Sum and Mixing of Frequencies
F1 x F2
eam=EcSin(Wct)+mEc/2Cos(Wc-Wm)t-mEc/2Cos(Wc+Wm)t
Carrier
fUSB = fc + fm
LSB
and
USB
fLSB = fc − fm
Sidebands and
the Frequency Domain
Figure 3-8: The relationship between the time and frequency domains.
Calculatiom of modulation index by envelope
m = Ea / Ec
Ea =
Emax − Emin
2
Ec = Emax - Ea
Ec
mEc/2
Fc-Fm
mEc/2
Fc
Fc+Fm
BW = fUSB−fLSB=2fm
Ec/2
mEc/4
mEc/4
-Fc-Fm
Ec/2
mEc/4
mEc/4
-Fc
-Fc+Fm
Two sided spectrum
Fc-Fm
Fc
Fc+Fm
Property of Active Device
Block Diagram of a Simple AM Transmitter
Power relations in AM
PT = (IT)2R
where IT is measured RF current and R is antenna impedance
PT=PC+PUSB+PLSB
Vrms 2 ( Ec / 2 ) 2 Ec2
Pc 


R
R
2R
mEc / 2 2 

2
Plsb  Pusb
R
2
m Ec

8 R
2
m 2 Pc
m 2 Pc
Pt 

 Pc
4
4
Pt
m2
 1
Pc
2
Plsb  Pusb
m 2 Pc

4
m2
Pt  [1 
]Pc
2
  Pt

m   2
 1 

  Pc
1
2
Power relations in AM in terms of current
PT = (IT)2R
Pt It R  It 
 2  
Pc IC R  IC 
2
2
PT=PC+PUSB+PLSB
Pc = (Ic)2R
2
But
1


2

m  2

It  IC 1 

2




m
 It 
 Ic   1  2
2
 It  2 
m  2    1
 Ic 

Pt
m2
 1
Pc
2

1
2

Transmission Efficiency
 m2
m2 
 4 PC  4 PC 
PLSB  PUSB 



PT
 m2 
1  2  PC


Useful Power /Total power
m2

2
2m
2
Percent efficiency
m

*100%
2
2m
Modulation by several sinewaves
Two modulating signals are given by
X1(t)=Em1CosWm1t
X2(t)=Em2CosWm2t
ec=Ec CosWct Carrier wave
eam=A CosWct
where A=Ec+X1(t)+X2(t)
eam= (Ec+Em1CosWm1t + Em2CosWm2t) CosWct
eam= Ec(1+Em1/Ec CosWm1t + Em2/ Ec CosWm2t) CosWct
eam= Ec(1+m1 CosWm1t + m2 CosWm2t) CosWct
eam= Ec CosWct+m1Ec/2 Cos(Wc+Wm1)t + m1Ec/2 Cos(Wc-Wm1)t+m2Ec/2
Cos(Wc+Wm2)t+m2Ec/2 Cos(Wc-Wm2)t
m2Ec/2
Fc-fm2
m1Ec/2
Fc-fm1
Ec
Fc
m1Ec/2
Fc+fm1
m2Ec/2
Fc+fm2
BW=2fm2
Total power in AM Wave=
Pt=PUSB1+PUSB2+PLSB1+PLSB2
m12 Pc
m2 2 Pc
m12 Pc
m2 2 Pc
Pt  Pc 



4
4
4
4
m12 m22
Pt  Pc1 

2
2

Modulation Index
mt  m1  m2
2
2
2
mt   m1  m2
2
2

1
2
Power relations in AM
PT = (IT)2R
where IT is measured RF current and R is antenna impedance
PT=PC+PUSB+PLSB
Vrms 2 ( Ec / 2 ) 2 Ec2
Pc 


R
R
2R
mEc / 2 2 

2
Plsb  Pusb
R
2
m Ec

8 R
2
m 2 Pc
m 2 Pc
Pt 

 Pc
4
4
Pt
m2
 1
Pc
2
Plsb  Pusb
m 2 Pc

4
m2
Pt  [1 
]Pc
2
  Pt

m   2
 1 

  Pc
1
2
Power relations in AM in terms of current
PT = (IT)2R
Pt It R  It 
 2  
Pc IC R  IC 
2
2
PT=PC+PUSB+PLSB
Pc = (Ic)2R
2
But
1


2

m  2

It  IC 1 

2




m
 It 
 Ic   1  2
2
 It  2 
m  2    1
 Ic 

Pt
m2
 1
Pc
2

1
2

Transmission Efficiency
 m2
m2 
 4 PC  4 PC 
PLSB  PUSB 



PT
 m2 
1  2  PC


Useful Power /Total power
m2

2
2m
2
Percent efficiency
m

*100%
2
2m
Modulation by several sinewaves
Two modulating signals are given by
X1(t)=Em1CosWm1t
X2(t)=Em2CosWm2t
ec=Ec CosWct Carrier wave
eam=A CosWct
where A=Ec+X1(t)+X2(t)
eam= (Ec+Em1CosWm1t + Em2CosWm2t) CosWct
eam= Ec(1+Em1/Ec CosWm1t + Em2/ Ec CosWm2t) CosWct
eam= Ec(1+m1 CosWm1t + m2 CosWm2t) CosWct
eam= Ec CosWct+m1Ec/2 Cos(Wc+Wm1)t + m1Ec/2 Cos(Wc-Wm1)t+m2Ec/2
Cos(Wc+Wm2)t+m2Ec/2 Cos(Wc-Wm2)t
m2Ec/2
Fc-fm2
m1Ec/2
Fc-fm1
Ec
Fc
m1Ec/2
Fc+fm1
m2Ec/2
Fc+fm2
BW=2fm2
Total power in AM Wave=
Pt=PUSB1+PUSB2+PLSB1+PLSB2
m12 Pc
m2 2 Pc
m12 Pc
m2 2 Pc
Pt  Pc 



4
4
4
4
m12 m22
Pt  Pc1 

2
2

Modulation Index
mt  m1  m2
2
2
2
mt   m1  m2
2
2

1
2
Amplitude Modulators
• There are two types of amplitude modulators. They are low-level and
high-level modulators.
• Low-level modulators generate AM with small signals and must be
amplified before transmission.
• High-level modulators produce AM at high power levels, usually in the
final amplifier stage of a transmitter.
• Modulators are class C amplifiers and at output tank circuit.
Low level AM Transmitter
540KHz to 1640KHz
540KHz to 1640KHz
modula
tor
Amplifier Classes
Class A - bias point is set so that the amplifier conducts through a complete
cycle (360 deg) of the input waveform. This class has low efficiency (~35%) but
high linearity.
Class AB - bias point is set so that the amplifier conducts through at least 180
deg but less than 360deg of the input waveform. This class has better
efficiency (~55%) but lower linearity.
Class B - bias point is set so that the amplifier conducts through a half cycle
(180 deg) of the input waveform. This class has higher efficiency (~60%),but
poor linearity.
Class C - bias point is set so that the amplifier conducts through less than 180
deg of the input waveform. This class has higher efficiency (~70%), but even
poorer linearity
Use of Tank circuit
Low level Class C Grid Modulator
High level Plate Modulator
Low level Transistor Modulator
Low level and High level AM Transmitter
540KHz to 1640KHz
modulat
or
Advantages of DSBFC =
1.Transmitters are less complex
2.Receivers are simple, detection is easy.
3.Cost efficient.
Disadvantages =
1.Power wastage - carrier doesn’t carry any information and USB & LSB
contains same information.
m2
Pwastage  Pc 
Pc
4
2. Needs larger Bandwidth
3. Gets affected by noise.
Types of AM=
180 phase shift
1. DSBFC
2. DSBSC
3. SSB
4. ISB
5. VSB
Modulatin
g signal
Balanced Modulator
carrier
DSBSC
DSB-SC Generation Methods
1.
2.
3.
Ring Balanced Modulator
Lattice Balanced Modulator
Push pull Balanced modulator
eam=mEc/2Cos(Wc-Wm)t-mEc/2Cos(Wc+Wm)t
180 phase shift
Ec
mEc/2
Fc-Fm
BW=2fm
mEc/2
Fc
Fc+Fm
Balanced Modulator
1.Ring modulator
2.Lattice-type
balanced
modulator.
Lattice Modulator
+
-
-
+
Push Pull Balanced Modulator
Drain Current
inet = aem
Modulating
signal
+
2becem
Two side bands
AM Waveforms
SSB Generation Methods
1.
2.
3.
Filter Method
Phase shift method
Third method (Weaver method)
mEc/2
Fc-Fm
mEc/2
Fc
mEc/2
Fc+Fm
Fc-Fm
BW=fm
mEc/2
Fc
Fc+Fm
SSB Circuits
Figure 4-31 An SSB transmitter using the filter method.
This technique can be used at relatively low carrier frequencies.
At high frequencies, the Q of the filter becomes unacceptably
high. The required Q necessary to filter off one of the sidebands
can be approximated by:
SSB Circuits
Figure 4-33 An SSB generator using the phasing method.
SSB phase shift
Important points=
1.
Sharp cutoff Filters are not required
2.
Freq Up conversion is not required
3.
Easy to switch between sidebands. Simply change the
oscillator position.
4.
Designing a phase shift network for AF range is dificult.
Weaver Method or Third method
LSB
Independent side band transmitter
10MHz to 30MHz
VESTIGIAL SIDEBAND MODULATION
• VSB is used in TV transmission to transmit Video signal.
• In VSB full USB is transmitted with some part of LSB.
• As filter response is not sharp at the edges it may attenuate
part of transmitted sideband if only SSB is used to transmit.
• Part of the LSB is called as Vestige.
• BW required is less than the DSBFC and DSBSC.
• No of channels can be increased.
VSB AM Technique-
Picture career
USB
LSB
0
0.5
Sound career
1.25
MHz
5 MHz
5.75MHz
AM Receivers
1.
Tuned Radio Frequency (TRF)
2.
Superheterodyne Receiver
+
+
fo - fs = fIF
Receiver Characteristics
Sensitivity- it must provide amplification to recover
the original modulating signal from a very weak
received signal.
Sensitivity refers to the weakest signal that can be
received and still produce an acceptable out.
Sensitivity can be specified as a minimum voltage
(microV) or as a power level (dBm).
Gain of RF and IF amp. decides sensitivity.
Selectivity =it must be able to select
the desired signal from the
thousands of other signals in the
spectrum.
It is the ability to select the desired
signal and reject all other.
Fidelity= Is A Measure Of The Ability Of A Communications System To
Produce At The Output Of The Receiver, An Exact Replica Of The Original
Source Information
540KHz to 1640KHz
Ganged
tuning
Problems of Tuned Radio Frequency (TRF) Receiver
1.
Instability- Overall gain of RF amplifiers is very very high so
a very small f/b from o/p to i/p with correct phase can
initiate oscillations . Due to stray capacitance at high freq.
2.
Variation in BW- For 535KHz – 1640KHz Range BW=10KHz
for fc=535 Q=fr/BW=535/10=53.5
for fc=1640 Q=164
But max value of Q is 120 so BW=fr/Q=1640/120=13.7K
So receiver picks adjacent channels.
3. Insufficient Selectivity- Due to variable BW selectivity of TRF
receiver is poor.
Superheterodyne Receivers
•
Superheterodyne receivers convert all incoming signals to a lower
frequency, known as the intermediate frequency (IF), at which a single
set of amplifiers is used to provide a fixed level of sensitivity and
selectivity.
•
Gain and selectivity are obtained in the IF amplifiers.
•
The key circuit is the mixer, which acts like a simple amplitude modulator
to produce sum and difference frequencies.
•
The incoming signal is mixed with a local oscillator signal.