FREQUENCY AND

PHASE MODULATION(ANGLE MODULATION)

• ANGLE MODULATION –• When frequency or phase of the carrier is varied

by the modulating signal , then it is called angle modulation.

• Frequency Modulation – When the frequency of the carrier varies as per amplitude of modulating signal, then it is called frequency modulation (FM).

• Phase Modulation - When the phase of the carrier varies as per amplitude of modulating signal, then it is called phase modulation (PM).

• Amplitude of the modulated carrier remains constant in both modulation systems.

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• An important feature of angle modulation:• It can provide a better discrimination

(robustness) against noise and interference than AM.

• This improvement is achieved at the expense of increased transmission bandwidth.

• In case of angle modulation, channel bandwidth may be exchanged for improved noise performance

• Such trade-off is not possible with AM

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• BASIC DEFINITIONS -Relationship between the angle and frequency of a sinusoidal signal

• Sinusoidal carrier c(t) =Ac cos[θi(t)]• Angle of carrier θi(t)[rad]• Instantaneous frequency of carrier

fi(t) =(1/2π)ωi(t) =(1/2π)di(t)/dt• =(1/2π)˙ θi(t)[Hz].• In the case of an un-modulated carrier,

the angle becomes θi(t) = 2πfct + θcBDG(xx) 4

Time domain representation

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• Compare FM-PM –• The basic difference between FM & PM lies in

which property of the carrier is directly varied by modulating signal.

• In FM, the frequency of carrier is varied directly.

• In PM, phase of the carrier is varied directly. Instantaneous phase deviation is represented by θ(t).

• Instantaneous phase= ωct + θ(t) rad.

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• Instantaneous frequency deviation =• d/dt {θ(t)} = θ’(t) Hz.• The instantaneous frequency deviation is the

instantaneous change in carrier frequency and is equal to the rate at which instantaneous phase deviation takes place.

• Instantaneous frequency is defined as frequency of the carrier at a given instant of time and is given as ωi(t) =d/dt [ωc.t + θ(t)] = ωc + θ’(t) rad/sec.

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• Instantaneous phase deviation θ (t) is proportional to modulating signal voltage, θ (t) = k em(t) rad. ( k is deviation sensitivity of phase.).

• Instantaneous frequency deviation θ’ (t) is proportional to modulating signal voltage, θ’ (t) = k1 em(t) rad. ( k1 is deviation sensitivity of frequency.)##2

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5.9

Frequency modulation

• Observations from the FM & PM waveforms – • 1. Both FM & PM waveforms are identical

except the phase shift.• 2. For FM, the maximum frequency deviation

takes place when modulating signal is at +ve and –ve peaks.

• 3. For PM, the maximum frequency deviation takes place near zero crossing of the modulating signal.

• 4. It is diffcult to know from modulated waveform whether the modulation is FM or PM. (##3)

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• Bandwidth Requirement – for FM- • The BW requirement can be obtained depending on

the modulation index (M.I).• The M.I. can be classified as high(more than 10),

medium (1 to 10) and low (less than 1).• The low index systems are called narrowband FM in

which frequency spectrum resembles AM. BW (fm) =2fm Hz.

• For high index modulation, BW = 2*δ.(Freq. dev.)• BW can also be found out by Bessel table-

BWfm = 2.n.fm where n is the number of sidebands obtained from table.

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• Carson’s Rule – • Rule gives approximate minimum BW of angle

modulated signal as • BW fm = 2{δ + fm(max)} Hz.• From the above equation, it is found that the

BW accommodates almost 98% of the total transmitted power

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• Bandwidth for PM –• BW for PM is expressed as • BWpm = 2(mp+1)fm.

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• Block Diagram of NBFM Generator –• Carrier is Ec cos ωc .t

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Integrator Product Modulator

90 degree Phase Shifter

Carrier Generator

Adder M(t) NBFM signal

• Phasor Diagram of NBFM –• USB phasor at an angle of (ωm .t) and LSB

phasor at an angle of (- ωm .t)

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USB PhasorLSB Phasor

Carrier Phasor

Resultant Phasor

Phase Shift

• Carrier phasor is Ec cos ωc .t (always fixed).• USB phasor in clockwise direction (ωm)• LSB phasor in counter clockwise direction (-ωm)• Resultant of two sideband phasor is always

perpendicular to carrier phasor.• The net resultant phasor of NBFM due to Carrier

and sidebands is as shown in the diagram.

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• Wideband Frequency Modulation –• If the modulation index is higher than 10, then

it is called wideband FM.• Spectrum contains infinite numbers of

sidebands and carrier as against two sidebands and carrier in NBFM.

• BW is = 2{δ+fm(max)} as against 2fm for NBFM.

• Used for broadcast and entertainment as against for mobile communication for NBFM.

• ##5.BDG(xx) 19

• Advantages of Angle Modulation over AM-• 1. As the amplitude of FM carrier is constant,

the noise interference is minimum.• 2. The amplitude of FM carrier is constant and

is independent of depth of modulation. Hence transmitter power remains constant in FM whereas it varies in AM.

• 3. As against the limitation of depth of modulation in AM, in FM depth of modulation can be increased to any value, without causing any distortion.

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• 4. Because of guard bands provided in FM, adjacent channel interference is very less.

• 5. Since FM uses VHF and UHF bands of frequencies, the noise interference is minimum as compared to AM which uses MF and HF ranges.

• 6. Radius of propagation is limited as FM uses space waves with line of sight. So it is possible to operate many independent transmitters on the same frequency with minimum interference.

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• Disadvantages of FM compared to AM-• 1. BW requirement of FM is very high as

compared to AM.• 2. FM equipments are more complex and

hence costly.• Area covered by FM is limited, to line of sight

area but AM coverage area is large.

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• Comparison between FM and AM -

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Parameter AM FM

Origin AM method of audio transmission was first successfully carried out in the mid 1870s.

FM radio was developed in the United states mainly by Edwin Armstrong in the 1930s.

Modulating differences

In AM, a radio wave known as the "carrier" or "carrier wave" is modulated in amplitude by the signal that is to be transmitted

In FM, a radio wave known as the "carrier" or "carrier wave" is modulated in frequency by the signal that is to be transmitted.

ImportanceIt is used in both analog and digital communication and telemetry

It is used in both analog and digital communication and telemetry

Frequency Range

AM radio ranges from 535 to 1705 KHz (OR) Up to 1200 Bits per second.

FM radio ranges in a higher spectrum from 88 to 108 MHz. (OR) 1200 to 2400 bits per second.

• Comparison between FM and AM -

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Parameter AM FM

Bandwidth Requirements

Twice the highest modulating frequency. In AM radio broadcasting, the modulating signal has bandwidth of 15kHz, and hence the bandwidth of an amplitude-modulated signal is 30kHz.

Twice the sum of the modulating signal frequency and the frequency deviation. If the frequency deviation is 75kHz and the modulating signal frequency is 15kHz, the bandwidth required is 180kHz.

Complexity Transmitter and receiver are simple but synchronization is needed in case of SSBSC AM carrier.

Transmitter and receiver are more complex as variation of modulating signal has to be converted and detected from corresponding variation in frequencies.(i.e. voltage to frequency and frequency to voltage conversion has to be done).

Noise AM is more susceptible to noise because noise affects amplitude, which is where information is "stored" in an AM signal.

FM is less susceptible to noise because information in an FM signal is transmitted through varying the frequency, and not the amplitude.

• Comparison between FM and PM -

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Sr No. FM PM

1 The max frequency deviation depends on amplitude of modulating signal and its frequency

The max phase deviation depends on amplitude of modulating signal

2 Frequency of the carrier is modulated by modulating signal.

Phase of the carrier is modulated by modulating signal.

3 Modulation index is increased as modulation frequency is reduced and vice versa.

Modulation index remains same if modulating signal frequency is change.

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• Modulators –• Carrier frequency can be generated by LC

oscillator.• By varying the values of L or C of tank circuit,

carrier frequency can be changed.• Properties of BJT,FET and varactor diodes can

be varied by changing the voltage across them.

• When these components are used with LC tank circuits, we are able to vary frequency of oscillator by changing the reactance of L or C.

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• TWO types of FM Modulators –• 1. Indirect FM – Modulation is obtained by

phase modulation of the carrier. An instantaneous phase of the carrier is directly proportional to the amplitude of the modulating signal.

• 2. Direct FM- The frequency of carrier is varied directly by modulating signal. An instantaneous frequency variation is directly proportional to the amplitude of the modulating signal.

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• There are two methods to derive FM by using FET and varactor.

• 1. Frequency modulation using Varactor Diode –• There exists small junction capacitance in the

reverse biased condition of all the diodes.• The varactor diodes are designed to optimise

this characteristic.• As the reverse bias across varactor diode is

varied, its junction capacitance changes.• These changes are linear and wide (1 to 200pF)

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• Frequency modulation using varactor diode –• All diodes show small junction capacitance in

the reverse biased condition.• ##6

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• Advantages of FM using Varactor Diode –• 1. High frequency stability as crystal oscillator

is isolated from modulator.• Disadvantages –• 1. To avoid distortion, the amplitude of

modulating signal is to be kept small.• 2. The varactor diode must have non linear

characteristics of capacitance vs. voltage.• Use –• This method is used for low index narrow

band FM generation. BDG(xx) 31

• FET Reactance Modulator –• There are a number of devices whose reactance

can be varied by the application of voltage. These include FET and BJT, varactor diode etc.

• If such a device is placed across the tank circuit of the L-C oscillator, then FM will be produced when the reactance of the device is varied by the modulating voltage.

• At the carrier frequency, the oscillator inductance is tuned by its own capacitance in parallel with the average reactance to the variable reactance device.

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• Advantages of FET Reactance Modulator –• 1. Due to FET characteristics, linear

relationship between modulating voltage and transconductance can be achieved.

• 2 This method produces enough frequency deviation and hence no frequency multiplication is required.

• Disadvantages - Frequency stability is poor as lumped components are used.

• Use – This method is used for low modulation index application.

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• Indirect FM –• Phase modulation is used to achieve

frequency modulation in the indirect method, • It is necessary to integrate the modulating

signal prior to applying it to the phase modulator,

• This transmitter is widely used in VHF and UHF radio telephone equipment.

• ##7

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• Advantage – • 1. The crystal oscillator is isolated from

modulator, so frequency stability is very good.• Disadvantages –• 1. Because of nonlinear capacitance Vs.

voltage characteristics of varactor diode, there is a distortion in the modulated output waveform.

• 2. Amplitude of modulating signal should be kept small to avoid distortion.

• Use –Used for narrow band low index FM.BDG(xx) 35

• FM Transmitters –• Two types of transmitters – Indirect FM and

Direct FM Transmitters.• Indirect FM Transmitters – Produces the FM

whose phase deviation is directly proportional to modulating signal amplitude. Frequency of oscillator is not directly varied. Hence crystal oscillators can be used.

• Direct FM Transmitters – Frequency deviation is directly proportional to modulating signal. Carrier frequency is directly deviated.

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• Need for Automatic Frequency Correction –• In FM transmitters, the frequency of the

oscillator is directly varied.• To obtain very stable frequency of oscillator,

automatic frequency correction technique is employed.

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• FM Transmitters –• Block Diagram –##8• The modulating signal is given to frequency

modulator ( may be reactance modulator or VCO ) and oscillator.

• Let fc = F Mhz. Multiplied by 18 to generate the transmitted frequency F*18 Mhz.

• AFC loop is to maintain stable centre frequency.

• Multiplier output given to mixer is F*6.

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• The crystal frequency oscillator - reference frequency is {(6*fc) – 2MHz.}

• The mixer generates 2 MHz difference frequency which is given to discriminator, which is tuned to 2 MHz.

• If there is a difference in the output frequency of mixer, discriminator generates d. c. correction voltage.

• If multiplier frequency is exactly 6*fc, then no correction is required and hence correction voltage must be zero.

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• But with FM, there is a frequency deviation in 6*fc, which is proportional to modulating signal amplitude.

• So d.c. correction voltage also have corresponding variation.

• Therefore this d.c. voltage is passed through low pass filter to remove effect of frequency variation due to modulation.

• The filtered voltage is used for frequency correction.

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• Phase Locked Loop direct FM transmitter –• This type is used to produce WBFM with high

mod index.• When both the input frequencies to phase

comparator are same , they are locked and output is zero.

• The modulating signal is used to control the output frequency of VCO.

• The frequency of output FM of VCO is a function of modulating signal.

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• If there is a deviation in the centre frequency of VCO, correction voltage is generated.

• This d.c. voltage, passing through LPF, is added to modulating signal to correct the VCO output.

• Function of LPF is to remove rapid changes in correction voltage due to frequency variations in FM signal.

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• Indirect FM Transmitter – Armstrong Method -• ( Phase Mod. is employed to produce FM)• Stability of the frequency is a major issue in

FM. So direct methods of FM generation are not suitable for broadcasting .

• To overcome this drawback, indirect method to generate FM from PM is employed. (block dia.)

• To get the modulating signal of same frequency of carrier, AM signal is generated and shifted by 90degrees and added to fc signal vector.

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• The resultant vector output is phase modulated.

• Since AM and carrier vectors are having same frequency(fc), the out put is FM.

• Thus phase modulation produces FM.• The phase modulated signal can be defined as

e(pm) = Ec sin (ωc t + m cos ωm t).• ##

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• FOSTER SEELEY DISCRIMINATOR – (Phase discriminator)-

• The Foster Seeley Discriminator is a common type of FM detector circuit used mainly within radio sets constructed using discrete components.

• The Foster Seeley detector (or the Foster Seeley discriminator) has many similarities to the ratio detector. The circuit topology looks very similar, having a transformer and a pair of diodes, but there is no third winding and instead a choke is used.

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• Cc,C1 & C2 offers short circuit for IF center frequency.

• Right side of L3 is at ground potential and IF(Vin) is fed directly (in phase)across L3.(VL3)

• 180 degree phase out by T1 – La & Lb equal division.

• At resonant frequency of tank circuit(IF) secondary current (Is) is in phase with Vs and 180degree out of phase with VL3.

• Like the ratio detector, the Foster-Seeley circuit operates using a phase difference between signals.

• To obtain the different phased signals a connection is made to the primary side of the transformer using a capacitor, and this is taken to the center tap of the transformer.

• This gives a signal that is 90 degrees out of phase.

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• Due to loose coupling , primary of T1 acts as inductor and Ip is 90 degree out of phase with Vin.

• Voltage induced in secondary is 90 degree out of phase with Vin(VL3)

• VLa and Vlb are 180 degree out of phase with each other and 90 degree out of phase with VL3.

• Voltage across VD1 is vector sum of VL3 and VLa and VD2 is vector sum of VL3 and VLb.

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• When IF > resonance, secondary tank circuit impedance becomes inductive and secondary current lags voltage by theta which is proportional to frequency deviation.

• When IF < resonance, secondary current leads secondary voltage by theta which is proportional to frequency deviation.

• F.S.D. is tunned by injecting a frequency equal to the IF center frequency and tunning Co for zero volts output.

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• Ratio Detector –• Ratio detector or discriminator is widely used

for FM demodulation within radio sets using discrete components. It was capable of providing a good level of performance.

• In recent years the Ratio detector has been less widely used.

• The main reason for this is that it requires the use of wire wound inductors and these are expensive to manufacture.

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• Ratio Detector Circuit –

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• Other types of FM demodulator have overtaken them, mainly as a result of the fact that the other FM demodulator configurations lend themselves more easily to being incorporated into integrated circuits.

• Ratio FM detector basics -• When circuits employing discrete components

were more widely used, the Ratio and Foster-Seeley detectors were widely used. Of these the ratio detector was the most popular as it offers a better level of amplitude modulation rejection.

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• This enables it to provide a greater level of noise immunity as most noise is amplitude noise, and it also enables the circuit to operate satisfactorily with lower levels of limiting in the preceding IF stages of the receiver.

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• The operation of the ratio detector centres around a frequency sensitive phase shift network with a transformer and the diodes that are effectively in series with one another.

• When a steady carrier is applied to the circuit the diodes act to produce a steady voltage across the resistors R1 and R2, and the capacitor C3 charges up as a result.

• The transformer enables the circuit to detect changes in the frequency of the incoming signal. It has three windings.

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• The primary and secondary act in the normal way to produce a signal at the output. The third winding is un-tuned and the coupling between the primary and the third winding is very tight, and this means that the phasing between signals in these two windings is the same.

• The primary and secondary windings are tuned and lightly coupled.

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• This means that there is a phase difference of 90 degrees between the signals in these windings at the centre frequency.

• If the signal moves away from the centre frequency the phase difference will change.

• In turn the phase difference between the secondary and third windings also varies.

• When this occurs the voltage will subtract from one side of the secondary and add to the other causing an imbalance across the resistors R1 and R2.

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• As a result this causes a current to flow in the third winding and the modulation to appear at the output.

• The capacitors C1 and C2 filter any remaining RF signal which may appear across the resistors.

• The capacitor C4 and R3 also act as filters ensuring no RF reaches the audio section of the receiver.

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• Ratio detector advantages & disadvantages -• As with any circuit there are a number of

advantages and disadvantages to be considered when choosing between several options.

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• Advantages –• Simple to construct using discrete

components• Offers good level of performance and

reasonable linearity.• Disadvantages –• High cost of transformer• Typically lends itself to use in only circuits

using discrete components and not integrated circuits.

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• Pre-emphasis• Pre-emphasis refers to boosting the relative

amplitudes of the modulating voltage for higher audio frequencies from 2 to approximately 15 KHz.

• De-emphasis• De-emphasis means attenuating those

frequencies by the amount by which they are boosted.

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• However pre-emphasis is done at the transmitter and the de-emphasis is done in the receiver.

• The purpose is to improve the signal-to-noise ratio for FM reception.

• A time constant of 75µs is specified in the RC or L/Z network for pre-emphasis and de-emphasis.

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• Pre-emphasis circuit• At the transmitter, the modulating signal is

passed through a simple network which amplifies the high frequency components more than the low-frequency components.

• The simplest form of such a circuit is a simple high pass filter of the type shown in fig.

• Specification dictate a time constant of 75 microseconds (µs) where t = RC. Any combination of resistor and capacitor (or resistor and inductor) giving this time constant will be satisfactory.

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• Such a circuit has a cut off frequency fco of 2122 Hz. This means that frequencies higher than 2122 Hz will he linearly enhanced.

• The output amplitude increases with frequency at a rate of 6 dB per octave.

• The pre-emphasis curve is shown in Fig. • This pre-emphasis circuit increases the energy

content of the higher-frequency signals so that they will tend to become stronger than the high frequency noise components. This improves the signal to noise ratio and increases intelligibility and fidelity.

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• The pre-emphasis circuit also has an upper break frequency fu where the signal enhancement flattens out.

• This upper break frequency is computed with the expression.

• fu = R1 +(R2/2πR1^2 *C)• It is usually set at some very high value

beyond the audio range. An fu of greater than 30KHz is typical.

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• De-emphasis Circuit-

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• To return the frequency response to its normal level, a de-emphasis circuit is used at the receiver.

• This is a simple low-pass filter with a constant of 75 πs. See figure (c).

• It features a cut off of 2122 Hz and causes signals above this frequency to be attenuated at the rate of 6bB per octave.

• The response curve is shown in Fig (d). As a result, the pre-emphasis at the transmitter is exactly offset by the de-emphasis circuit in the receiver, providing a normal frequency response.

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• The combined effect of pre-emphasis and de-emphasis is to increase the high-frequency components during transmission so that they will be stronger and not masked by noise.

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