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Frequency modulation (modulator /demodulator)

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Page 1: Chapt 3 Part 3

Frequency modulation (modulator /demodulator)

Page 2: Chapt 3 Part 3

Generation of FM signalGeneration of FM signal

2 techniques – direct and indirect methods

Require a system that able the frequency of the output signal to vary in accordance to an information signal amplitude.

3.9.1 Direct method

1. Varactor diode

2. Reactance modulation

3. VCO

Page 3: Chapt 3 Part 3

Direct FM Modulator

The carrier is generated by LC or crystal oscillator circuits. Figure below shows simple direct FM modulator

Page 4: Chapt 3 Part 3

Frequency Modulators

In LC oscillators, the carrier frequency can be changed by varying either the inductance or capacitance.

The idea is to find a circuit or component that converts a modulating voltage to a corresponding change in capacitance or inductance.

In crystal oscillators, the frequency is fixed by the crystal.

A varactor is a variable capacitance diode used to change oscillator frequencies.

Page 5: Chapt 3 Part 3

Frequency Modulators

Figure 6-4: A direct-frequency-modulated carrier oscillator using a varactor diode.

Page 6: Chapt 3 Part 3

Varactor diode Direct FM modulator

Page 7: Chapt 3 Part 3

For voltage controlled oscillator (VCO) Fm generator, the center frequency for the oscillator is:

Where L = inductance of the primary winding (henries)

C = varactor diode capacitance (farads) When a modulating signal applied, the frequency is

Where f = the new frequency of oscillation

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

The change in frequency is

Hz2

1

LCfc

Hz)(2

1

CCLfc

|| fff c

Page 8: Chapt 3 Part 3

Frequency Modulators

Varactor Modulator Most LC oscillators are not stable enough to

provide a carrier signal. The frequency of LC oscillators will vary with

temperature changes, variations in circuit voltage, and other factors.

As a result, crystal oscillators are normally used to set carrier frequency.

Page 9: Chapt 3 Part 3

Frequency Modulators

Frequency-Modulating a Crystal Oscillator Crystal oscillators provide highly accurate carrier

frequencies and their stability is superior to LC oscillators.

The frequency of a crystal oscillator can be varied by changing the value of capacitance in series or parallel with the crystal.

By making the series capacitance a varactor diode, frequency modulation can be achieved.

Page 10: Chapt 3 Part 3

Frequency Modulators

Figure 6-5: Frequency modulation of a crystal oscillator with a VVC.

Page 11: Chapt 3 Part 3

Frequency Modulators

Voltage-Controlled Oscillators Oscillators whose frequencies are controlled by

an external input voltage are generally referred to as voltage-controlled oscillators (VCOs).

Voltage-controlled crystal oscillators are generally referred to as VXOs.

VCOs are primarily used in FM. VCOs are also used in voltage-to-frequency

conversion applications.

Page 12: Chapt 3 Part 3

Eg (VCO):Linear integrated-circuit direct FM modulator

High-frequency deviations and high modulation indices.

Page 13: Chapt 3 Part 3

Frequency Modulators

Reactance Modulator A reactance modulator is a circuit that uses a transistor

amplifier that acts like either a variable capacitor or an inductor.

When the circuit is connected across the tuned circuit of an oscillator, the oscillator frequency can be varied by applying the modulating signal to the amplifier.

Reactance modulators can produce frequency deviation over a wide range.

Reactance modulators are highly linear, so distortion is minimal.

Page 14: Chapt 3 Part 3

Frequency Modulators

Figure 6-10: A reactance modulator.

Page 15: Chapt 3 Part 3
Page 16: Chapt 3 Part 3

Direct FM Modulator Disadvantages

Relatively unstable LC oscillators must be used to produce the carrier frequency which prohibits using crystal oscillators

Requires the addition of some form of automatic frequency control circuitry to maintain the carrier frequency

Advantages Relatively high-frequency deviations and modulation

indices are easily obtained because the oscillator are inherently unstable

Page 17: Chapt 3 Part 3

Demodulation of FM signalDemodulation of FM signal Demodulation process is done in order to recover/get back the information

signal transmitted. Basic concepts of demodulation circuit is to detect the frequency

variation. Two techniques can be used:

Pemodulatan Sudut

Penyahmodulatan FM

IndirectDirect

• Pembezalayan/Discriminator Phase Lock Loop(PLL)/Quadrature detector

Page 18: Chapt 3 Part 3

Demodulator

Five most commonly used demodulator are:

Slope detector

Foster-Seeley discriminator

Ratio detector

PLL demodulator

Quadrature detector

Tuned-circuit frequency discriminator

Page 19: Chapt 3 Part 3

Conversion circuit - FM to AM Conversion circuit - FM to AM ((DiscriminatorDiscriminator) – Direct) – Direct

Pemodulatan Sudut

This technique is required to convert FM signal to AM signal and then by using AM demodulation circuit is to get back the information signal.

This technique is called (slope detection) or discriminator. Block diagram of the detection circuit is as shown below:

t t t

y(t)

Pengesan Sampuldt

dvFM(t) y(t) tvFM

tvFMvFM(t)

Page 20: Chapt 3 Part 3

Demodulator: Slope detector

Slope Detector Envelope Detector

Convert FM to AM and then demodulate the AM signal with conventional peak detector

Single-ended slope detector. Tuned circuit produces an output voltage proportional to the input frequency When ∆f is above fc (+ ∆f ), Vout increase When ∆f is below fc (- ∆f ), Vout decrease

Page 21: Chapt 3 Part 3

Pemodulatan Sudut

))(cos()(0t

mfccFM dttvktEtv

)]([ tvkE mfcc

Mathematical analysis :

Differentiate; yields :

FM equation :

dttvkttvkEdt

tdvmfcmfcc

FM sin

• From the above equation it can be seen that the amplitude of the signal contains the information signal.

• The amplitude of the signal is an envelope of the signal and the equation is given by :

Page 22: Chapt 3 Part 3

For envelope detector to be used the frequency deviation, Δω required must be smaller than the carrier frequency, ωc or otherwise an envelope detector cannot be used.

Pemodulatan Sudut

cmf tvk )(

0][ ccE for all t

)()( tvkEty mfc

• In practice a limiter circuit (litar penghad amplitude) can be used.

• It is due to the FM signal received at the antenna was influenced by the noise and therefore the amplitudes of the signal were varied and not constant.

• Hence the output equation of the envelope detector :

• Therefore the envelope equation can be written as:

Page 23: Chapt 3 Part 3

Pemodulatan Sudut

For effective detection the constant amplitude of the FM signal is required. Therefore an amplitude limiter is used.

Below is a block diagram of FM detection circuit with limiter circuits.

11

)(ovcos(θ) > 0

cos(θ) < 0 vi(θ)

vo(θ)

1

-1

Penghad BPF )](cos[)( tttE ccc )](cos[4

tt cc

Penghad Amplitud (Limiter)

PenghadAmplitud

Pengesan Sampuldt

dvFM(t) y(t)

Discriminator

• A limiter will limits the output to +1 or -1 depends on the positive or negative cycles of the FM signal and Ec(t) ≥ 0.

Page 24: Chapt 3 Part 3

Output of the limiter is a square wave signal as shown below.

For FM signal the angle varied in accordance to the amplitude of the information signal.

Pemodulatan Sudut

])([)]([0t

mfcoo dttvktvtv

...)5cos(

5

1)3cos(

3

1)cos(

4)(

ov

vo(θ)

θ

2

2

32

5-1

1 Fourier series equation for square wave:

t

mfc dttvktt0

)()(

t

vo[θ(t)]

• Therefore the limiter output is a function of θ(t) and the equation can be written as :

Page 25: Chapt 3 Part 3

Output of limiter :

Output of BPF :

Pemodulatan Sudut

])(cos[4

)(0t

mfco dttvktte

eo(t)

4

t

4

...])(55cos[5

1

])(33cos[3

1])(cos[

4

])([)]([

0

00

0

t

mfc

t

mfc

t

mfc

t

mfcoo

dttvkt

dttvktdttvkt

dttvktvtv

Page 26: Chapt 3 Part 3

Analysis (continued) : Pengesan kecerunan/Slope detection

Bandpasslimiter

Pengesan Sampuldt

dvFM(t) y(t)

v2(t)v1(t)

Limiter output : ]cos[

4)(1 ttVtv cL

Differentiator output : ]sin[4

)(2 ttdt

tdVtv ccL

)](cos[)()( tttEtv ccFM t

mf dttvkt0

)()(where

FM signal :

Output of the envelope detector :

dt

tdVty cL

4

)(

Since dt

dc

dt

tdVty cL

4

)(;

Page 27: Chapt 3 Part 3

tvkVVty mfLcL

44

)(

which indicates that the output consists of a dc voltage plus the ac voltage, which is proportional to the modulation on the FM signal.

Therefore :

dc ac

Slope detector circuit

The slope detector is essentially a tank circuit which is tuned to a frequency either slightly above or below the FM carrier frequency. It is not widely used

because of the characteristics of LC tuned circuit which is nonlinear especially for FM signal with large f .

t

Page 28: Chapt 3 Part 3

Frequency Demodulators

Figure 6-16: Slope detector operation.

Page 29: Chapt 3 Part 3

Is addressed by using - Balanced Slope Detector (Pembezalayan terimbang) – Using two tuned circuit.

To create wider linear region for signal with large f – achieved by using two diodes and tuned at two different tuning frequency.

Vout α ΔfVout = kd Δf

Vout = demodulated output signal ,Vpeak (volts)kd=demodulator transfer function (volts per hertz)

Page 30: Chapt 3 Part 3

Litar Foster SeeleyLitar Foster Seeley

Pemodulatan Sudut

D 1

D 2

C 2

C

C 3

C 4

R 1

R 2

V 12V o

I1

I2

C 1L

Ip

1

2

6

7

3

4

5

http://en.wikipedia.org/wiki/Detector_(radio)

The Foster-Seeley discriminator is a widely used FM detector. The detector consists of a special center-tapped transformer feeding two diodes in a full wave DC rectifier circuit. When the input transformer is tuned to the signal frequency, the output of the discriminator is zero when there is no deviation of the carrier; both halves of the center tapped transformer are balanced. As the FM signal swings in frequency above and below the carrier frequency, the balance between the two halves of the center-tapped secondary are destroyed and there is an output voltage proportional to the frequency deviation.

Page 31: Chapt 3 Part 3

Ratio detector Ratio detector

Pemodulatan Sudut

L1 L2

D 1

D 2

C

C R

R 1

R 2

V 12

V o

C 1L

Ip

1

2

3

4

5

V DC

+

-

The ratio detector is a variant of the Foster-Seely discriminator, but, the diodes conduct in opposite directions. The output in this case is taken between the sum of the diode voltages and the center tap. The output across the diodes is connected to a large value capacitor, which eliminates AM noise in the ratio detector output. While unlike the Foster-Seely discriminator, the ratio detector will not respond to AM signals, however the output is only 50% of the output of a discriminator for the same input signal.

Page 32: Chapt 3 Part 3

Frequency Demodulators

Quadrature Detector The quadrature detector is probably the single

most widely used FM demodulator. The quadrature detector is primarily used in TV

demodulation. This detector is used in some FM radio stations. The quadrature detector uses a phase-shift circuit

to produce a phase shift of 90 degrees at the unmodulated carrier frequency.

Page 33: Chapt 3 Part 3

Frequency Demodulators

Figure 6-19: A quadrature FM detector.

Page 34: Chapt 3 Part 3

Phase-Locked Loop (PLL) – Phase-Locked Loop (PLL) – Indirect MethodIndirect Method• The best frequency demodulator is the phase-locked-loop

(PLL).

PLLs have three basic elements. They are: Phase detector Low-pass filter Voltage-controlled oscillator

• PLL consists of a Phase Detector or Mixer to compare the input or reference signal to the output of VCO (Voltage-Controlled-Oscillator).

• PLL is synchronized or locked when the input and VCO frequencies are equal.

Page 35: Chapt 3 Part 3

Phase-Locked Loop (PLL) – Indirect Phase-Locked Loop (PLL) – Indirect MethodMethod

Figure 6-21: Block diagram of a PLL.

compare the two input signals and generate an output signal that,

when filtered, will control the VCO.

adjusts the VCO frequency in an attempt to correct for the original frequency or phase difference.

Page 36: Chapt 3 Part 3

Phase-Locked Loop (PLL) – Indirect Phase-Locked Loop (PLL) – Indirect MethodMethodPhase-Locked Loops

The primary job of the phase detector is to compare the two input signals and generate an output signal that, when filtered, will control the VCO.

If there is a phase or frequency difference between the FM input and VCO signals, the phase detector output varies in proportion to the difference.

The filtered output adjusts the VCO frequency in an attempt to correct for the original frequency or phase difference.

Page 37: Chapt 3 Part 3

Phase-Locked Loop (PLL) – Indirect Phase-Locked Loop (PLL) – Indirect MethodMethod

Phase-Locked Loops This dc control voltage, called the error signal, is

also the feedback in this circuit. When no input signal is applied, the phase

detector and low-pass filter outputs are zero. The VCO then operates at what is called the free-

running frequency, its normal operating frequency as determined by internal frequency-determining components.

Page 38: Chapt 3 Part 3

Phase-Locked Loop (PLL) – Indirect Phase-Locked Loop (PLL) – Indirect MethodMethod

Above is a block diagram of FM detector using Phase-Locked Loop (PLL). The input is FM signal:

Pemodulatan Sudut

Penapis Lulus Rendah

Voltage-ControlledOscillator (VCO)

Xvin(t)ve(t)

vvco(t)

vo(t)

))(cos(

)](cos[)(

0

t

mfcc

cccin

dttvktE

ttEtv

)](sin[)( ttEtv ocovco

Page 39: Chapt 3 Part 3

)()]()([ ttt eoin

)()](sin[ tt ee Then

1)( teIf

Phase-Locked LoopPhase-Locked Loop VCO output:

Multiplier in the circuit will function as a phase variation detector/pengesan perubahan fasa :

LPF will pass all the lower frequency components and filtered all the higher frequency components:

)]()(sin[2

)]()(2sin[2

)](sin[)](cos[

)()()(

ttEE

tttEE

ttttEE

tvtvtv

oinoc

oincoc

ocincoc

vcoine

)(2

)(sin2

)]()(sin[2

)(

tEE

tEE

ttEE

tv

eoc

eoc

oinoc

o

)](sin[)( ttEtv ocovco t

ooo dttvkt0

)()(where

Page 40: Chapt 3 Part 3

Frequency generated at the VCO output is proportional to the input voltage of the VCO.

Therefore

Output of the PLL is given by:

Given:

Hence:

)()( tvkt ooo

dttvkdtttt

oo

t

oo )()()(00

dt

td

ktv o

oo

)(1)(

1)()()( ttt oine )()( tt oin

)()()(1)(1

)( tkvtvk

k

dt

td

kdt

td

ktv mm

o

fin

o

o

oo

Therefore, the peak output voltage is the voltage necessary to move the local oscillator by the amount of the Δf. That is,

Vo (peak) = Δf / kf

Page 41: Chapt 3 Part 3

Modulating signal source

IntegratorPhase

modulatorFM wave

cos 2c cV f t

Frequency modulator

FM wave

cos 2c cV f t

Modulating signal source

Direct

Indirect

FM Transmitter

Crosby

Phase Locked Loop

Armstrong

Page 42: Chapt 3 Part 3

GROUP ACTIVITY

Crosby (female - 1 group)Armstrong (male -1 group)Generation of NBFM (female - 1 group)Generation of WBFM (male -1 group)

Page 43: Chapt 3 Part 3

Crosby Direct FM Modulator

Page 44: Chapt 3 Part 3

Armstrong Indirect FM Transmitter

Page 45: Chapt 3 Part 3

m < 1

max = 1.67 miliradiance

m

fm

f

15 kHzmf 200 kHzcf

Aim f = 75 kHz and ft = 90 MHz

Fig 7-28

max arctan m m

c c

V Vm

V V

Page 46: Chapt 3 Part 3

Direct method - Crosby circuit

AFC Circuit

To transmit and fed back an error control voltage to a modulator in order to control frequency oscillator at 5 MHz (to prevent drift of the carrier and frequency deviation). This method is called Automatic Frequency Control (Kawalan frekuensi automatic).

Crosby circuit – to generate WBFM

Page 47: Chapt 3 Part 3

Let us look at an example. An FM station operates at 106.5 MHz with a maximum deviation of 75 KHz. The FM signal is generated by a reactance modulator that operates at 3.9444 MHz, with a maximum deviation of 2.7778 KHz. The resulting FM signal is fed through 3 frequency triplers, multiplying the carrier frequency and deviation 27 times. The final carrier frequency is 27*3.9444 = 106.5 MHz and the final deviation is 27*2.7778 = 75 KHz.

It is important to remember that frequency multiplication multiplies both the carrier frequency and the deviation.

Page 48: Chapt 3 Part 3

http://www.see.ed.ac.uk/~gjrp/EE3/Comms/Lecture10/sld004.htm

Page 49: Chapt 3 Part 3

3.9.2 Indirect method

Pemodulatan Sudut

~

vWBFM(t) Mixer Penapis Lulus Jalur

Local Oscillator cos(ωLOt)

vz(t)vy(t)

ωc1 Nωc1

PemodulatNBFM

Pekali Frekuensi, N

vm(t)

vNBFM(t)

Armstrong methodArmstrong method

First generate NBFM. Then multiplies NBFM frequency with multiplier N. This frequency multiplication multiplies both the carrier frequency and the deviation.

Then signal vy(t) is tuned at the frequency desired and is suitable to the ranges of LO frequency, fLO . BPF is then used to filter the desired

frequency components.

Page 50: Chapt 3 Part 3

Generation of NBFMGeneration of NBFM

FM modulation : The amplitude of the modulated carrier is held constant and the time derivative of the phase of the carrier is varied linearly with the information signal.

The instantaneous frequency of FM is given by:

Hence

Pemodulatan Sudut

)()( tvkt mfci

)()( tvkt mfc tdt

tdt cc

ci

)()( where

~

∫dt

k fvm(t))(tc

X ∑

90°

vNBFM(t)

Eccos(ωct)Ecsin(ωct)

-

+Pemodulat Fasa

Page 51: Chapt 3 Part 3

The angle of the FM signal can be obtained by integrating the instantaneous frequency.

vm(t) is a sinusoidal signal, hence:

Pemodulatan Sudut

)sin(

)sin(

)cos()(0

t

tEk

dttEkt

m

mm

mf

t

mmfc

ttdttt cc

t

ic 0

)()(

t

mfc dttvkt0

)()(Notes:

1)()(0

t

mfc dttvkt

Notes:

1)sin( tmFor NBFM

Therefore

t

mfc

t

mfcc

dttvkt

dttvkt

0

0

)(

)()(

Page 52: Chapt 3 Part 3

General equation for FM signal

Pemodulatan Sudut

)](sin[)(sin)](cos[)(cos

)]([cos)(

ttEttE

ttEtv

cccccc

cccFM

)(sin)()(cos)( tEttEtv cccccNBFM

• Therefore NBFM signal can be generated using phase modulator circuit as shown.

• To obtain WBFM signal, the output of the modulator circuit (NBFM) is fed into frequency multiplier circuit and the mixer circuit.

• The function of the frequency multiplier is to increase the frequency deviation or modulation index so that WBFM can be generated.

• Hence :

1)( tcFor NBFM therefore 1)](cos[ tc )()](sin[ tt cc and

Summary:

Page 53: Chapt 3 Part 3

vWBFM(t)

~

Mixer Penapis Lulus Jalur

Penjana Tempatan cos(ωLOt)

vz(t)vy(t)

ωc1 Nωc1

PemodulatNBFM

Pekali Frekuensi, N

vm(t)

vNBFM(t)

Generation of WBFMGeneration of WBFM

Analisa Matematik :

• The instantaneous value of the carrier frequency is increased by N times.

)()()( 1 ttt cci Let :

)(

)]([

)()(

2

12

tN

tN

tNt

cc

cc

Output of the frequency multiplier :

cc N 2

Notes

Page 54: Chapt 3 Part 3

And :

Pemodulatan Sudut

)()()( 222 tNttdt

dt cc

cc N 2

Nota:)sin(

)sin()(

2

1

t

tNtN

m

mc

12 N

• It is proven that the modulation index was increased by N times following this equation.

)sin(

)sin(

)cos()(0

t

tEk

dttEkt

m

mm

mf

t

mmfc

Page 55: Chapt 3 Part 3

The output equation of the frequency multiplier :

Pass the signal through the mixer, then WBFM signal is obtained :

BPF is used to filter the WBFM signal desired either at ωc2+ ωLO

or at ωc2- ωLO . Hence the output equation :

)]([

)]([cos)(

2

2

tNtkosE

tEtv

ccc

cFM

Pemodulatan Sudut

)]()cos[()]()cos[(

)cos(2 x )]([cos)(

22

2

tNtEtNtE

ttNtEtv

cLOcccLOcc

LOcccFM

)]()[(

)]()[()(

2

2

tNtkosE

tNtkosEtv

cLOcc

cLOccWBFM