Frequency modulation (modulator /demodulator)
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
Direct FM Modulator
The carrier is generated by LC or crystal oscillator circuits. Figure below shows simple direct FM modulator
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.
Frequency Modulators
Figure 6-4: A direct-frequency-modulated carrier oscillator using a varactor diode.
Varactor diode Direct FM modulator
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
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.
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.
Frequency Modulators
Figure 6-5: Frequency modulation of a crystal oscillator with a VVC.
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.
Eg (VCO):Linear integrated-circuit direct FM modulator
High-frequency deviations and high modulation indices.
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.
Frequency Modulators
Figure 6-10: A reactance modulator.
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
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
Demodulator
Five most commonly used demodulator are:
Slope detector
Foster-Seeley discriminator
Ratio detector
PLL demodulator
Quadrature detector
Tuned-circuit frequency discriminator
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)
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
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 :
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:
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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.
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 :
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
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
)(;
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
Frequency Demodulators
Figure 6-16: Slope detector operation.
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)
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.
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.
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.
Frequency Demodulators
Figure 6-19: A quadrature FM detector.
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.
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.
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.
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.
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
)()]()([ 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
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
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
GROUP ACTIVITY
Crosby (female - 1 group)Armstrong (male -1 group)Generation of NBFM (female - 1 group)Generation of WBFM (male -1 group)
Crosby Direct FM Modulator
Armstrong Indirect FM Transmitter
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
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
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.
http://www.see.ed.ac.uk/~gjrp/EE3/Comms/Lecture10/sld004.htm
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.
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
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
)(
)()(
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:
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
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
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