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
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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
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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
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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
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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
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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.
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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)
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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)
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9. 4.2 : Mathematical Analysis
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.
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10. 4.2 : Mathematical Analysis
substituting a modulating signal vm(t) = Vmcos(ωmt), equation (8) and (9) into equation (1) yields
PM :
(10)
FM : as
(11)
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11. 4.2 : Mathematical Analysis
Summarized table :
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12. 4.3 : FM and PM Waveforms
Waveforms of FM and PM of a sinusoidal carrier by a single-frequency modulating signal.
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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).
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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.
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)
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15. 4.4.1 : Modulation Index and Percent Modulation for PM
therefore, for PM :
(14)
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)
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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
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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
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18. 4.4.2 : Modulation Index and Percent Modulation for FM
Summarized :
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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)
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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.
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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)
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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
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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.
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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.
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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.
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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.
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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.
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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)
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Chapter 4 : Angle Modulation 28 28

29. 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
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Chapter 4 : Angle Modulation 29 29

30. 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 :
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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
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32. 4.7 : FM/PM Modulators 4.7.1 : Direct FM 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
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 :
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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).
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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.
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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.
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36. : VCO FM Modulator
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
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37. : 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)
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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 :
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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.
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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
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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.
the frequency deviation, rate of change, modulation index, phase deviation and bandwidth are unaffected by the heterodyne process.
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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
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43. 4.9 : FM Transmitter 4.9.1 : 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.
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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
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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)
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46. : 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.
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47. : 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.
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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.
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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
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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
the frequency deviation at the output of the combining network :
Δf = mfm = x = 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 However, this would produce a transmission carrier at the antenna of
ft = 5208 x 200 kHz = MHz
This value is beyond the limits for the commercial FM broadcast band (30 ~ 300MHz).
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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 = rad
Δf = 72 x 14.4 Hz = Hz
this signal is then mixed with a MHz crystal-controlled frequency f0 to produce a difference signal f2 with the following characteristics :
f2 = 14.4 – = 1.25 MHz (down-converted)
m = rad (unchanged)
Δf = 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 rad = 4.98 rad
Δf = 72 x Hz = kHz
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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 :
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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.
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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.
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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)
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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 :
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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.
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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.
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59. 4.11.1 : Tuned-circuit Frequency Discriminator
2) 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.
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60. 4.11.1 : Tuned-circuit Frequency Discriminator
2) 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.
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61. Balanced Slope Detector
: 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
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62. : 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.
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63. : 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
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Chapter 4 : Angle Modulation

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

65. 4.12 : FM Stereo
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation

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

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

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

69. : 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.
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation

70. : 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.
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation

71. : 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.
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation

72. : 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.
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation

73. 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)
BENG 2413 Communication Principles Faculty of Electrical Engineering
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation
Chapter 4 : Angle Modulation 73 73

74. 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)
BENG 2413 Communication Principles Faculty of Electrical Engineering
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation
Chapter 4 : Angle Modulation 74 74

75. 4.13 : Average Power of An Angle-Modulated Wave
Ex. 7-6
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BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation
Chapter 4 : Angle Modulation 75 75

76. 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.
BENG 2413 Communication Principles Faculty of Electrical Engineering
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation
Chapter 4 : Angle Modulation 76 76

77. 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.
BENG 2413 Communication Principles Faculty of Electrical Engineering
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation
Chapter 4 : Angle Modulation 77 77

78. 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.
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BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation
Chapter 4 : Angle Modulation 78 78

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

80. 4.15 Noise and Angle Modulation
therefore, 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.
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation

81. 4.15 Noise and Angle Modulation
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : 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 :
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation

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

84. 4.16 Pre-emphasis & De-emphasis
schematic diagrams for pre-emphasis & de-emphasis circuit (a) and their corresponding frequency response curves (b):
BENG 2413 Communication Principles Faculty of Electrical Engineering
Chapter 4 : Angle Modulation

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

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