6 Frequency Modulation Part2

Chapter 3 : Frequency Modulation

DEKC 3343 Communication Engineering

Faculty of Electrical Engineering 1

3.8: FM Modulators• Direct FM is obtained when frequency of the carrier oscillator is modulated by

the information signal.

• Direct FM modulator

1. Varactor diode modulator

2. FM reactance modulators

3.8.1 : 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 :




3.8.1 : 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).




3.8.2 : 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.




3.8.2 : 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.




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

to changes in frequency :

� the center frequency for the oscillator :

(1)

where fc = carrier frequency

L = inductance of the primary winding of T1

C = varactor diode capacitance

3.8.2: VCO FM Modulator

LCfc

π2

1=




3.8.2 : VCO FM Modulator

� when a modulating signal is applied, the frequency is

(2)

where f = new frequency

∆C = change in varactor diode capacitance due to modulating signal

� the change in frequency is (3)

where ∆f = peak frequency deviation (hertz)

)(2

1

CCLfc

∆+=

π

fff c −=∆




3.8.3 : 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 :




3.8.3 : 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.




3.9 : 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

3.9.1 : Heterodyne Method




3.9.1 : 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.




3.9.2 : 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(

3.10 FM Transmitter

� DIRECT FM TRANSMITTER

Direct FM transmitters produce an output waveform in which the

frequency deviation is directly proportional to the modulating

signal.

1. Crosby Direct FM transmitter

2. Phase-Locked-Loop Direct FM transmitter

� INDIRECT FM TRANSMITTERS

1. Armstrong Indirect FM transmitter







3.10 : FM Transmitter

3.10.1 : 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 =

5.1 MHz, which is multiplied by 18 to produce a final transmission carrier

frequency ft = 91.8 MHz.





� the frequency and frequency 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===∆





The modulation index at the output of the modulator,

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

Thus, modulation index at antenna is m= 0.2778 (18) = 5

mfm

7.4166=

2778.015000

7.4166==m




3.10.2 : 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.




3.10.2 : 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.




3.11 : 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 – crystal can be used

without use of AFC loop.

� 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.





� 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(cos)( tmtVtm mcc ωω +=

[ ]))cos(sin()sin())cos(cos()cos()( tmttmtVtm mcmcc ωωωω −=

)cos())cos(sin(

1)0cos())cos(cos(

tmtm

tm

mm

c

ωω

ω

≈

≈≈

)cos()sin()cos()( ttmVtVtm mcccc ωωω −=





� 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 :

∆f = 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).





� 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

∆f = 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)

∆f = 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

∆f = 72 x 1036.8 Hz = 74.65 kHz





� 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.




3.12 : 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.




3.12 : FM Receiver

� Limiter is used to remove amplitude variations caused by noise (which is one of

AM’s drawback).

� frequency discriminator (demodulator) 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.




3.13 : 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)

∆f = difference between input frequency and the centre frequency of

demodulator (hertz)

f

VK d =

fKtv dout ∆=)(




3.13 : 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 : For an FM demodulator circuit with a transfer function of Kd = 0.2V/kHz

and an FM input signal with 20 kHz of peak frequency deviation, determine

the peak output voltage.

3.14 Advantages of FM compared to AM

� All the transmitted power in FM is useful, whereas in AM most of it in

the transmitted carrier, which contains no useful information.

� In FM, it is possible to reduce noise still further by increasing the

deviation frequency.

� FM has the advantage over AM, of providing greater protection from

noise for the lowest modulating frequency.

� FM operate in the upper VHF and UHF frequency ranges, at which

there is less effect on noise than in the MF and HF ranges occupies by

AM.




� In FM frequency allocation by ITU, guard bands are provided between

the adjacent channels to avoid or reduce channel interference.

� The use of pre-emphasis and de-emphasis in FM will reduce the effect

of noise. With emphasis, the highest modulating frequencies are

artificially boosted before transmission and correspondingly attenuated

after reception.

� In FM, the transmitted amplitude is constant. This characteristics has the

advantages of significantly improving immunity to noise and

interference.




3.15 Disadvantages of FM compared to AM

� Since reception is limited to line of sight, the area or reception for FM is

much smaller than AM.

� Equipment for the transmitter and receiver are more expensive and

complex.

� A much wider bandwidth is required by FM, up to 10 times larger than

needed by AM. This is the most significant disadvantage of FM.




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6 Frequency Modulation Part2