This document discusses amplitude modulation (AM) and its various types. It describes the mathematical equations for double-sideband AM modulation and demodulation. It explains that AM is wasteful of transmitted power and channel bandwidth, but has simpler and less expensive modulators and demodulators compared to other modulation techniques.

1. EECE 309
Communication Theory
Amplitude Modulation

2. 2
Amplitude Modulation Types
 Double-sideband (DSB) modulation
 Double-sideband with carrier (DSB-WC) / AM
 Double-sideband suppressed-carrier (DSB-SC)
 Double-sideband reduced carrier (DSB-RC)
 Single-sideband (SSB) modulation
 SSB with carrier (SSB-WC)
 SSB suppressed carrier (SSB-SC)
 Vestigial sideband (VSB) modulation
 Quadrature amplitude modulation (QAM)

3. 3
DSB-WC / AM (1)
  tfAtAtc cccc  2coscos 
       ttmtAttmAt cccccAM  coscoscos 
 tm
The Carrier Signal:
The baseband message (modulating) signal:
The AM signal:
, fc = Carrier frequency (Hz)
         tctmkttmkAt
A
tm
A acacc
c
c 





 1cos1cos1 
(Carrier) (Modulated carrier)
 Thus, we transmit an unmodulated carrier in addition to the modulated carrier
 Ka = 1/Ac: Amplitude sensitivity of the modulator

4. 4
AM (2): Frequency Domain
 The baseband message (modulating) signal:
           cccc
c
AM ffMffMffff
A
f 
2
1
2

 Amplitude spectrum of AM signal:
           cccccAM wwMwwMwwwwAw 
2
1
Or,
- 2πB 0 2πB
USBLSB
 Bandwidth of AM signal: BAM = 2B, Hz
 BW of message signal= B Hz
USBLSBLSBUSB
Carrier
Carrier
ωc -2πB ωc ωc +2πB-(ωc +2πB) -ωc -(ωc -2πB)

5. 5
Time Domain of AM (3)
 Thus, the carrier component oscillates between the envelope |Ac + m(t)| and its
negative image –|Ac + m(t)|
 Envelope of the modulated carrier: e(t) = [Ac + m(t)]
 The envelope is an accurate representation of the message, provided -
a. fc >> B, B is the message bandwidth
b. Ac + m(t) > = 0, for all t
 Condition a relates to the overlap of the frequency spectrum components
 Condition b ensures that the message can be recovered from the envelope
Envelope detection
can be used
Envelope detection
can’t be used

6. 6
AM (4): Modulation Index, μ
Case I: m(t) with zero offset
(i.e., m(t)|max = - m(t)|min = mp):
Ac – mp ≥ 0
 μ < 1: Undermodulation
 μ = 1: 100% modulation
 μ > 1: Overmodulation => Envelope detection creates distortion
An example of over modulation
=> 0 < μ ≤ 1
For envelope detection:
c
p
A
m

Case II: m(t) with non-zero offset (rare
case) (i.e., m(t)|max ≠ - m(t)|min):
   
    minmax
minmax
||2
||
tmtmA
tmtm
c 


minmax
minmax





Modulation Index:
φmax = Maximum of φAM(t)
φmin = Minimum of φAM(t)

7. 7
AM (5): Example
Example for Single Tone Modulation
  tAtm mm cos
    ttAt cmcAM  coscos1
Let,
Then,
50% modulation 100% modulation
 Amplitude spectrum: Try yourself

8. 8
AM (6): Sideband and Carrier Power
      tt
A
tAt mcmc
c
ccAM 

  coscos
2
cos
Carrier Power:
2
2
c
C
A
P 
USB power:
8
22
c
USB
A
P 
8
22
c
LSB
A
P LSB power: Total sideband power:
4
22
c
S
A
P 
    ttmtAt cccAM  coscos Transmitted signal:
Sideband power:
 Power efficiency:
Special Case: Single Tone Modulation
Then
 Under the best condition (μ=1):
This ratio increases monotonically from 0 to 1/3 as μ increases from 0 to 1
Thus, for tone modulation, under the best conditions, only one-third of the power is used for
carrying message, which is even lower (less than 25% or worse) under practical conditions

9. 9
Demodulation of AM Signals
Envelope Detector:
 For proper operation, the discharge time constant RC
must be chosen properly
 Difference between the rectifier detector and the envelope detector? (Think first and consult with the text books)
(for μ ≤ 1)

10. 10
Demodulation of AM Signals
Synchronous/ Coherent / Homodyne Detector:
tccos
 tAM
 td
      
   
     ttmAtm
A
ttmA
ttmAtttp
cc
c
cc
cccAM



2cos
2
1
2
1
2
2cos1
2
1
coscos 2



After LPF and DC blocking:
   tmCtd 
LPF &
DC blocking
 tp
 Phase and frequency of the local carrier have to be same as those of the carrier:
Synchronization required between transmitter and receiver
 More complex and expensive than an envelop detector
 Rectifier detector is effectively a coherent detector
(no restriction on μ)
C: constant

11. 11
AM: Summary
 Wasteful of transmitted power: power efficiency
very low
 Wasteful of channel bandwidth: twice of the
message bandwidth
 Easy to be affected by noise
 Simpler modulator and demodulator
 Less expensive modulator and demodulator