with argument m. If eqn. (2) is applied into eqn. (1), it can be written as, ----(3)

Bessel function (cont’d) Expanding eqn. (3),

B. F. (cont’d) n n n It is seen that each pair of side band is preceded by J coefficients. The order of the coefficient is denoted by subscript m. The Bessel function can be written as n= number of the side frequency or J mf = modulation index

Bessel Functions of the First Kind, Jn(m) for some value of modulation index

B. F. (cont’d)

Representation of frequency spectrum

Angle Modulation Part 2 FM Bandwidth n. Power distribution of FM n. Generation & Detection of FM n. Application of FM n

FM Bandwidth n n Theoretically, the generation and transmission of FM requires infinite bandwidth. Practically, FM systems have finite bandwidth and they perform well. The value of modulation index determine the number of sidebands that have the significant relative amplitudes Estimation of FM bandwidth can be made by 2 methods : a) Bessel Function b) Carson’s rule

FM Bandwidth (cont’d) a) Bessel Function If n is the number of sideband pairs, and line of frequency spectrum are spaced by fm, thus the bandwidth is: where , number of significant sidebands fm --- modulating signal freq. This is the equation to determine the minimum BW for angle mod. wave using Bessel table.

FM Bandwidth (cont’d) b) Carson’s rule is an approximation and gives transmission BW slightly narrower than the BW determined using the Bessel table. Carson’s rule is, where ------ peak freq. deviation fm ------ modulating signal freq.

FM Bandwidth (cont’d) For low mod. index (where m<1), the freq. spectrum resembles AM DSBFC, and the min. BW is approximate by, For high mod. index (where by, ), the min. BW is given

Deviation Ratio (DR) n n The worse case modulation index which produces the widest output frequency spectrum. Where n ∆f(max) = max. peak frequency deviation n fm(max) = max. modulating signal frequency

FM Power Distribution n n As seen in Bessel function table, it shows that as the sideband relative amplitude increases, the carrier amplitude, J 0 decreases. This is because, in FM, the total transmitted power is always constant and the total average power is equal to the unmodulated carrier power, that is the amplitude of the FM remains constant whether or not it is modulated.

FM Power Distribution (cont’d) n n In FM, the total power that is originally in the carrier is redistributed between all components of the spectrum, in an amount determined by the modulation index, mf and the corresponding Bessel functions. At certain value of modulation index, the carrier component goes to zero, where in this condition, the power is carried by the sidebands only. (refer to Bessel Table : at mf = 2. 4, 5. 45 and 8. 65)

FM Power Distribution (cont’d) n The average power in unmodulated carrier n The total instantaneous power in the angle modulated carrier. n The total modulated power

Generation of FM Two methods of FM generation: n A. Direct method: i) iii) iv) straight forward, requires a VCO whose oscillation frequency has linear dependence on applied voltage. Advantage: large frequency deviation Disadvantage: the carrier frequency tends to drift and must be stabilized. Example circuits: 1) Reactance modulator 2) Varactor diode

Generation of FM (cont’d) 1) Reactance modulator

Generation of FM (cont’d) 2) Varactor diode modulator

Generation of FM (cont’d) B) Indirect method: Armstrong modulator by using frequency-up conversion that involves 2 methods : a. Heterodyne method b. Multiplication method

Wideband Armstrong Modulator

A complete Armstrong modulator is supposed to provide a 75 k. Hz frequency deviation. It uses a balanced modulator and 90 o phase shifter to phasemodulate a crystal oscillator. Required deviation is obtained by combination of multipliers and mixing, raise the signal from suitable for broadcasting.

FM Detection/Demodulation n Is a process of getting back or regenerate the original modulating signal from the modulated FM signal. n It can be achieved by converting the frequency deviation of FM signal to the variation of equivalent voltage. n n The demodulator will produce an output where its instantaneous amplitude is proportional to the instantaneous frequency of the input FM signal. To detect an FM signal, it is necessary to have a circuit whose output voltage varies linearly with the frequency of the input signal

FM detection (cont’d) Several types : a) PLL (Phase-Locked Loop) demodulator b) Slope detection / FM discriminator c) Foster-Seeley Phase-Shift discriminator d) Ratio detector e) Quadrature FM detector Except for PLL, others are traditional FM detectors having tuned circuits for detection. The most commonly used demodulator presently is the PLL demodulator because of its simplicity and small size. Can be use to detect either NBFM or WBFM.

PLL Demodulator FM input, fi(t) V 0(t) Phase detector Low pass filter Amplifier fvco VCO Vc(t) Demod. signal output

PLL Demodulator Brief operation : The phase detector produces an average output voltage that is linear function of the phase difference between the two input signals. Then the low frequency component is passed through the LPF to get a small DC average voltage to the amplifier. After amplification, part of the signal is fed back through VCO where it results in frequency modulation of the VCO frequency. When the loop is in lock, the VCO frequency follows or tracks the incoming frequency.

PLL Demodulator n n Let instantaneous freq of FM Input, fi(t)=fc +k 1 vm(t), and the VCO output frequency, f VCO(t)=f 0 + k 2 Vc(t); f 0 is the free running frequency. For the VCO frequency to track the instantaneous incoming frequency, fvco = fi; or

PLL Demodulator n f 0 + k 2 Vc(t)= fc +k 1 vm(t), so, n If VCO can be tuned so that fc=f 0, then n Where Vc(t) is also taken as the output voltage, which therefore is the demodulated output

Comparison AM and FM n n Its SNR can be increased without increasing transmitted power about 25 d. B higher than in AM Certain forms of interference at the receiver are more easily to suppressed, as FM receiver has a limiter which eliminates the amplitude variations and fluctuations. n The modulation process can take place at a low level power stage in the transmitter, thus a low modulating power is needed. n Power content is constant and fixed, and there is no waste of power transmitted n There are guard bands in FM systems allocated by the standardization body, which can reduce interference between the adjacent channels.

Applications of FM n n Used as WBFM in FM broadcasting and TV audio modulation. Used as NBFM in VHF communication equipment such as portable, mobile and based stations. It is preferred because of its immunity to noise or interference and at the frequencies which used the antennas of a reasonable size.

Summary of angle modulation -what you need to be familiar with

Summary (cont’d)

Summary (cont’d) n a) Bandwidth: Actual minimum bandwidth from Bessel table: b) Approximate minimum bandwidth using Carson’s rule:

Summary (cont’d) n Multitone modulation (equation in general):

Summary (cont’d)

Summary (cont’d)Comparison NBFM&WBFM

ANGLE MODULATION Part 3 Advantages n. Disadvantages n

Advantages n n n Wideband FM gives significant improvement in the SNR at the output of the RX which proportional to the square of modulation index. Angle modulation is resistant to propagation-induced selective fading since amplitude variations are unimportant and are removed at the receiver using a limiting circuit. Angle modulation is very effective in rejecting interference. (minimizes the effect of noise). Angle modulation allows the use of more efficient transmitter power in information. Angle modulation is capable of handling a greater dynamic range of modulating signal without distortion than AM.

Disadvantages n n Angle modulation requires a transmission bandwidth much larger than the message signal bandwidth. Angle modulation requires more complex and expensive circuits than AM.

END OF ANGLE MODULATION