FREQUENCY
AND
PHASE MODULATION
(ANGLE MODULATION)
• ANGLE MODULATION –
• When frequency or phase of the carrier is varied
by the modulating signal , then it is called angle
modulation.
• Frequency Modulation – When the frequency of
the carrier varies as per amplitude of modulating
signal, then it is called frequency modulation (FM).
• Phase Modulation - When the phase of the
carrier varies as per amplitude of modulating
signal, then it is called phase modulation (PM).
• Amplitude of the modulated carrier remains
constant in both modulation systems.
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• An important feature of angle modulation:
• It can provide a better discrimination
(robustness) against noise and interference
than AM.
• This improvement is achieved at the expense
of increased transmission bandwidth.
• In case of angle modulation, channel
bandwidth may be exchanged for improved
noise performance
• Such trade-off is not possible with AM
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• BASIC DEFINITIONS -Relationship
between the angle and frequency of a
sinusoidal signal
• Sinusoidal carrier c(t) =Ac cos[θi(t)]
• Angle of carrier θi(t)[rad]
• Instantaneous frequency of carrier
fi(t) =(1/2π)ωi(t) =(1/2π)di(t)/dt
• =(1/2π)˙ θi(t)[Hz].
• In the case of an un-modulated carrier,
the angle becomes θi(t) = 2πfct + θc
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Time domain representation
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• Compare FM-PM –
• The basic difference between FM & PM lies in
which property of the carrier is directly varied
by modulating signal.
• In FM, the frequency of carrier is varied
directly.
• In PM, phase of the carrier is varied directly.
Instantaneous phase deviation is represented
by θ(t).
• Instantaneous phase= ωct + θ(t) rad.
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• Instantaneous frequency deviation =
• d/dt {θ(t)} = θ’(t) Hz.
• The instantaneous frequency deviation is the
instantaneous change in carrier frequency and
is equal to the rate at which instantaneous
phase deviation takes place.
• Instantaneous frequency is defined as
frequency of the carrier at a given instant of
time and is given as
ωi(t) =d/dt [ωc.t + θ(t)] = ωc + θ’(t) rad/sec.
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• Instantaneous phase deviation θ (t) is
proportional to modulating signal voltage,
θ (t) = k em(t) rad. ( k is deviation sensitivity of
phase.).
• Instantaneous frequency deviation θ’ (t) is
proportional to modulating signal voltage,
θ’ (t) = k1 em(t) rad. ( k1 is deviation
sensitivity of frequency.)##2
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Frequency modulation
5.9
• Observations from the FM & PM waveforms –
• 1. Both FM & PM waveforms are identical
except the phase shift.
• 2. For FM, the maximum frequency deviation
takes place when modulating signal is at +ve
and –ve peaks.
• 3. For PM, the maximum frequency deviation
takes place near zero crossing of the
modulating signal.
• 4. It is diffcult to know from modulated
waveform whether the modulation is FM or
PM. (##3)
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• Bandwidth Requirement – for FM• The BW requirement can be obtained depending on
the modulation index (M.I).
• The M.I. can be classified as high(more than 10),
medium (1 to 10) and low (less than 1).
• The low index systems are called narrowband FM in
which frequency spectrum resembles AM. BW (fm)
=2fm Hz.
• For high index modulation, BW = 2*δ.(Freq. dev.)
• BW can also be found out by Bessel tableBWfm = 2.n.fm where n is the number of sidebands
obtained from table.
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• Carson’s Rule –
• Rule gives approximate minimum BW of angle
modulated signal as
• BW fm = 2{δ + fm(max)} Hz.
• From the above equation, it is found that the
BW accommodates almost 98% of the total
transmitted power
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• Bandwidth for PM –
• BW for PM is expressed as
• BWpm = 2(mp+1)fm.
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• Block Diagram of NBFM Generator –
• Carrier is Ec cos ωc .t
M(t)
Integrator
Product
Modulator
90 degree
Phase Shifter
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Adder
NBFM
signal
Carrier
Generator
16
• Phasor Diagram of NBFM –
• USB phasor at an angle of (ωm .t) and LSB
phasor at an angle of (- ωm .t)
Resultant
Phasor
Phase
Shift
LSB Phasor
USB Phasor
Carrier Phasor
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•
•
•
•
Carrier phasor is Ec cos ωc .t (always fixed).
USB phasor in clockwise direction (ωm)
LSB phasor in counter clockwise direction (-ωm)
Resultant of two sideband phasor is always
perpendicular to carrier phasor.
• The net resultant phasor of NBFM due to Carrier
and sidebands is as shown in the diagram.
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• Wideband Frequency Modulation –
• If the modulation index is higher than 10, then
it is called wideband FM.
• Spectrum contains infinite numbers of
sidebands and carrier as against two
sidebands and carrier in NBFM.
• BW is = 2{δ+fm(max)} as against 2fm for
NBFM.
• Used for broadcast and entertainment as
against for mobile communication for NBFM.
• ##5.
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• Advantages of Angle Modulation over AM• 1. As the amplitude of FM carrier is constant,
the noise interference is minimum.
• 2. The amplitude of FM carrier is constant and
is independent of depth of modulation. Hence
transmitter power remains constant in FM
whereas it varies in AM.
• 3. As against the limitation of depth of
modulation in AM, in FM depth of modulation
can be increased to any value, without causing
any distortion.
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• 4. Because of guard bands provided in FM,
adjacent channel interference is very less.
• 5. Since FM uses VHF and UHF bands of
frequencies, the noise interference is
minimum as compared to AM which uses MF
and HF ranges.
• 6. Radius of propagation is limited as FM uses
space waves with line of sight. So it is possible
to operate many independent transmitters on
the same frequency with minimum
interference.
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• Disadvantages of FM compared to AM• 1. BW requirement of FM is very high as
compared to AM.
• 2. FM equipments are more complex and
hence costly.
• Area covered by FM is limited, to line of sight
area but AM coverage area is large.
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• Comparison between FM and AM Parameter
Origin
Modulating
differences
Importance
Frequency
Range
AM
FM
AM method of audio
transmission was first
successfully carried out in the
mid 1870s.
In AM, a radio wave known as
the "carrier" or "carrier wave"
is modulated in amplitude by
the signal that is to be
transmitted
It is used in both analog and
digital communication and
telemetry
AM radio ranges from 535 to
1705 KHz (OR) Up to 1200 Bits
per second.
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FM radio was developed in the
United states mainly by Edwin
Armstrong in the 1930s.
In FM, a radio wave known as the
"carrier" or "carrier wave" is
modulated in frequency by the
signal that is to be transmitted.
It is used in both analog and digital
communication and telemetry
FM radio ranges in a higher
spectrum from 88 to 108 MHz. (OR)
1200 to 2400 bits per second.
23
• Comparison between FM and AM Parameter
AM
FM
Bandwidth
Requirements
Twice the highest modulating
frequency. In AM radio broadcasting,
the modulating signal has bandwidth
of 15kHz, and hence the bandwidth of
an amplitude-modulated signal is
30kHz.
Twice the sum of the modulating
signal frequency and the frequency
deviation. If the frequency deviation is
75kHz and the modulating signal
frequency is 15kHz, the bandwidth
required is 180kHz.
Complexity
Transmitter and receiver are simple
Transmitter and receiver are more
but synchronization is needed in case complex as variation of modulating
of SSBSC AM carrier.
signal has to be converted and
detected from corresponding variation
in frequencies.(i.e. voltage to
frequency and frequency to voltage
conversion has to be done).
AM is more susceptible to noise
FM is less susceptible to noise because
because noise affects amplitude,
information in an FM signal is
which is where information is
transmitted through varying the
"stored" in an AM signal.
frequency, and not the amplitude.
Noise
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• Comparison between FM and PM Sr No.
FM
PM
1
The max frequency deviation
depends on amplitude of
modulating signal and its frequency
The max phase deviation depends
on amplitude of modulating signal
2
Frequency of the carrier is
modulated by modulating signal.
Phase of the carrier is modulated
by modulating signal.
3
Modulation index is increased as
modulation frequency is reduced
and vice versa.
Modulation index remains same if
modulating signal frequency is
change.
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• Modulators –
• Carrier frequency can be generated by LC
oscillator.
• By varying the values of L or C of tank circuit,
carrier frequency can be changed.
• Properties of BJT,FET and varactor diodes can
be varied by changing the voltage across
them.
• When these components are used with LC
tank circuits, we are able to vary frequency of
oscillator by changing the reactance of L or C.
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• TWO types of FM Modulators –
• 1. Indirect FM – Modulation is obtained by
phase modulation of the carrier.
An instantaneous phase of the carrier is
directly proportional to the amplitude of the
modulating signal.
• 2. Direct FM- The frequency of carrier is varied
directly by modulating signal.
An instantaneous frequency variation is
directly proportional to the amplitude of the
modulating signal.
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• There are two methods to derive FM by using
FET and varactor.
• 1. Frequency modulation using Varactor Diode –
• There exists small junction capacitance in the
reverse biased condition of all the diodes.
• The varactor diodes are designed to optimise
this characteristic.
• As the reverse bias across varactor diode is
varied, its junction capacitance changes.
• These changes are linear and wide (1 to 200pF)
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• Frequency modulation using varactor diode –
• All diodes show small junction capacitance in
the reverse biased condition.
• ##6
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• Advantages of FM using Varactor Diode –
• 1. High frequency stability as crystal oscillator
is isolated from modulator.
• Disadvantages –
• 1. To avoid distortion, the amplitude of
modulating signal is to be kept small.
• 2. The varactor diode must have non linear
characteristics of capacitance vs. voltage.
• Use –
• This method is used for low index narrow
band FM generation.
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• FET Reactance Modulator –
• There are a number of devices whose reactance
can be varied by the application of voltage.
These include FET and BJT, varactor diode etc.
• If such a device is placed across the tank circuit
of the L-C oscillator, then FM will be produced
when the reactance of the device is varied by
the modulating voltage.
• At the carrier frequency, the oscillator
inductance is tuned by its own capacitance in
parallel with the average reactance to the
variable reactance device.
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• Advantages of FET Reactance Modulator –
• 1. Due to FET characteristics, linear
relationship between modulating voltage and
transconductance can be achieved.
• 2 This method produces enough frequency
deviation and hence no frequency
multiplication is required.
• Disadvantages - Frequency stability is poor as
lumped components are used.
• Use – This method is used for low modulation
index application.
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• Indirect FM –
• Phase modulation is used to achieve
frequency modulation in the indirect method,
• It is necessary to integrate the modulating
signal prior to applying it to the phase
modulator,
• This transmitter is widely used in VHF and UHF
radio telephone equipment.
• ##7
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• Advantage –
• 1. The crystal oscillator is isolated from
modulator, so frequency stability is very good.
• Disadvantages –
• 1. Because of nonlinear capacitance Vs.
voltage characteristics of varactor diode, there
is a distortion in the modulated output
waveform.
• 2. Amplitude of modulating signal should be
kept small to avoid distortion.
• Use –Used for narrow band low index FM.
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• FM Transmitters –
• Two types of transmitters – Indirect FM and
Direct FM Transmitters.
• Indirect FM Transmitters – Produces the FM
whose phase deviation is directly proportional
to modulating signal amplitude. Frequency of
oscillator is not directly varied. Hence crystal
oscillators can be used.
• Direct FM Transmitters – Frequency deviation
is directly proportional to modulating signal.
Carrier frequency is directly deviated.
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• Need for Automatic Frequency Correction –
• In FM transmitters, the frequency of the
oscillator is directly varied.
• To obtain very stable frequency of oscillator,
automatic frequency correction technique is
employed.
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• FM Transmitters –
• Block Diagram –##8
• The modulating signal is given to frequency
modulator ( may be reactance modulator or
VCO ) and oscillator.
• Let fc = F Mhz. Multiplied by 18 to generate
the transmitted frequency F*18 Mhz.
• AFC loop is to maintain stable centre
frequency.
• Multiplier output given to mixer is F*6.
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• The crystal frequency oscillator - reference
frequency is {(6*fc) – 2MHz.}
• The mixer generates 2 MHz difference
frequency which is given to discriminator,
which is tuned to 2 MHz.
• If there is a difference in the output frequency
of mixer, discriminator generates d. c.
correction voltage.
• If multiplier frequency is exactly 6*fc, then no
correction is required and hence correction
voltage must be zero.
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• But with FM, there is a frequency deviation in
6*fc, which is proportional to modulating
signal amplitude.
• So d.c. correction voltage also have
corresponding variation.
• Therefore this d.c. voltage is passed through
low pass filter to remove effect of frequency
variation due to modulation.
• The filtered voltage is used for frequency
correction.
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• Phase Locked Loop direct FM transmitter –
• This type is used to produce WBFM with high
mod index.
• When both the input frequencies to phase
comparator are same , they are locked and
output is zero.
• The modulating signal is used to control the
output frequency of VCO.
• The frequency of output FM of VCO is a
function of modulating signal.
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• If there is a deviation in the centre frequency
of VCO, correction voltage is generated.
• This d.c. voltage, passing through LPF, is added
to modulating signal to correct the VCO
output.
• Function of LPF is to remove rapid changes in
correction voltage due to frequency variations
in FM signal.
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• Indirect FM Transmitter – Armstrong Method • ( Phase Mod. is employed to produce FM)
• Stability of the frequency is a major issue in
FM. So direct methods of FM generation are
not suitable for broadcasting .
• To overcome this drawback, indirect method to
generate FM from PM is employed. (block dia.)
• To get the modulating signal of same frequency
of carrier, AM signal is generated and shifted
by 90degrees and added to fc signal vector.
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• The resultant vector output is phase
modulated.
• Since AM and carrier vectors are having same
frequency(fc), the out put is FM.
• Thus phase modulation produces FM.
• The phase modulated signal can be defined as
e(pm) = Ec sin (ωc t + m cos ωm t).
• ##
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• FOSTER SEELEY DISCRIMINATOR – (Phase
discriminator)• The Foster Seeley Discriminator is a common
type of FM detector circuit used mainly within
radio sets constructed using discrete
components.
• The Foster Seeley detector (or the Foster
Seeley discriminator) has many similarities to
the ratio detector. The circuit topology looks
very similar, having a transformer and a pair of
diodes, but there is no third winding and
instead a choke is used.
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• Cc,C1 & C2 offers short circuit for IF center
frequency.
• Right side of L3 is at ground potential and
IF(Vin) is fed directly (in phase)across L3.(VL3)
• 180 degree phase out by T1 – La & Lb equal
division.
• At resonant frequency of tank circuit(IF)
secondary current (Is) is in phase with Vs and
180degree out of phase with VL3.
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• Like the ratio detector, the Foster-Seeley
circuit operates using a phase difference
between signals.
• To obtain the different phased signals a
connection is made to the primary side of the
transformer using a capacitor, and this is taken
to the center tap of the transformer.
• This gives a signal that is 90 degrees out of
phase.
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• Due to loose coupling , primary of T1 acts as
inductor and Ip is 90 degree out of phase with
Vin.
• Voltage induced in secondary is 90 degree out
of phase with Vin(VL3)
• VLa and Vlb are 180 degree out of phase with
each other and 90 degree out of phase with
VL3.
• Voltage across VD1 is vector sum of VL3 and
VLa and VD2 is vector sum of VL3 and VLb.
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• When IF > resonance, secondary tank circuit
impedance becomes inductive and secondary
current lags voltage by theta which is
proportional to frequency deviation.
• When IF < resonance, secondary current
leads secondary voltage by theta which is
proportional to frequency deviation.
• F.S.D. is tunned by injecting a frequency equal
to the IF center frequency and tunning Co for
zero volts output.
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• Ratio Detector –
• Ratio detector or discriminator is widely used
for FM demodulation within radio sets using
discrete components. It was capable of
providing a good level of performance.
• In recent years the Ratio detector has been
less widely used.
• The main reason for this is that it requires the
use of wire wound inductors and these are
expensive to manufacture.
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• Ratio Detector Circuit –
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• Other types of FM demodulator have
overtaken them, mainly as a result of the fact
that the other FM demodulator configurations
lend themselves more easily to being
incorporated into integrated circuits.
• Ratio FM detector basics • When circuits employing discrete components
were more widely used, the Ratio and FosterSeeley detectors were widely used. Of these
the ratio detector was the most popular as it
offers a better level of amplitude modulation
rejection.
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• This enables it to provide a greater level of
noise immunity as most noise is amplitude
noise, and it also enables the circuit to
operate satisfactorily with lower levels of
limiting in the preceding IF stages of the
receiver.
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• The operation of the ratio detector centres
around a frequency sensitive phase shift
network with a transformer and the diodes
that are effectively in series with one another.
• When a steady carrier is applied to the circuit
the diodes act to produce a steady voltage
across the resistors R1 and R2, and the
capacitor C3 charges up as a result.
• The transformer enables the circuit to detect
changes in the frequency of the incoming
signal. It has three windings.
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• The primary and secondary act in the normal
way to produce a signal at the output. The
third winding is un-tuned and the coupling
between the primary and the third winding is
very tight, and this means that the phasing
between signals in these two windings is the
same.
• The primary and secondary windings are
tuned and lightly coupled.
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• This means that there is a phase difference of
90 degrees between the signals in these
windings at the centre frequency.
• If the signal moves away from the centre
frequency the phase difference will change.
• In turn the phase difference between the
secondary and third windings also varies.
• When this occurs the voltage will subtract
from one side of the secondary and add to the
other causing an imbalance across the
resistors R1 and R2.
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• As a result this causes a current to flow in the
third winding and the modulation to appear at
the output.
• The capacitors C1 and C2 filter any remaining
RF signal which may appear across the
resistors.
• The capacitor C4 and R3 also act as filters
ensuring no RF reaches the audio section of
the receiver.
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• Ratio detector advantages & disadvantages • As with any circuit there are a number of
advantages and disadvantages to be
considered when choosing between several
options.
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• Advantages –
• Simple to construct using discrete
components
• Offers good level of performance and
reasonable linearity.
• Disadvantages –
• High cost of transformer
• Typically lends itself to use in only circuits
using discrete components and not integrated
circuits.
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• Pre-emphasis
• Pre-emphasis refers to boosting the relative
amplitudes of the modulating voltage for
higher audio frequencies from 2 to
approximately 15 KHz.
• De-emphasis
• De-emphasis means attenuating those
frequencies by the amount by which they are
boosted.
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• However pre-emphasis is done at the
transmitter and the de-emphasis is done in
the receiver.
• The purpose is to improve the signal-to-noise
ratio for FM reception.
• A time constant of 75µs is specified in the RC
or L/Z network for pre-emphasis and deemphasis.
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• Pre-emphasis circuit
• At the transmitter, the modulating signal is
passed through a simple network which
amplifies the high frequency components
more than the low-frequency components.
• The simplest form of such a circuit is a simple
high pass filter of the type shown in fig.
• Specification dictate a time constant of 75
microseconds (µs) where t = RC. Any
combination of resistor and capacitor (or
resistor and inductor) giving this time constant
will be satisfactory.
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• Such a circuit has a cut off frequency fco of 2122
Hz. This means that frequencies higher than 2122
Hz will he linearly enhanced.
• The output amplitude increases with frequency at
a rate of 6 dB per octave.
• The pre-emphasis curve is shown in Fig.
• This pre-emphasis circuit increases the energy
content of the higher-frequency signals so that
they will tend to become stronger than the high
frequency noise components. This improves the
signal to noise ratio and increases intelligibility and
fidelity.
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• The pre-emphasis circuit also has an upper
break frequency fu where the signal
enhancement flattens out.
• This upper break frequency is computed with
the expression.
• fu = R1 +(R2/2πR1^2 *C)
• It is usually set at some very high value
beyond the audio range. An fu of greater than
30KHz is typical.
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• De-emphasis Circuit-
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• To return the frequency response to its normal
level, a de-emphasis circuit is used at the
receiver.
• This is a simple low-pass filter with a constant of
75 πs. See figure (c).
• It features a cut off of 2122 Hz and causes
signals above this frequency to be attenuated at
the rate of 6bB per octave.
• The response curve is shown in Fig (d). As a
result, the pre-emphasis at the transmitter is
exactly offset by the de-emphasis circuit in the
receiver, providing a normal frequency response.
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• The combined effect of pre-emphasis and deemphasis is to increase the high-frequency
components during transmission so that they
will be stronger and not masked by noise.
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