chapter 4 : angle modulation transmission and reception

Chapter 4 : Angle Modulation BENG 2413 Communication Principles Faculty of Electrical Engineering

1

Chapter 4 : Angle Modulation Transmission and Reception 4.1 Introduction to Angle Modulation 4.2 Mathematical Analysis 4.3 FM and PM Waveform 4.4 Modulation Index and Percent Modulation 4.5 Frequency and Bandwidth Analysis of Angle-Modulated Waves 4.6 Deviation Ratio 4.7 FM / PM Modulators 4.8 Frequency-up Conversion in modulators 4.9 FM Transmitters 4.10 FM Receivers 4.11 FM Demodulators 4.12 FM Stereo 4.13 Average Power of an Angle-modulated wave 4.14 Angle Modulation vs Amplitude Modulation 4.15 Noise and Angle Modulation 4.16 Pre-emphasis & De-emphasis


2

4.1 : Introduction to Angle Modulation 2 forms of angle modulation :

Frequency modulation (FM) Phase modulation (PM)

Several advantages over AM – noise reduction, improved system fidelity and more efficient use of power

Several disadvantages over AM – wider bandwidth requirement, utilization of more complex circuits.

used extensively for commercial radio broadcasting, television sound transmission, cellular radio, microwave and satellite communications systems


3

4.1 : Introduction to Angle Modulation angle modulation results whenever the phase angle, θof a sinusoidal wave is

varied with respect to time and can be expressed as

(1)

where m(t) = angle-modulated wave

Vc = peak carrier amplitude

ωc = carrier radian frequency

θ(t) = instantaneous phase deviation

where θ(t) is a function of the modulating signal given by

(2)

where ωc = modulating signal radian frequency

Vm = peak amplitude of the modulating signal

)(cos)( ttVtm cc

)sin()( tVFt mm


4

4.1 : Introduction to Angle Modulation the difference between FM and PM lies in which property of the carrier is

directly varied by the modulating signal and which property is indirectly varied.

FM results when the frequency of the carrier is varied directly by the modulating signal

PM results when the phase of the carrier is varied directly by the modulating signal Frequency Modulation (FM)

variation of the frequency of the modulating signal with constant amplitude frequency variation is directly proportional to the amplitude of the

modulating signal rate of variation equal to the frequency of the modulating signal


5

4.1 : Introduction to Angle Modulation Phase Modulation (PM)

variation of the phase of the modulating signal with constant amplitude phase variation is directly proportional to the amplitude of the modulating

signal rate of variation equal to the frequency of the modulating signal


6

4.1.1 : Angle Modulation Representation in Frequency and Time Domain An angle modulated signal in

the frequency domain :

the carrier frequency, fc is changed when acted on by the modulating signal.

the magnitude and direction of the frequency deviation, Δf is proportional to the amplitude and polarity of the modulating signal.


7

4.1.1 : Angle Modulation Representation in Frequency and Time Domain An angle modulated signal in the

time domain : the phase of the carrier is changing

proportional to the amplitude of the modulating signal.

the phase shift is called phase deviation Δθ. This shift is also produces a corresponding change in the frequency, known as frequency deviation Δf.

peak-to-peak frequency deviation is determine by (as shown in figure (b)),

(3) maxmin

11

TTf pp


8

4.2 : Mathematical Analysis

to differentiate between FM and PM, the following terms need to be defined : 1. Instantaneous Phase Deviation

the instantaneous change in the phase of the carrier at a given instant of time.

Instantaneous phase deviation = θ(t) rad (4) 2. Instantaneous phase

the precise phase of the carrier at a given instant of time.

Instantaneous phase = ωct + θ(t) rad (5)

3. Instantaneous frequency deviation the instantaneous change in the frequency of the carrier and is defined as the

first time derivative of the instantaneous phase deviation.

Instantaneous frequency deviation = θ’(t) rad/s (6) 4. Instantaneous frequency

the precise frequency of the carrier at a given instant of time and is defined as the first time derivative of the instantaneous phase.

Instantaneous frequency = ωi = ωc + θ’(t) rad/s (7)


9


from the previous 4 terms, (3) ~ (7), PM and FM can be defined as : PM : an angle modulation in which θ(t) is proportional to the amplitude of the

modulating signal. FM : an angle modulation in which θ’(t) is proportional to the amplitude of the

modulating signal.

For a modulating signal vm(t),

θ(t) = Kvm(t) rad (8)

θ’(t) = K1vm(t) rad/s (9)

where K and K1 are constants and are the deviation sensitivities of the phase and frequency modulators, respectively.


10


substituting a modulating signal vm(t) = Vmcos(ωmt), equation (8) and (9) into equation (1) yields

PM :

(10)

FM : as

(11)

)(cos)( ttVtm cc

)(')( tt

)('cos)( ttVtm cc

)cos(cos tKVtV mmcc

dttVKtV mmcc )cos(cos 1

)sin(cos

1t

VmKtV m

mcc


11


Summarized table :


12

4.3 : FM and PM Waveforms

Waveforms of FM and PM of a sinusoidal carrier by a single-frequency modulating signal.


13

4.3 : FM and PM Waveforms FM and PM waveforms are identical except for their time relationship. for FM, the maximum frequency deviation occurs during the maximum positive

and negative peaks of the modulating signal. for PM, the maximum frequency deviation occurs during the zero crossings of the

modulating signal (i.e. the frequency deviation is proportional to the slope of first derivative of the modulating signal).


14

4.4 : Modulation Index and Percent Modulation

comparing equation (10) and (11), equation (1) can be rewritten in general form as

(12)

where m is called the modulation index.

)cos(cos)( tmtVtm mcc

4.4.1 : Modulation Index and Percent Modulation for PM

for PM, the modulation index is also known as peak phase deviation Δθ, and is proportional to the amplitude of the modulating signal and is expressed as

(13)

where m = modulation index

K = deviation sensitivity (radians/volt)

Vm = peak modulating signal amplitude (volt)

)(radiansKVm m


15

4.4.1 : Modulation Index and Percent Modulation for PM therefore, for PM :

(14)

)cos(cos)( tKVtVtm mmcc

)cos(cos ttV mcc

)cos(cos tmtV mcc

4.4.2 : Modulation Index and Percent Modulation for FM for FM, the modulation index is directly proportional to the amplitude of the

modulating signal and inversely proportional to the frequency of the modulating signal.

(15)

where K1 = deviation sensitivities (radians/second per volt or cycles/second per vol

Vm = peak modulating signal amplitude (volt)

ωm = radian frequency (radians/second)

fm = cyclic frequency (cycles/second or hertz)

)(11

unitlessf

VKVKm

m

m

m

m


16

4.4.2 : Modulation Index and Percent Modulation for FM

also for FM, the peak frequency deviation Δf is simply the product of the deviation sensitivity and the peak modulating signal voltage. I.e.

(16) therefore, for FM, equation (11) can be rewritten as

(17) figure 7.4 & table 7.2

)(1 unitlessf

fmVKf

mm

)sin(cos)(

1tw

f

VKtVtm m

m

mcc

)sin(cos tw

ftV m

m

fcc

)sin(cos twmtV mcc


17

4.4.2 : Modulation Index and Percent Modulation for FM

Relationship between modulation index, frequency deviation and phase deviation in respect to the modulation signal amplitude and frequency : (a) modulation index vs amplitude (b) frequency deviation vs modulating frequency (c) phase deviation vs amplitude (d) frequency deviation vs amplitude


18

4.4.2 : Modulation Index and Percent Modulation for FM Summarized :


19

4.4.3 : Percent Modulation

percent modulation for angle modulation is determined in different manner than for amplitude modulation.

with angle modulation, percent modulation is the ratio of frequency deviation actually produced to the maximum frequency deviation allowed, stated in percent form

Percent modulation (18) %100(max)

)(

f

f actual


20

4.5 : Frequency and Bandwidth Analysis of Angle-Modulated Waves

frequency analysis of the angle-modulated wave is much more complex compared to the amplitude modulation analysis.

in phase/frequency modulator, a modulating signal produces an infinite number of side frequencies pairs (i.e. it has infinite bandwidth), where each side frequency is displaced from the carrier by an integral multiple of the modulating frequency.

4.5.1 : Bessel Function

from equation (12), the angle-modulated wave is expressed as

based on the above equation, the individual frequency components of the angle-modulated wave is not obvious.



21

4.5.1 : Bessel Function Bessel function identities can be used to determine the side frequencies

components

(19)

where Jn(m) is the Bessel function of the first kind. applying equation (19) to equation (12) yields,

(20)

)2

cos()()coscos(

n

nn

nmJm

)2

cos()()(

n

mcnn

tntmJVctm


22

4.5.1 : Bessel Function expanding (20),

where m(t) = angle modulated wave

m = modulation index

Vc = peak carrier ampitude

J0(m) = carrier component

J1(m) = first set of side frequencies displaced from carrier by ωm

J2(m) = second set of side frequencies displaced from carrier by 2ωm

Jn(m) = nth set of side frequencies displaced from carrier by n ωm

)(

)2(cos)(2

)(cos)(

2)(cos)()cos()()(

21

10

mJn

tmJtmJ

tmJtmJVtm

mcmc

mccc


23

4.5.1 : Bessel Function in other words, angle modulation produces infinite number of sidebands,

called as first-order sidebands, second-order sidebands, and so on. Also their magnitude are determined by the coefficients J1(m), J2(m),...Jn(m).

Bessel function of the first kind for several values of modulation index.


24

4.5.1 : Bessel Function Curves for the relative amplitudes of the carrier and several sets of side

frequencies for values of m up to 10.


25

4.5.1 : Bessel Function Conclusion from the table & graph :

modulation index m of 0 produces zero side frequencies. the larger the m, the more sets of side frequencies are produced. values shown for Jn are relative to the amplitude of the unmodulated carrier. as the m decreases below unity, the amplitude of the higher-order side frequencies

rapidly becomes insignificant. as the m increases from 0, the magnitude of the carrier J0(m) decreases.

the negative values for Jn simply indicate the relative phase of that side frequency set

a side frequency is not considered significant unless its amplitude is equal or greater that 1% of the unmodulated carrier amplitude (Jn ≥ 0.01).

as m increases, the number of significant side frequencies increases. I.e. the bandwidth of an angle-modulated wave is a function of the modulation index.


26

4.5.2 : Bandwidth Requirement angle-modulated wave consumes larger bandwidth than an amplitude-modulated wave. bandwidth of an angle-modulated wave is a function of the modulating signal and the

modulation index. the actual bandwidth required to pass all the significant sidebands for an angle-

modulated wave is equal to 2 times the product of the highest modulating signal frequency and the number of significant sidebands determined from the table of Bessel function. I.e. the minimum bandwidth for angle-modulated wave using the Bessel table,

(21) Carson’s Rule

it is a general rule to estimate the bandwidth for all angle-modulated systems regardless of the modulation index.

the Carson’s Rule states that the bandwidth necessary to transmit an angle-modulated wave as twice the sum of the peak frequency deviation and the highest modulating signal frequency.

HzfnB m)(2


27

4.5.2 : Bandwidth Requirement Carson’s Rule

(22) for a low modulation index ( fm is much larger than Δf ),

(23) for a high modulation index (Δf is much larger than fm )

(24)

Carson’s Rule approximate and gives a narrower bandwidth than the bandwidth determined using Bessel function. Therefore, a system designed using Carson’s Rule would have a narrower bandwidth but a poorer performance than system designed using the Bessel table.

for modulation index above 5, Carson’s Rule is a close approximation to the actual bandwidth required.

HzffB m)(2

)(2 HzfB m

)(2 HzfB


28Chapter 4 : Angle Modulation

BENG 2413 Communication Principles Faculty of Electrical Engineering 28

4.6 : Deviation Ratio Deviation ratio DR is the worst case modulation index and is equal to the

maximum peak frequency deviation divided by the maximum modulating-signal frequency – producing the widest frequency spectrum.

where DR = deviation ratio (unitless)

Δf(max) = maximum peak frequency deviation (Hertz)

fm(max) = maximum modulating-signal frequency (Hertz)

(max)

(max)

mf

fDR




4.6 : Deviation Ratio Ex : a. Determine the deviation ratio and bandwidth for the worst-case

(widest bandwidth) modulation index for an FM broadcast-band transmitter with a maximum frequency deviation of 75 kHz and a maximum modulating-signal frequency of 15 kHz.

From Bessel Table, a modulation index of 5 produces 8 significant sidebands Thus, the bandwidth is

B = 2(8 x 15000) = 240 kHz

Ex : b. For a 37.5 kHz frequency deviation and a modulating-signal frequency fm = 7.5 kHz, the modulation index is

and the bandwidth is B = 2(8 x 7500) = 120 kHz

515

75

kHz

kHzDR

55.7

5.37

kHz

kHzm




4.6 : Deviation Ratio From Ex. a & b, although the same modulation index (5) was achieved with 2

different modulating-signal frequencies and amplitudes, 2 different bandwidths were produced.

The widest bandwidth will only be produced from the maximum modulating-signal frequency and maximum frequency deviation.

The same condition applies in the case of using the Carson’s rule :

(max)(max)2 mffB

kHz

kHzkHz

180

15752


31

4.7 : FM/PM Modulators a phase modulator is a circuit in which the carrier instantaneous phase is

proportional to the modulating signal. a frequency modulator is a circuit in which the carrier instantaneous phase is

proportional to the integral of the modulating signal.

PM modulator :

FM modulator :

considering the FM modulator, if the modulating signal is v(t) is differentiate before being applied to the FM modulator, the instantaneous phase is now proportional to the modulating signal (i.e. PM modulator).

Differentiator + FM modulator = = PM modulator

)()( tvt

)()( tvt

)()()(

)( tvtdt

tdvt


32

4.7 : FM/PM Modulators Meanwhile, if the modulating signal is integrated before being applied to the PM

modulator, the instantaneous phase is now proportional to the integral of the modulating signal (i.e. FM modulator).

Integrator + PM modulator = = FM modulator

)()( tvt

4.7.1 : Direct FM Modulators with direct FM, the

instantaneous frequency deviation is directly proportional to the amplitude of the modulating signal.

schematic diagram of a simple direct FM generator :


33

4.7.1 : Direct FM Modulators

the tank circuit (L and Cm) is the frequency determining section for a standard LC oscillator.

Cm is a capacitor microphone that converts the acoustical energy into a mechanical energy, which is used to vary the distance between the plates of Cm and consequently change its capacitance.

as Cm is varied, the resonant frequency is varied. I.e. the oscillator output frequency varies directly with the external sound forces (i.e. direct FM).


34

4.7.1.1 : Varactor diode modulator

Direct FM generator using varactor diode to deviate the frequency of a crystal oscillator :

R1 and R2 develop a DC voltage that reverse bias the varactor diode VD1 and determine the resonant frequency of the oscillator.

external modulating signal voltage added or subtracted from the DC bias, which changes the capacitance of the diode and consequently changes the frequency of the oscillation.


35

4.7.1.1 : Varactor diode modulator

positive alternations of the modulating signal increase the reverse bias of VD1, which decrease its capacitance and increase the frequency of the oscillation.

negative alternations of the modulating signal decrease the reverse bias of VD1, which increase its capacitance and decrease the frequency of the oscillation.

simple to use, stable and reliable but limited peak frequency deviation thus limited use to the low index applications.


36

the use of varactor diode to transform changes in modulating signal amplitude to changes in frequency :

the center frequency for the oscillator :

(25)where fc = carrier frequency

L = inductance of the primary winding of T1

C = varactor diode capacitance

4.7.1.2 : VCO FM Modulator

LCfc

21


37

4.7.1.2 : VCO FM Modulator

when a modulating signal is applied, the frequency is

(26)where f = new frequency

ΔC = change in varactor diode capacitance due to modulating signal

the change in frequency is (27)where Δf = peak frequency deviation (hertz)

)(2

1

CCLfc

fff c


38

4.7.2 : Indirect FM (Direct PM) Modulator

with indirect FM, the instantaneous phase deviation rather than instantaneous frequency deviation is directly proportional to the modulating signal.

I.e. the indirect FM is accomplished by directly changing the phase of the carrier.

schematic diagram of an indirect FM modulator using a varactor diode :


39

4.7.2 : Indirect FM (Direct PM) Modulator

varactor diode VD1 placed in series with the inductive network (L1 and R1). this combined series-parallel network appears as series resonant circuit to the output

frequency from the crystal oscillator. the modulating signal is applied to VD1, which changes its capacitance and

subsequently the phase angle of the impedance seen by the carrier also varies, which results in a corresponding phase shift in the carrier.

advantage of using indirect FM modulator is it is more stable than the direct modulator.

However, it has more distortion in the modulated waveform compared to direct FM.


40

4.8 : Frequency Up-conversion

after the modulation, the frequency of the modulated-wave is up-converted to the desired frequency of transmission.

2 basic methods of frequency up-conversion : heterodyning process frequency multiplication

4.8.1 : Heterodyne Method


41

4.8.1 : Heterodyne Method

2 inputs to the balanced modulator : angle-modulated carrier and its side frequencies, an also the unmodulated RF carrier signal.

the 2 inputs mix nonlinearly in the balanced modulator producing the sum and difference frequencies at its output.

the BPF (bandpass filter) is tuned to the sum frequency with a passband wide enough to pass carrier plus the upper and lower side frequencies while the difference frequencies are blocked.

RFincoutc fff )()(

the frequency deviation, rate of change, modulation index, phase deviation and bandwidth are unaffected by the heterodyne process.


42

4.8.2 : Multiplication method

with multiplication method, the frequency of the modulated carrier is multiplied by a factor of N in the frequency multiplier.

frequency deviation, phase deviation and modulation index are also multiplied. However, the rate of the deviation is unaffected (i.e. the separation between

adjacent side frequencies remains unchanged). as frequency deviation and modulation index are multiplied, the number of side

frequency also increases. Thus, the bandwidth also increases. For modulation index higher than 10, Carson’s Rule can be applied

inout NBfNB )2(


43

4.9 : FM Transmitter4.9.1 : Direct FM Transmitter Block diagram for

a commercial broadcast-band

transmitter :

also known as Crosby direct FM transmitter (includes an automatic frequency control –AFC loop)

the carrier frequency is basically the center frequency of the master oscillator fc = 1.5 MHz, which is multiplied by 18 to produce a final transmission carrier frequency ft = 98.1 MHz.


44

4.9.1 : Direct FM Transmitter

the frequency and phase deviations at the output of the modulator are also multiplied by 18.

To achieve maximum deviation allowed for FM stations at antenna (75 kHz), the deviation at the output of the modulator is

HzN

kHzf 7.4166

18

7500075


45

4.9.1 : Direct FM Transmitter

The modulation index at the output of the modulator,

For maximum modulating signal frequency allowed for FM (15 kHz)

mfm

7.4166

2778.015000

7.4166m


46

4.9.1.1 : AFC Loop

for medium and high index FM systems, the oscillator cannot be a crystal type because the frequency at which the crystal oscillates cannot be significantly deviated.

as a result, the stability of the oscillator in the direct FM is low. to overcome this problem, AFC loop is used.

with AFC, the carrier signal is mixed in a nonlinear device with the signal from a crystal reference oscillator (the output is down-converted in frequency).

the output is then fed back to the input of a frequency discriminator. It is a frequency-selective device whose output voltage is proportional to the difference between the input frequency and its resonant frequency.


47

4.9.1.1 : AFC Loop if there is a master oscillator frequency drift (resulting in a change of carrier center

frequency), the discriminator responds by producing a DC correction voltage. this voltage is added to the modulating signal to automatically adjust the master

oscillator’s center frequency.


48

4.9.2 : Indirect FM Transmitter Indirect FM transmitters produce an output

waveform in which the phase deviation is directly proportional to the modulating signal.

Consequently, the carrier oscillator is not directly deviated. As a result, the stability of the oscillators can be achieved without using an AFC circuit.

Block diagram for wideband Armstrong indirect FM transmitter : low frequency sub-carrier fc is phase

shifted 90˚ and fed to a balanced modulator. It is mixed with the modulating signal fm.

the output from the balanced modulator is DSBSC wave that is combined with the original carrier in a combining network to produce a low-index, phase-modulated waveform.


49

4.9.2 : Indirect FM Transmitter Proof :

By using trigonometric function : cos (A+B) =cos A cos B – sin A sin B

For a small modulation index,

Thus,

where Vccos(ωct) = original carrier

Vcsin(ωct ) = phase-shifted carrier

cos(ωmt ) = modulating signal


))cos(sin()sin())cos(cos()cos()( tmttmtVtm mcmcc

)cos())cos(sin(

1)0cos())cos(cos(

tmtm

tm

mm

c

)cos()sin()cos()( ttmVtVtm mcccc


50

4.9.2 : Indirect FM Transmitter Ex :

Consider a 200 kHz carrier being phase-modulated with a 15 kHz modulating signal producing modulation index of 0.00096. the frequency deviation at the output of the combining network :

Δf = mfm = 0.00096 x 15000 = 14.4 Hz

in order to achieve the required 75 kHz deviation for the FM broadcast at the antenna, the frequency must be multiplied by approximately 5208. However, this would produce a transmission carrier at the antenna of

ft = 5208 x 200 kHz = 1041.6 MHz

This value is beyond the limits for the commercial FM broadcast band (30 ~ 300MHz).


51

4.9.2 : Indirect FM Transmitter Ex : (continue)

Let the output waveform of the network is multiplied by 72, producing the following signal,

f1 = 72 x 200 kHz = 14.4 MHz

m = 72 x 0.00096 = 0.06912 rad

Δf = 72 x 14.4 Hz = 1036.8 Hz this signal is then mixed with a 13.15 MHz crystal-controlled frequency f0 to produce a

difference signal f2 with the following characteristics :

f2 = 14.4 – 13.15 = 1.25 MHz (down-converted)

m = 0.06912 rad (unchanged)

Δf = 1036.8 Hz (unchanged) the output of the mixer is once again multiplied by 72 to produce the transmit signal with

the following characteristics :

ft = 72 x 1.25 MHz = 90 MHz

m = 72 x 0.06912 rad = 4.98 rad

Δf = 72 x 1036.8 Hz = 74.65 kHz


52

4.9.2 : Indirect FM Transmitter with Armstrong transmitter, the phase of the carrier is directly modulated in

the combining network producing indirect frequency modulation. the magnitude of peak phase deviation (i.e. the modulation index) is directly

proportional to the amplitude of the modulating signal but independent of its frequency (m = KVm).

the modulation index remains constant for all modulating signal frequencies of given amplitude.

Ex :


53

4.10 : FM Receiver Block diagram for a double conversion superheterodyne FM receiver :

the pre-selector, RF amplifier, first and second mixers, and IF amplifier sections of an FM receiver perform same functions as the AM receiver.

Automatic Gain Control (AGC) is used to prevent mixer saturation when strong RF signals are received.

the peak detector used in AM receiver is replaced by a limiter, frequency discriminator and de-emphasis network.


54

4.10 : FM Receiver

Limiter is used to remove amplitude variations caused by noise (which is one of AM’s drawback).

frequency discriminator extracts the information from the modulated wave. de-emphasis network contributes to the improvement in signal-to-noise ratio. the first IF is a relatively high frequency (often 10.7 MHz) for good image

frequency rejection. the second IF is a relatively low frequency (often 455 kHz) that allows the IF

amplifiers to have high gain.


55

4.11 : FM Demodulator FM demodulator is a frequency-dependent circuits designed to produce an

output voltage that is proportional to the instantaneous frequency at its input. the overall transfer function for the FM demodulator is nonlinear but when

operating over its linear range,

(28)

the output from the FM demodulator is

(29)

where vout(t) = demodulated output signal (volts)

Kd = demodulator transfer function (volts per hertz)

Δf = difference between input frequency and the centre frequency of

demodulator (hertz)

f

VKd

fKtv dout )(


56

4.11 : FM Demodulator the most common circuits used for FM signal demodulation are slope

detector, balanced slope detector and PLL demodulator. the slope detector and balanced slope detector are categorized as tuned-circuit

frequency discriminator. Ex :


57

4.11.1 : Tuned-circuit Frequency Discriminator convert FM to AM and then demodulate the AM envelope with the

conventional peak detector.

1) Slope Detector

the tuned circuit (La and Ca) produces an output voltage that is proportional to the input frequency.

the maximum output voltage occurs at the resonant frequency f0 and its output decreases proportionally as the input frequency deviates above or below f0.


58

4.11.1 : Tuned-circuit Frequency Discriminator

the circuit is designed so that the IF centre frequency fc falls in the centre of the most linear portion of the voltage-versus-frequency (figure (b)). when IF deviates below fc, the output voltage decreases

when IF deviates below fc, the output voltage increases the tuned-circuit therefore, converts frequency variations to amplitude variations. Di, Ci & Ri make up a simple peak detector to demodulate the AM signals.


59

4.11.1 : Tuned-circuit Frequency Discriminator2) Balanced Slope

Detector

Balanced slope detector is simply two single-ended slope detector connected in parallel and fed 180˚ out of phase.

Phase inversion accomplished by centre tapping secondary windings of T1.

Tuned circuits (La, Ca & Lh, Ch) perform an FM-to-AM conversion.

Balanced peak detectors (D1, C1, R1 & D2, C2, R2) remove the information from the AM envelope.

La & Ca is tuned to frequency fa that is above the IF centre frequency fc.

Lh & Ch is tuned to frequency fh that is below the IF centre frequency fc.


60

4.11.1 : Tuned-circuit Frequency Discriminator2) Balanced Slope Detector

Operation the IF centre frequency fc falls exactly halfway between the resonant frequency of the

two tuned circuits. at fc, the output voltage from the tuned circuits are equal in amplitude but opposite in

polarity. I.e. the rectified voltage across R1 & R2, when added, produce an output voltage Vout = 0.

when IF deviates above the resonance, the top tuned circuit produces higher output voltage than the lower tuned circuit, and Vout goes positive.

when IF deviates below the resonance, the output voltage from lower tuned circuit is larger than the voltage from top tuned circuit, and Vout goes negative.


61

4.11.1 : Tuned-circuit Frequency Discriminator Comparison Slope Detector vs Balanced Slope Detector

Slope Detector Balanced Slope Detector

simpler circuit poor linearity, difficult to tune need to use separate limiter stage to

compensate amplitude variation

more complex circuit better linearity and tuning does not need limiter stage


62

4.11.2 : PLL FM Demodulator A PLL frequency demodulator requires no tuned circuits and automatically

compensates for changes in the carrier frequency that is caused by the instability in the transmitter’s oscillator.

after the frequency lock had occurred, the VCO tracks frequency changes in the input signal by maintaining the phase error at the input of the phase comparator.

if the input is deviated FM signal and the VCO natural frequency is equal to the centre IF frequency, the correction voltage produced at the phase comparator is proportional to the frequency deviation.

I.e. correction voltage produced is proportional to the modulating/information signal.

fVd


63

4.11.2 : PLL FM Demodulator

if the amplitude is sufficiently limited before reaching the PLL and the loop is properly compensated, the PLL loop gain Kv is constant.

Therefore the demodulated signal can be taken directly from the output and is mathematically expressed as

(30)

where Δf = frequency deviation, Kd = phase comparator gain,

Ka = amplifier gain

adout KfKV


64

4.11 : FM Stereo until 1961, all commercial FM transmission were monophonic. That is, a

single 50 Hz to 15 kHz audio channel made up the entire voice and music information spectrum.

this single audio channel modulated a carrier and was transmitted through a 200 kHz bandwidth FM channel.

with mono transmission, each speaker assembly at the receiver reproduces exactly the same information. I.e. the entire information signal sounds as though it is coming from the same direction (no sound directivity).

in 1961, Federal Communication Commission (FCC) authorized stereophonic transmission. With stereo transmission, the signal is spatially divided into two 50 ~ 15 kHz channels (a left and a right).

Music originated on the left side is reproduced on the left speaker and vice versa. Therefore, it is possible to reproduce music with unique directivity and spatial dimension. Also it is possible to separate sound by tonal quality, such as percussion, strings, horns etc.


65

4.12 : FM Stereo


66

4.12 : FM Stereo FM stereo spectrum :

it comprises the 50 ~ 15 kHz stereo channel plus an additional stereo channel frequency division multiplexed (FDM) into a composite baseband signal with a 19 kHz pilot and a Subsidiary Communications Authorization (SCA) channel. the left (L) plus the right (R) audio channels (L+R) the left plus the inverted right audio channels (L-R) SCA channel

the L+R stereo channel occupies the 50 ~ 15 kHz passband (mono combination). the L-R audio channel amplitude modulates a 38 kHz sub-carrier and produces the

L-R stereo channel occupying the 23 kHz ~ 53 kHz passband. SCA channel used to broadcast music to private subscribers such as department

stores, restaurants and offices, occupying the 60 kHz ~ 74 kHz spectrum. Identical information is contained in the L+R and L-R except for their phase info on stereo :


67

4.12.1 : FM Stereo Transmission Block diagram for a stereo FM Transmitter :

the L and R audio channels are combined in a matrix network to produce the L+R and L-R audio channel.

the L-R audio channel then modulates a 38 kHz sub-carrier and produces a 23 kHz ~ 53 kHz L-R stereo channel.

L in

R in


68

4.12.1 : FM Stereo Transmission

the L+R channel must be delayed to maintain phase integrity with the L-R stereo channel for demodulation purpose.

a 19 kHz pilot is transmitted rather than 38 kHz sub-carrier because it is easier to recover the pilot in the receiver.

this composite/whole baseband signal is fed to the FM transmitter where it modulates the main carrier.

L in

R in


69

4.12.2 : FM Stereo Reception FM Stereo receiver is basically same as the standard FM receiver up to the

output of the audio detector stage. the output of the discriminator is the total baseband spectrum shown below.


70

4.12.2 : FM Stereo Reception

Block diagram for an FM receiver with mono & stereo outputs : for mono section of the signal

processor, the L+R stereo channel which contains all the original information from both the L and R audio channels, is simply filtered, amplified and then fed to both the L and R speakers.

for stereo section, the L+R and L-R stereo channels and the 19 kHz pilot are separated from the composite baseband with filters.

the L+R stereo channel is filtered by a lowpass filter with an upper cutoff frequency of 15 kHz.


71

4.12.2 : FM Stereo Reception the 19 kHz pilot is filtered with a

high-Q bandpass filter, multiplied by 2, amplified and then fed to the L-R demodulator.

the L-R double sideband signal is separated with a broadly tuned bandpass filter and then mixed with the recovered 38 kHz carrier in a balanced modulator to produce the L-R audio channel.

the matrix network combines the L+R and L-R signals in such a way as to separate the L and R audio signals, which are fed to their respective speaker.


72

4.12.2 : FM Stereo Reception the matrix network combines the L+R and L-R signals in such a way as to separate

the L and R audio signals, which are fed to their respective speaker.




4.13 : Average Power of An Angle-Modulated Wave The average power in the unmodulated carrier is defined as

(1)

where Pc = carrier power (watts)

Vc = peak umodulated carrier voltage (volts)

R = load resistance (ohms) The total instantaneous power in an angle-modulated carrier is defined as

(2)

substituting for m(t) gives

(3)

WR

VP

cc

2

2

WR

tmPt

2)(

)(cos22

ttR

VP c

ct

)(22cos

2

1

2

12

ttR

Vc

c




4.13 : Average Power of An Angle-Modulated Wave In (3), the second term consists of an infinite number of sinusoidal side

frequency components about the frequency equal to twice the carrier frequency (2ωc). Consequently, the average value of the second term is zero, and the average power of the modulated wave reduced to

(4)

(1) and (4) are identical, the average power of the modulated carrier must be equal to the average power of the unmodulated carrier. The modulated carrier power is the sum of the powers of the carrier and the side frequency components.

Therefore, the total modulated wave power is

(5)

WR

VP

ct

2

2

nt PPPPPP 3210

R

V

R

V

R

V

R

V

R

V nc

2

2

2

2

2

2

2

2

2

223

22

21

2




4.13 : Average Power of An Angle-Modulated Wave Ex. 7-6




4.14 : Angle Modulation vs Amplitude Modulation Advantages of Angle Modulation

Noise immunity – most noise results in unwanted amplitude variations in the modulated wave (i.e. AM noise). FM and PM receivers include limiters that remove most of the Am noise from the received signal before the final demodulation process occurs – a process that cannot be used with AM receivers because the information is also contained in amplitude variations, and removing the noise would also remove the information.

Noise performance and S/N improvement – with the use of limiters, FM and PM actually reduce the noise level and improve the S/N ratio during the demodulation process.

Capture effect - with FM and PM, a phenomenon of capture effect allows a receiver to differentiate between two signals received with the same frequency by capturing the stronger signal and eliminate the weaker one. With AM, both signals will be demodulated and produce audio signals.




4.14 : Angle Modulation vs Amplitude Modulation Advantages of Angle Modulation

Power Utilization and efficiency

- with AM transmission, (especially DSBFC), - most of the transmitted power is contained in the carrier while the information is contained in the much lower power sidebands.

- with AM, the carrier power remains constant with modulation, and the sideband power simply adds to the carrier power.

- with angle modulation, the total power remains constant regardless if modulation is present.

- with angle modulation, power is taken from the carrier with modulation and redistributed in the sidebands – puts most of its power in the information.




4.14 : Angle Modulation vs Amplitude Modulation Disadvantages of Angle Modulation

Bandwidth

- high quality angle modulation produces many side frequencies, thus necessitating a much wider bandwidth than is necessary for AM transmission.

Circuit complexity and cost

- PM and FM modulators, demodulators, transmitters, and receivers are more complex to design and build than their AM counterparts.

- At one time, more complex means more expensive.

- However with the advent of inexpensive, large-scale integration ICs, the cost is

comparable to their AM counterparts.


79

4.15 Noise and Angle Modulation when a constant density of thermal noise is added to an angle-modulated signal,

unwanted deviation of carrier frequency is expected. magnitude of the unwanted deviation depends on the relative amplitude of the

noise with respect to the carrier amplitude. Consider a noise signal with amplitude Vn and frequency fn :

for PM, the unwanted peak phase deviation due to this interfering noise signal is given by

(6.13)

for FM, when Vc > Vn, the unwanted instantaneous phase deviation is approximately,

(6.14)taking derivative,

(6.15)

radV

V

c

npeak

radtV

Vt nn

c

n)sin()(

sradtV

Vt nnn

c

n/)cos()(


80

4.15 Noise and Angle Modulationtherefore, the unwanted peak frequency deviation is

(6.16)

when the above unwanted carrier deviation is demodulated, it becomes noise.- the frequency of the demodulated noise signal is equal to the difference between

the carrier frequency and the interfering signal frequency (fc – fn).- the signal-to-noise ratio at the demodulator output due to the unwanted frequency deviation from an interfering signal defined as

(6.17)

- the spectral shape of the demodulated noise depends on whether an FM or PM demodulator is used :

→ noise voltage at the PM demodulator output is constant with frequency.→ noise voltage at the FM demodulator output increases linearly with

frequency.

sradV

Vn

c

npeak / Hzf

V

Vf n

c

npeak

noise

signal

f

f

N

S


81

4.15 Noise and Angle Modulation


82

4.16 Preemphasis & Deemphasis based on the previous figure, noise is distributed non-uniformly in FM. noise at the higher modulating signal frequency is greater than noise at lower

frequencies. for that, for information signal with uniform signal level, a non-uniform signal-

to-noise ratio is produced as follow :


83

4.16 Pre-emphasis & De-emphasis

S/Nratio is lower at the high frequency ends of the triangle (figure a). to compensate for this, the high frequency modulating signal is emphasized or

boosted in amplitude prior to performing modulation (figure b). at the receiver, to compensate this boot, the high frequency signal is de-emphasized

or attenuated after the demodulation is performed. pre-emphasis network allows the high frequency modulating signal to modulate

the carrier at a higher level while the de-emphasis network restores the original amplitude-versus-frequency characteristics to the information signal. pre-emphasis network is a high pass filter (i.e. a differentiator). de-emphasis network is a low pass filter (i.e. integrator).


84

4.16 Pre-emphasis & De-emphasis schematic diagrams for pre-emphasis & de-emphasis circuit (a) and their

corresponding frequency response curves (b):


85

4.16 Pre-emphasis & De-emphasis the break frequency (the frequency where pre-emphasis & de-emphasis begins) is

determined by the RC or L/R time constant of the network.

(6.18)

from the preceding explanation, it can be seen that the output amplitude from a pre-emphasis network increases with frequency for frequencies above the break frequency fb. from equation 4.15, if changes in fm produce corresponding changes in Vm, the

modulation index m remains constant.- this is the characteristic of phase modulation (modulation index is independent of

frequency : m = Δθ= KVm).- i.e. for frequencies below 2.12 kHz produce FM, and frequencies above 2.12 kHz produce PM.

(4.15)

RLRCfb

/2

1

2

1

)(11

unitlessf

VKVKm

m

m

m

m


86

A story to think about…On January 31, 1954 a 64 year old man wrote a letter to his wife, dressed for

work, and walked out of his 13th floor apartment window, plunging to his death. Colonel Edwin Armstrong, the father of modern radio, and the creator of the first F.M. system, had committed suicide. A brilliant but sensitive man, Armstrong allowed the U.S. military to use his patents royalty-free for the duration of World War II. Before that he played a crucial role in communications during the First World War. He believed, rightly so, that F.M. was a revolutionary operating system and that it should replace A.M. equipment for broadcasting. Tired and despondent after fighting one lawsuit after another against RCA and others, his personal fortune spent on promoting and defending F.M., Armstrong finally gave up and killed himself. Every modern radio has circuits Armstrong designed.

Source : Internet

chapter 4 : angle modulation transmission and reception

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