Signals and Systems
Fall 2003
Lecture #15
28 October 2003
1,Complex Exponential Amplitude Modulation
2,Sinusoidal AM
3,Demodulation of Sinusoidal AM
4,Single-Sideband (SSB) AM
5,Frequency-Division Multiplexing
6,Superheterodyne Receivers
The Concept of Modulation
Why?
More efficient to transmit E&M signals at higher frequencies
Transmitting multiple signals through the same medium using
different carriers
Transmitting through,channels” with limited passbands
Others.
Many methods
Focus here for the most part on Amplitude Modulation (AM)
How?
Transmitted Signal
x(t)
Carrier Signal
Amplitude Modulation (AM) of a
Complex Exponential Carrier
Demodulation of Complex Exponential AM
Corresponds to two separate modulation channels (quadratures)
with carriers 90
o
out of phase
Sinusoidal AM
Drawn assuming
ω
c
> ω
M
Synchronous Demodulation of Sinusoidal AM
Suppose θ = 0 for now,
Local oscillator is in
phase with the carrier,
Synchronous Demodulation in the Time Domain
Two special cases:
1) θ = π/2,the local oscillator is 90
o
out of phase with the carrier,
r(t) = 0,signal unrecoverable.
Now suppose there is a phase difference,i.e,θ ≠ 0,then
2) θ = θ(t) — slowly varying with time,? r(t)? cos[θ(t)]? x(t),
time-varying,gain”.
Synchronous Demodulation (with phase error) in the
Frequency Domain
Again,the low-frequency signal (ω < ω
M
) = 0 when θ = π/2.
Demodulating signal –
has phase difference θ w.r.t.
the modulating signal
Alternative,Asynchronous Demodulation
Assume ω
c
>> ω
M
,so signal envelope looks like x(t)
Add same carrier with amplitude A to signal
A = 0? DSB/SC (Double Side Band,Suppressed Carrier)
A > 0? DSB/WC (Double Side Band,With Carrier)
Time Domain
Frequency Domain
Asynchronous Demodulation (continued)
Envelope Detector
Disadvantages of asynchronous demodulation:
— Requires extra transmitting power [Acosω
c
t]
2
to make sure
A + x(t) > 0? Maximum power efficiency = 1/3 (P8.27)
In order for it to function properly,the envelope function must be positive
for all time,i.e,A + x(t) > 0 for all t.
Demo,Envelope detection for asynchronous demodulation.
Advantages of asynchronous demodulation:
— Simpler in design and implementation.
Double-Sideband (DSB) and Single-Sideband (SSB) AM
Since x(t) and y(t) are
real,from conjugate
symmetry both LSB
and USB signals carry
exactly the same
information.
DSB,occupies
2ω
M
bandwidth
in ω > 0.
Each sideband
approach only
occupies ω
M
bandwidth in
ω > 0.
USB
LSB
Single Sideband Modulation
Can also get SSB/SC
or SSB/WC
Frequency-Division Multiplexing (FDM)
(Examples,Radio-station signals and analog cell phones)
air
All the channels
can share the same
medium.
FDM in the Frequency-Domain
“Baseband”
signals
Channel a
Channel b
Channel c
Multiplexed
signals
Demultiplexing and Demodulation
Channels must not overlap? Bandwidth Allocation
It is difficult (and expensive) to design a highly selective
bandpass filter with a tunable center frequency
Solution – Superheterodyne Receivers
ω
a
needs to be tunable
The Superheterodyne Receiver
Operation principle:
— Down convert from ω
c
to ω
IF
,and use a coarse tunable BPF for the front end.
— Use a sharp-cutoff fixed BPF at ω
IF
to get rid of other signals.
AM,
ω
c
2π
= 535?1605 kHz — RF
FCC,
ω
IF
2π
= 455 kHz — IF