MODULATION TECHNIQUES
What is Modulation ?
• Modulation is the process of encoding information
from a message source in a manner suitable for
transmission
• It involves translating a baseband message signal
to a bandpass signal at frequencies that are very
high compared to the baseband frequency.
• Baseband signal is called modulating signal
• Bandpass signal is called modulated signal
Modulation Techniques
• Modulation can be done by varying the
– Amplitude
– Phase, or
– Frequency
of a high frequency carrier in accordance with
the amplitude of the message signal.
• Demodulation is the inverse operation:
extracting the baseband message from the
carrier so that it may be processed at the
receiver.
Why Carrier?
• Effective radiation of EM waves requires
antenna dimensions comparable with the
wavelength:
– Antenna for 3 kHz would be ~100 km long
– Antenna for 3 GHz carrier is 10 cm long
• Sharing the access to the
telecommunication channel resources
Demodulation & Detection
• Demodulation
– Is process of removing the carrier signal to
obtain the original signal waveform
• Detection – extracts the symbols from the
waveform
– Coherent detection
– Non-coherent detection
Coherent Detection
• An estimate of the channel phase and
attenuation is recovered. It is then possible to
reproduce the transmitted signal and
demodulate.
• Requires a replica carrier wave of the same
frequency and phase at the receiver.
• The received signal and replica carrier are
cross-correlated using information contained in
their amplitudes and phases.
• Also known as synchronous detection
Coherent Detection
• Carrier recovery methods include
– Pilot Tone (such as Transparent Tone in
Band)
• Less power in the information bearing
signal, High peak-to-mean power ratio
– Carrier recovery from the information signal
• E.g. Costas loop
Non-Coherent Detection
• Requires no reference wave; does not
exploit phase reference information
(envelope detection)
– Differential Phase Shift Keying (DPSK)
– Frequency Shift Keying (FSK)
– Amplitude Shift Keying (ASK)
– Non coherent detection is less complex than
coherent detection (easier to implement), but
has worse performance.
Analog/Digital Modulation
• Analog Modulation
– The input is continues signal
– Used in broadcasting radio, first generation
mobile radio systems such as AMPS in USA.
• Digital Modulation
– The input is time sequence of symbols or
pulses.
– Are used in current and future mobile radio
systems
Goal of Modulation Techniques
• Modulation is difficult task given channel,
e.g. the hostile mobile radio channels
• Small-scale fading and multipath conditions.
• The goal of a modulation scheme is:
– Transport the message signal through the
channel with best possible quality
– Occupy least amount of radio (RF) spectrum.
Amplitude Modulation
•
Amplitude Modulation (AM)
–
–
–
–
–
Changes the amplitude of the carrier signal
according to the amplitude of the message signal
All info is carried in the amplitude of the carrier
There is a linear relationship between the received
signal quality and received signal power.
AM systems usually occupy less bandwidth then
FM systems.
AM carrier signal has time-varying envelope.
Analogue Modulation – Amplitude Modulation
Consider a 'sine wave' carrier.
vc(t) = Vc cos(ct), peak amplitude = Vc, carrier frequency c radians per second.
Since c = 2fc, frequency = fc Hz where fc = 1/T.
Amplitude Modulation AM
In AM, the modulating signal (the message signal) m(t) is 'impressed' on to the
amplitude of the carrier.
Message Signal m(t)
In general m(t) will be a band of signals, for example speech or video signals. A
notation or convention to show baseband signals for m(t) is shown below
Message Signal m(t)
In general m(t) will be band limited. Consider for example, speech via a microphone.
The envelope of the spectrum would be like:
EXAMPLE
EXAMPLE
Message Signal m(t)
In order to make the analysis and indeed the testing of AM systems easier, it is common to make
m(t) a test signal, i.e. a signal with a constant amplitude and frequency given by
m t
V m cos
m
t
Schematic Diagram for Amplitude
Modulation
VDC is a variable voltage, which can be set between 0 Volts and +V Volts. This
schematic diagram is very useful; from this all the important properties of AM and
various forms of AM may be derived.
Equations for AM
From the diagram vs (t)= (VDC +m(t ))cos(ωct) where VDC is the DC voltage that can
be varied. The equation is in the form Amp cos ct and we may 'see' that the amplitude
is a function of m(t) and VDC. Expanding the equation we get:
vs (t)=V DC cos(ωct )+m(t )cos(ωct )
Equations for AM
Now let m(t) = Vm cos mt, i.e. a 'test' signal,
Using the trig identity
we have
cosAcosB =
v s (t)=V DC cos(ωc t )+
vs (t)=VDC cos(ωct )+Vm cos(ωmt )cos(ωct )
1
cos( A+ B) + cos( A − B)
2
Vm
V
cos((ωc +ω m )t)+ m cos((ωc − ωm )t)
2
2
Components:
Carrier upper sideband USB
Amplitude:
VDC
Frequency:
c
fc
Vm/2
c + m
fc + fm
lower sideband LSB
Vm/2
c – m
fc + fm
This equation represents Double Amplitude Modulation – DSBAM
Spectrum and Waveforms
The following diagrams
represent the spectrum
of the input signals,
namely (VDC + m(t)),
with m(t) = Vm cos mt,
and the carrier cos ct
and corresponding
waveforms.
Spectrum and Waveforms
The above are input signals. The diagram below shows the spectrum and
corresponding waveform of the output signal, given by
Vm
Vm
cos
cos
vs t V DC cos c t
c
m t
c
m t
2
2
Spektrum 2 Side Band
Double Sideband AM, DSBAM
The component at the output at the carrier frequency fc is shown as a broken line with
amplitude VDC to show that the amplitude depends on VDC. The structure of the
waveform will now be considered in a little more detail.
Waveforms
Consider again the diagram
VDC is a variable DC offset added to the message; m(t) = Vm cos mt
Double Sideband AM, DSBAM
This is multiplied by a carrier, cos ct. We effectively multiply (VDC + m(t)) waveform
by +1, -1, +1, -1, ...
The product gives the output signal
vs t
VDC m t cos
c
t
Double Sideband AM, DSBAM
Modulation Depth
Consider again the equation
vs (t)= (VDC +Vm cos(ωmt ))cos(ωct) , which may be written as


V
vs (t)=V DC 1+ m cos(ωmt )cos(ωct )
 VDC

The ratio is
Vm
V
Modulation Depth m = m
defined
as
the
modulation
depth,
m,
i.e.
VDC
VDC
From an oscilloscope display the modulation depth for Double Sideband AM may be
determined as follows:
Modulation Depth
2Emax = maximum peak-to-peak of waveform
2Emin = minimum peak-to-peak of waveform
Modulation Depth m =
2Emax − 2Emin
2Emax + 2Emin
Vm
This may be shown to equal
as follows:
VDC
2 Emax
m=
2 V DC V m
2 Emin
2 V DC V m
2VDC + 2Vm − 2VDC + 2Vm
Vm
4Vm
=
=
VDC
2VDC + 2Vm + 2VDC − 2Vm
4VDC
Double Sideband Modulation 'Types'
There are 3 main types of DSB
• Double Sideband Amplitude Modulation, DSBAM – with carrier
• Double Sideband Diminished (Pilot) Carrier, DSB Dim C
• Double Sideband Suppressed Carrier, DSBSC
•
The type of modulation is determined by the modulation depth,
which for a fixed m(t) depends on the DC offset, VDC. Note, when a
modulator is set up, VDC is fixed at a particular value. In the following
illustrations we will have a fixed message, Vm cos mt and vary VDC
to obtain different types of Double Sideband modulation.
Graphical Representation of Modulation
Depth and Modulation Types
Graphical Representation of Modulation
Depth and Modulation Types 2
Graphical Representation of Modulation
Depth and Modulation Types 3
Note then that VDC may be set to give
the modulation depth and modulation
type.
DSBAM VDC >> Vm, m  1
DSB Dim C 0 < VDC < Vm,
m > 1 (1 < m < )
DSBSC VDC = 0, m = 
The spectrum for the 3 main types of
amplitude modulation are summarised
Bandwidth Requirement for
DSBAM
In general, the message signal m(t) will not be a single 'sine' wave, but a band of frequencies
extending up to B Hz as shown
Remember – the 'shape' is used for convenience to distinguish low frequencies from high
frequencies in the baseband signal.
Power Considerations in
DSBAM
V 
Remembering that Normalised Average Power = (VRMS)2 =  pk 
 2
2
we may tabulate for AM components as follows:
vs (t )=V DC cos(ωc t )+
Vm
V
cos((ωc +ω m )t)+ m cos((ωc − ωm )t)
2
2
Component
Carrier
USB
Amplitude pk
VDC
Vm
2
Power
VDC
2
2
Power
VDC
2
2
LSB
Vm
2
2
V 2
V 2  V 
 V 
 m  = m  m  = m
8
8 2 2
2 2
2
2
2
mV
DC
8
2
2
mV
DC
8
Total Power P T =
Carrier Power Pc
+ PUSB
+ PLSB
Power Considerations in
DSBAM
From this we may write two equivalent equations for the total power PT, in a DSBAM signal
2
2
2
2
V
V
V
V
V
PT = DC + m + m = DC + m
2
8
8
2
4
The carrier power
V
Pc = DC
2
2
i.e.
2
2
2
V DC
m2V DC
m2V DC
PT =
+
+
2
8
8
and
m2
m2
PT = Pc + Pc
+ Pc
4
4
or
2
 m2
PT = Pc  1+
 2




Either of these forms may be useful. Since both USB and LSB contain the same information a
useful ratio which shows the proportion of 'useful' power to total power is
PUSB
=
PT
Pc
m2
4
 m2
Pc 1+
2





=
m2
4+ 2m2
Power Considerations in
DSBAM
For DSBAM (m  1), allowing for m(t) with a dynamic range, the average value of m
may be assumed to be m = 0.3
Hence,
m2
(0.3) 2
=
= 0.0215
2
2
4 + 2m
4 + 2(0.3)
Hence, on average only about 2.15% of the total power transmitted may be regarded
as 'useful' power. ( 95.7% of the total power is in the carrier!)
m2
=1
Even for a maximum modulation depth of m = 1 for DSBAM the ratio
4 + 2m2 6
i.e. only 1/6th of the total power is 'useful' power (with 2/3 of the total power in the
carrier).
Graphic
Example
Suppose you have a portable (for example you carry it in your ' back pack') DSBAM transmitter
which needs to transmit an average power of 10 Watts in each sideband when modulation depth
m = 0.3. Assume that the transmitter is powered by a 12 Volt battery. The total power will be
m2
m2
PT = Pc + Pc
+ Pc
4
4
2
m
4(10)
40
P
= 444.44 Watts
where
= 10 Watts, i.e.
Pc = 2 =
c
2
4
m
(0.3)
Hence, total power PT = 444.44 + 10 + 10 = 464.44 Watts.
Hence, battery current (assuming ideal transmitter) = Power / Volts =
i.e. a large and heavy 12 Volt battery.
464.44 amps!
12
Suppose we could remove one sideband and the carrier, power transmitted would be
10 Watts, i.e. 0.833 amps from a 12 Volt battery, which is more reasonable for a
portable radio transmitter.
Single Sideband Amplitude Modulation
One method to produce signal sideband (SSB) amplitude modulation is to produce
DSBAM, and pass the DSBAM signal through a band pass filter, usually called a
single sideband filter, which passes one of the sidebands as illustrated in the diagram
below.
The type of SSB may be SSBAM (with a 'large' carrier component), SSBDimC or
SSBSC depending on VDC at the input. A sequence of spectral diagrams are shown
on the next page.
Single Sideband Amplitude Modulation
Single Sideband Amplitude Modulation
Note that the bandwidth of the SSB signal B Hz is half of the DSB signal bandwidth.
Note also that an ideal SSB filter response is shown. In practice the filter will not be
ideal as illustrated.
As shown, with practical filters some part of the rejected sideband (the LSB in this
case) will be present in the SSB signal. A method which eases the problem is to
produce SSBSC from DSBSC and then add the carrier to the SSB signal.
Single Sideband Amplitude Modulation
Single Sideband Amplitude Modulation
with m(t) = Vm cos mt, we may write:
vs (t)=V DC cos(ωct )+
Vm
V
cos((ωc +ω m )t)+ m cos((ωc − ωm )t)
2
2
The SSB filter removes the LSB (say) and the output is
vs (t)=V DC cos(ωc t )+
Again, note that the output may be
SSBAM, VDC large
SSBDimC, VDC small
SSBSC, VDC = 0
Vm
cos((ωc +ω m )t)
2
For SSBSC, output signal =
V
v s (t)= m cos((ωc +ω m )t)
2
Power in SSB
 m2 
From previous discussion, the total power in the DSB signal is PT = Pc  1+ 
2 

2
2
m
m
= PT = Pc + Pc
+ Pc
for DSBAM.
4
4
Hence, if Pc and m are known, the carrier power and power in one sideband may be
determined. Alternatively, since SSB signal =
vs (t )=V DC cos(ωc t )+
Vm
cos((ωc +ω m )t)
2
then the power in SSB signal (Normalised Average Power) is
2
2
2
VDC
Vm
V DC
 Vm 
+
=
+
 =
2
2
8
2 2
2
PSSB
VDC 2 Vm 2
+
Power in SSB signal =
2
8
Demodulation of Amplitude Modulated
Signals
There are 2 main methods of AM Demodulation:
• Envelope or non-coherent Detection/Demodulation.
• Synchronised or coherent Demodulation.
Envelope or Non-Coherent Detection
An envelope detector for AM is shown below:
This is obviously simple, low cost. But the AM input must be DSBAM with m << 1, i.e.
it does not demodulate DSBDimC, DSBSC or SSBxx.
Large Signal Operation
For large signal inputs, ( Volts) the diode is switched i.e. forward biased  ON, reverse
biased  OFF, and acts as a half wave rectifier. The 'RC' combination acts as a 'smoothing
circuit' and the output is m(t) plus 'distortion'.
If the modulation depth is > 1, the distortion below occurs
Small Signal Operation – Square Law
Detector
For small AM signals (~ millivolts) demodulation depends on the diode square law
characteristic.
The diode characteristic is of the form i(t) = av + bv2 + cv3 + ..., where
v = (VDC +m(t ))cos(ωct)
i.e. DSBAM signal.
Small Signal Operation – Square Law
Detector
i.e.
a(VDC +m(t ))cos(ωct )+b((VDC +m(t ))cos(ωct )) +...
2
(
= aV DC +am(t )cos(ωc t )+b VDC + 2VDC m(t )+m(t )
(
2
2
)cos (ω t )+...
2
c
)12
2
2
= aV DC +am(t )cos(ωct )+ bVDC + 2bV DC m(t )+bm(t )  +
= aVDC +am (t )cos(ωct )+
bVDC 2
2
1
cos(2ωc t )
2

2bVDC m(t ) bm(t )2
2
V
+
+
+b DC cos(2ωct )+...
2
2
2
'LPF' removes components.
2
Signal out = aVDC +
bVDC
+bVDC m(t ) i.e. the output contains m(t)
2
Synchronous or Coherent Demodulation
A synchronous demodulator is shown below
This is relatively more complex and more expensive. The Local Oscillator (LO) must be
synchronised or coherent, i.e. at the same frequency and in phase with the carrier in the
AM input signal. This additional requirement adds to the complexity and the cost.
However, the AM input may be any form of AM, i.e. DSBAM, DSBDimC, DSBSC or
SSBAM, SSBDimC, SSBSC. (Note – this is a 'universal' AM demodulator and the
process is similar to correlation – the LPF is similar to an integrator).
Synchronous or Coherent Demodulation
If the AM input contains a small or large component at the carrier frequency, the LO
may be derived from the AM input as shown below.
Synchronous (Coherent) Local Oscillator
If we assume zero path delay between the modulator and demodulator, then the ideal
LO signal is cos(ct). Note – in general the will be a path delay, say , and the LO
would then be cos(c(t – ), i.e. the LO is synchronous with the carrier implicit in the
received signal. Hence for an ideal system with zero path delay
Analysing this for a DSBAM input =
(VDC +m(t ))cos(ωct)
Synchronous (Coherent) Local Oscillator
VX = AM input x LO
=
(VDC +m(t ))cos2 (ωc t )
=
(VDC +m(t ))cos(ωct ) cos(ωct )
=
(VDC +m(t ))1 + 1 cos( 2ωc t )
2
2

V DC V DC
m(t ) m(t )
+
cos(2ωc t )+
+
cos( 2ω c t )
Vx =
2
2
2
2
We will now examine the signal spectra from 'modulator to Vx'
Synchronous (Coherent) Local Oscillator
Synchronous (Coherent) Local Oscillator
and
Note – the AM input has been 'split into two' – 'half' has moved or shifted up to
V
m(t )
 m(t )

2 fc
cos(2ωct )+VDC cos( 2ωct ) and half shifted down to baseband, DC and
 2
2
2

Synchronous (Coherent) Local Oscillator
The LPF with a cut-off frequency  fc will pass only the baseband signal i.e.
Vout =
VDC m(t)
+
2
2
In general the LO may have a frequency offset, , and/or a phase offset, , i.e.
The AM input is essentially either:
• DSB
• SSB
(DSBAM, DSBDimC, DSBSC)
(SSBAM, SSBDimC, SSBSC)
Double Sideband (DSB) AM Inputs
The equation for DSB is
(VDC +m(t ))cos(ωct ) where VDC allows full carrier (DSBAM),
diminished carrier or suppressed carrier to be set.
Hence, Vx = AM Input x LO
Since cosAcosB =
Vx
Vx = (VDC +m(t ))cos(ωct ).cos((ωc + Δω)t + Δφ)
1
cos( A+ B) + cos( A − B)
2
(
VDC +m(t ))
=
cos((ω +ω
2
c
c
+ Δω)t + Δφ) + cos((ωc + Δω)t + Δφ − ωct )
m(t )
V
V x =  DC +
cos((2ωc + Δω)t + Δφ) + cos( Δωt + Δφ)
2
2


VDC
V
cos((2ωc + Δω)t + Δφ) + DC cos( Δωt + Δφ)
2
2
m(t )
m(t )
+
cos((2ωc + Δω)t + Δφ) +
cos( Δωt + Δφ)
2
2
Vx =
Double Sideband (DSB) AM Inputs
The LPF with a cut-off frequency  fc Hz will remove the components at 2c (i.e.
components above c) and hence
Vout =
VDC
m(t )
cos( Δt )+ Δφ+
cos( Δωt + Δφ)
2
2
VDC m(t )
+
2
2
Consider now if  is equivalent to a few Hz offset from the ideal LO. We may then
say
V
m(t )
Vout = DC cos( Δωt )+
cos( Δωt )
2
2
Obviously, if
Δω = 0 and Δφ we have, as previously V out =
The output, if speech and processed by the human brain may be intelligible, but
would include a low frequency 'buzz' at , and the message amplitude would
fluctuate. The requirement  = 0 is necessary for DSBAM.
Double Sideband (DSB) AM Inputs
Consider now if  is equivalent to a few Hz offset from the ideal LO. We may then
say
V
m(t)
Vout = DC cos( Δωt )+
cos( Δωt )
2
2
The output, if speech and processed by the human brain may be intelligible, but would
include a low frequency 'buzz' at , and the message amplitude would fluctuate. The
requirement  = 0 is necessary for DSBAM.
Consider now that  = 0 but   0, i.e. the frequency is correct at c but there is a
phase offset. Now we have
Vout =
VDC
m(t )
cos( Δφ) +
cos( Δφ)
2
2
'cos()' causes fading (i.e. amplitude reduction) of the output.
Double Sideband (DSB) AM Inputs
The 'VDC' component is not important, but consider for m(t),
• if Δφ=
m(t )  π 
π
cos  = 0
(900), cos π  = 0 i.e. Vout =
2
2
 2
2
• if Δφ= π (180 ), cos(π )= −1
0
2
i.e. Vout =
m(t )
cos(π )= −m(t )
2
The phase inversion if  =  may not be a problem for speech or music, but it may be
a problem if this type of modulator is used to demodulate PRK
π
the signal strength
However, the major problem is that as  increases towards
2
π
output gets weaker (fades) and at
2
the output is zero
Double Sideband (DSB) AM Inputs
If the phase offset varies with time, then the signal fades in and out. The variation of
amplitude of the output, with phase offset  is illustrated below
Thus the requirement for  = 0 and  = 0 is a 'strong' requirement for DSB amplitude
modulation.
Single Sideband (SSB) AM Input
The equation for SSB with a carrier depending on VDC is
Vm
V DC cos(ωc t )+
cos(ωc +ω m t )
2
i.e. assuming m(t )=V m cos(ωmt )
V

Hence V x = VDC cos(ωc t )+ m cos(ωc +ω mt )cos((ωc +ω m )+ Δφ)
2


VDC
V
cos((2ωc + Δω)t + Δφ) + DC cos( Δωt + Δφ)
2
2
V
V
+ m cos((2ωc +ω m + Δω)t+ Δφ) + m cos((ωm − Δω)t − Δφ)
4
4
=
Single Sideband (SSB) AM Input
The LPF removes the 2c components and hence
VDC
V
cos( Δωt + Δφ) + m cos((ωm − Δω)t − Δφ)
2
4
Note, if  = 0 and  = 0,
V DC Vm
+
cos(ωmt ) ,i.e. m(t )=Vmcos(ωmt ) has been
2
4
recovered.
Consider first that   0, e.g. an offset of say 50Hz. Then
Vout =
VDC
V
cos( Δωt )+ m cos((ωm − Δω)t )
2
4
If m(t) is a signal at say 1kHz, the output contains a signal a 50Hz, depending on VDC
and the 1kHz signal is shifted to 1000Hz - 50Hz = 950Hz.
Single Sideband (SSB) AM Input
The spectrum for Vout with  offset is shown
Hence, the effect of the offset  is to shift the baseband output, up or down, by .
For speech, this shift is not serious (for example if we receive a 'whistle' at 1kHz and
the offset is 50Hz, you hear the whistle at 950Hz ( = +ve) which is not very
noticeable. Hence, small frequency offsets in SSB for speech may be tolerated.
Consider now that  = 0,  = 0, then
Vout
VDC
Vm
=
cos( Δφ) +
cos(ωm t − Δφ)
2
4
Single Sideband (SSB) AM Input
• This indicates a fading VDC and a phase shift in the
output. If the variation in  with time is relatively slow,
thus phase shift variation of the output is not serious for
speech.
• Hence, for SSB small frequency and phase variations in
the LO are tolerable. The requirement for a coherent LO
is not as a stringent as for DSB. For this reason, SSBSC
(suppressed carrier) is widely used since the receiver is
relatively more simple than for DSB and power and
bandwidth requirements are reduced.
Comments
•
In terms of 'evolution', early radio schemes and radio on long wave (LW) and
medium wave (MW) to this day use DSBAM with m < 1. The reason for this was the
reduced complexity and cost of 'millions' of receivers compared to the extra cost
and power requirements of a few large LW/MW transmitters for broadcast radio, i.e.
simple envelope detectors only are required.
•
Nowadays, with modern integrated circuits, the cost and complexity of synchronous
demodulators is much reduced especially compared to the additional features such
as synthesised LO, display, FM etc. available in modern receivers.
Amplitude Modulation forms the basis for:
•
•
•
•
•
Digital Modulation – Amplitude Shift Keying ASK
Digital Modulation – Phase Reversal Keying PRK
Multiplexing – Frequency Division Multiplexing FDM
Up conversion – Radio transmitters
Down conversion – Radio receivers
Phase Shift Method for SSB Generation
The diagram below shows the Phase Shift Method for generating SSBSC
fm and fc denote phase shifts at the message frequency (fm) and the carrier
frequency (fc).
Phase Shift Method for SSB Generation
Solving for Vout in general terms
i.e.
Vout =V a +Vb
Vout =V m cos(ωmt )cos(ωct )+Vm cos(ωmt +φ m )cos(ωct +φ c )
Since cosAcosB =
Vout =
1
cos( A+ B) + cos( A − B)
2
Vm
V
V
cos((ωc +ω m )t)+ m cos((ωc − ωm )t)+ m cos((ωc +ω m )t+φ c +φ m )
2
2
2
V
+ m cos((ωc − ωm )t+ (φc − φm ))
2
The actual form of the modulation at the output will depend on the phase shifts fm
and fc.
Phase Shift Method for SSB Generation
π
Consider Vout when φm =
2
Vout =
Since
φc =
π
(i.e.900)
2
Vm
V
V
cos((ωc +ω m )t)+ m cos((ωc − ωm )t)+ m cos((ωc +ω m )t+π )
2
2
2
V
+ m cos((ωc − ωm )t+ 0)
2
Vcos(θ +π )= −Vcosθ
then Vout
=V m cos((ωc −ωm )t), i.e. SSBSC/LSB.
When fm = 900 and fc = 900 the output is Single Sideband Suppressed Carrier –
Lower Sideband.
Phase Shift Method for SSB Generation
Consider Vout when φm =
Vout
π
π
, φc = −
2
2
Vm
Vm
Vm
cos((ωc +ω m )t)+
cos((ωc − ωm )t)+
=
cos((ωc +ω m )t+ 0)
2
2
2
Vm
+
cos((ωc − ωm )t − π )
2
and since
Vcos(θ − π )= −Vcosθ
then
Vout =Vmcos((ωc +ωm )t)
i.e. SSBSC/USB. When fm = 900 and fc = -900 the output is Single Sideband
Suppressed Carrier – Upper Sideband.
Note – for m(t) as a band of signals, the phase shift fm must be the same e.g. /2 or
900 at all frequencies.
Quadrature Modulation
A variation on the Phase Shift Method is shown below
In this form of the method, 2 different message signals m1(t) and m2(t) are input.
Quadrature Modulation
The carrier cos(ωct ) is phase shifted by 900 to give
sin(ωct )
The two carriers, cos(ωct ) and sin(ωct ) are in phase quadrature (orthogonal).
The process is described as
.
Quadrature Modulation or Quadrature Multiplexing
and as
Independent Sideband ISB.
Clearly,
Vout = m1 (t)cos(ωct )+m 2 (t)cos(ωct )
Quadrature Modulation
Each 'term' in the output is a DSBSC signal occupying the same bandwidth, but
phase shifted by 900 relative to each other
Quadrature Modulation
Demodulation will require synchronous demodulators as shown below.
Vin = m1 (t)cos(ωct )+m 2 (t)cos(ωct )
Quadrature Modulation
2
Clearly V x1 = m 1(t)cos (ωct )+m 2(t)cos(ω ct )sin(ω ct )
1
sin( A+ B) + sin( A − B)
2
m (t)
m (t)
(t) m (t)
Vx1 = m1 + 1 cos( 2ωc t )+ 2 sin( 2ωc t )+ 2 sin0
2
2
2
2
Since sinAcosB =
Since the LPF with cut-off frequency = fc, the output V1out =
Similarly,
V x2 = m1(t)cos(ωct )sin(ωc t )+m 2 (t)sin2 (ωc t )
Since sin 2 A=
Vx2 =
m1 (t)
2
1
(1− cos2A)
2
m1 (t)
m (t)
m (t) m (t)
sin(2ωc t )+ 2 sin0+ 2 − 2 cos(2ωc t )
2
2
2
2
Again, LPF removes the '2wc components, i.e. V2 out =
m2 (t )
2
Quadrature Modulation
This type of modulation/multiplexing is used in radio systems, television and as a
form of stereo multiplexing for AM radio.
Vestigial Sideband Modulation
Some signals, such as TV signals contain low frequencies, or even extend down to DC.
When DSB modulated we have
Vestigial Sideband Modulation
It is now impossible to produce SSB, because the SSB filter would need to be ideal,
as shown above. In practice the filter is as below
The signal produced is called vestigial sideband, it contains the USB and a 'vestige'
of the lower sideband. The BPF design is therefore less stringent. When demodulated
the baseband signal is the sum of the USB and the vestige of the LSB
Vestigial Sideband Modulation
Hence the original baseband signal. VSB is used in TV systems.
ANGLE MODULATION
• With Amplitude Modulation System, the amplitude of the
carrier signal was varied in some way with the message but
with angle modulation the amplitude of the signal would stay
constant but varying factor would either be the frequency or
the phase of the carrier.
• Angle modulation encompasses phase modulation (PM) and
frequency modulation (FM). The phase angle of a sinusoidal
carrier signal is varied according to the modulating signal.
• In angle modulation, the spectral components of the
modulated signal are not related in a simple fashion to the
spectrum of the modulating signal. Superposition does not
apply and the bandwidth of the modulated signal is usually
much greater than the modulating signal bandwidth.
z
ANGLE MODULATION
• A bandpass signal is represented by
sc(t) = A cosq(t)
where A is the amplitude and q(t) = ct + (t) = 2fct + (t)
• For angle modulation, we can write
sc(t) = A cos [2fct + (t)]
where A is a constant and (t) is a function of the modulating
signal. (t) is called the instantaneous phase deviation of sc(t).
• In a certain time period Δt, the argument increases from
2fct + (t) radians to 2fc(t+ Δt) + (t) radians. Means the
phase increases by 2fc Δt radians in Δt seconds. Thus over
the interval Δt, the phase changes at the rate of 2fc radians
per second.
• But when the frequency varies continuously with time then
we can define instantaneous angular frequency of sc(t) as
i(t) = dq(t)
dt
ANGLE MODULATION
In terms of frequency the instantaneous frequency of sc(t) is
fi(t) = 1 dq(t)
2 dt
In terms of frequency the instantaneous frequency of sc(t) is
fi(t) = 1 dq(t)
2 dt
fi(t) = fc + 1 d(t)
2 dt
1 d(t) is the instantaneous frequency deviation.
2 dt
The maximum frequency deviation is Δf =max 1 d(t)
=max[fi(t) - fc]
2 dt
ANGLE MODULATION
A phase modulator interprets the input as phase, the Phase
Modulator generates an output sinusoid whose phase varies
with the message signal, therefore for PM, the instantaneous
phase deviation is proportional to the modulating signal mp(t):
(t) = kpmp(t)
Where kp is constant representing the sensitivity in radians per
volt
sc(t) = A cos [2fct + kpmp(t)]
fi(t) = fc + 1 kpdmp(t)
2 dt
So the maximum phase deviation is
Δ = max[(t)]
Δ = kpmax[mp(t)]
Phase Modulation Index is bp = Δ
FREQUENCY MODULATION
A Frequency Modulator accepts the input as frequency. The
FM generates the output sinusoid whose instantaneous
frequency varies with the message signal. the instantaneous
frequency deviation is proportional to the modulating signal
mf(t)
d(t) = kfmf(t)
dt
Where kf is constant representing the sensitivity in Hertz per
volt
t
(t) = kf∫ mf() d  + (-)
-
(-) is usually set to 0. Thus, a frequency-modulated signal is
represented by
t
sc(t) = A cos [2fct + kf∫ mf() d 
-
FREQUENCY MODULATION
the instantaneous frequency of sc(t) can be written as
fi(t) = fc + 1 kfmf(t)
2
The frequency deviation from the carrier
frequency is
fd(t) = fi(t) – fc = 1 d(t) = 1 kfmf(t)
2 dt
2
And peak frequency deviation is
f = max 1 d(t)
2 dt
= 1 kf max[mf(t)]
2
FREQUENCY MODULATION
Modulating Signal, Instantaneous
frequency and FM signal
INTERELATIONSHIP
BETWEEN FM AND PM
F(t) in cases of phase and frequency modulation differ only by
a possible integration or differentiation of the modulating
signal. The relationship can then be developed between them as
mf(t) = kp dmp(t)
kf dt
Or
t
mp(t) = kf ∫ mf() d 
kp-
If we differentiate the modulating signal mp(t) and frequencymodulate using the differentiated signal, we get a PM signal.
On the other hand, if we integrate the modulating signal mf(t)
and phase-modulate using the integrated signal, we get a FM
signal. Therefore, we can generate a PM signal using a
frequency modulator or we can generate a FM signal using a
PM modulator.
INTERELATIONSHIP
BETWEEN FM AND PM
Kp/kf
Kf/kp
INTERELATIONSHIP
BETWEEN FM AND PM
Since frequency is the derivative of phase, region of sc(t) where
m(t) has positive slope demonstrate higher frequencies and
negative slope will demonstrate lower frequencies.
As a frequency modulator, original message m(t) is
differentiated to get the Phase Modulated Signal and is otherwise
for frequency modulated waveform.
SPECTRUM OF ANGLE
MODULATED SIGNAL
Since sc(t) = A cos [2fct + (t)]
= A Re{ej[2fct + (t)]}
= A Re{ej2fctej(t)}
Expanding ej(t) in the power series
= A Re{ej2fct[1+j(t)-2(t) - …+ jnn(t) + …]}
2!
n!
= A cos[2fct–(t)sin 2fct–2(t) cos 2fct+3(t)sin 2fct+…]
2!
3!
It can be seen that the spectrum of an angle-modulated signal consists
of an unmodulated carrier plus spectra of (t), 2(t), ..., and is not
related to the spectrum of the modulating signal in a simple fashion.
NARROWBAND ANGLE
MODULATION
If max | f(t)| << 1, we can neglect all higher-power terms of (t)
and we have a narrowband angle-modulated signal
sc(t)  A[cos 2fct - (t)sin 2fct]
For PM,
sc(t)  A[cos 2fct - kpmp(t)sin 2fct]
For FM,
t
sc(t) = A {cos 2fct - [kf∫ mf() d ]sin 2fct}
-
NARROWBAND ANGLE
MODULATION
Because of the difficulty of analyzing general angle-modulated
signals, we shall only consider a sinusoidal modulating signal.
Let the modulating signal of a narrowband FM signal be
mf(t) = amcos 2fmt
(t) = kf amsin 2fmt
2fm
= bfsin 2fmt
Where bf is the frequency modulation index and = kf am
2fm
References
• Shanmugam, “Analog Digital Communication,
Prentice Hall, 1989.
• Jerzy Dabrowsky, “CMOS RF Transceiver
Design”, 2004.
• A.W. Krings, “Data Communication Lecture”,
2002.