Title: Chapter 3 Analog Signal Transmission and Reception
1Chapter 3Analog Signal Transmission and Reception
2CONTENTS
- Introduction to Modulations
- Amplitude Modulation
- Angle Modulation
- Radio and Television Broadcasting
- Mobile Radio Systems
33.1 INTRODUCTION TO MODULATION
- Denote m(t) as the analog signal to be
transmitted. - The signal m(t) is assumed to be a lowpass signal
of bandwidth W and is a power-type signal with - The message signal m(t) is transmitted through
the communication channel by putting it on a
carrier signal of the form
carrier amplitude
carrier amplitude
carrier phase
4- The signal m(t) modulates the carrier signal c(t)
in three forms - Amplitude Modulation (AM)
- Frequency Modulation (FM)
- Phase Modulation (PM)
- Objectives of modulation
- Translate the low pass signal m(t) to bandpass
signal to match the passband characteristics of
the channel. - Accommodate for simultaneous transmission -
frequency-division multiplexing (FDM). - Increase the noise immunity in transmission by
expanding the bandwidth of the transmitted
signal.
53.2 AMPLITUDE MODULATION (AM)
- The message signal m(t) is impressed on the
amplitude of the carrier signal c(t). - Types of amplitude modulation
- Double-sideband, suppressed carruer AM (DSB-SC
AM) - Conventional double-sideband AM
- Single-sideband AM (SSB AM)
- Vestigial-sideband AM (VSB AM)
63.2.1 Double-Sideband Suppressed Carrier AM
- A double-sideband, suppressed carrier (DSB-SC) AM
signal is obtained by multiplying the message
signal m(t) with the carrier signal c(t). - Amplitude modulated signal
- The spectrum of the modulated signal can be
obtained by taking the Fourier transform of u(t).
7upper sideband
upper sideband
lower sideband
8(No Transcript)
9- The magnitude of the spectrum of the message
signal m(t) has been translated or shifted in
frequency by an amount - The phase of the message signal has been
translated in frequency and offset by the carrier
phase - The bandwidth of the AM signal is 2W, where W is
the bandwidth of m(t). - The upper sideband of U(f) contains all the
frequency contain of the message signal M(f). - u(t) does not contain carrier components - u(t)
is called a suppressed-carrier signal (DSB-SC AM
signal)
10- To compute power content of DSB-SC signal, we
first evaluate the time-average autocorrelation
function of the signal u(t) - We may show that the following equation equals to
zero.
Parsevals relation
No frequency overlap
11- Finally, we have
- Taking Fourier transform of both sides
- The power spectral density of the DSB-SC signal
is the power spectral density of the message
shifted upward and downward by and scaled
by - The power of the modulated signal
-
- where is the power of the
message signal
12Demodulation of DSB-SC AM Signal
- In the absence of noise, and with the assumption
of an ideal channel, the received signal can be
expressed as - Demodulation of DSB-SC AM signal
- Multiply r(t) by a locally generated sinusoid
- Pass the product signal through an ideal lowpass
filter having a bandwidth W. - Multiplication
13- The lowpass filter rejects the high frequency
components and pass only the low frequency
component. Hence, the output of the filter is - Note that m(t) is multiplied by
. Thus the desired signal is scaled by a factor
that depends on the phase difference between the
pahse of the carrier and the phase of
the locally generated sinusoid. - If the amplitude of the
desired signal is reduced by - If the desired signal
component vanishes. - For perfect demodulation, (Phase
coherent)
14Pilot Tone for Carrier Recovery in DSB AM
- Addition a pilot tone to a DSB AM signal-
additional power requirement - Carrier recovery by a narrow band filter
153.2.2 Conventional Amplitude Modulation
- A conventional AM signal consists of a large
carrier component in addition to the double
sideband AM modulated signal. The transmitted
signal can be expressed as - Advantage easy to demodulate
16(No Transcript)
17- It is convenient to express m(t) as
- where is normalized such that
- The above equation can be done by using
- The scale factor a is called the modulation
index. The modulated signal can be expressed as
18Overmodulated (a gt 1)
19- The spectrum of the amplitude modulated signal
u(t) is - The spectrum of a conventional AM signal occupies
bandwidth twice the bandwidth of the message
signal.
20(No Transcript)
21- Example Suppose that the modulating signal
is a sinusoid of the form - Determine the DSB AM signal, its upper and
lower sidebands, and its spectrum, assuming a
modulation index of a. - Solution The DSB AM signal
22- The spectrum of the DSB AM signal
23- We have already proved in the DSB-SC case, the
power in the modulated signal is - For the conventional AM
- Finally, we have
contains no DC component
Message power
Carrier power
24- Advantage of conventional AM signal easy to be
demodulated - Envelope detector
25- Output of the envelope detector
263.2.3 Single-Sideband AM
- DSB-SC AM signal requires a channel bandwidth
- of
- The transmission of either sideband is sufficient
to reconstruct the message signal m(t) at the
receiver. - We may reduce the transmitted bandwidth to W Hz
by transmitting only the upper sideband or the
lower sideband. - A single sideband AM signal can be represented
mathematically as - Hilbert transform of m(t).
27- Generation of a single-sideband AM signal by
Hilbert transform
28- Generation of a single-sideband AM signal by
bandpass filter
29(No Transcript)
30- Let m(t) be a signal with Fourier transform M(f).
- An upper sideband AM signal is obtained by
eliminating the lower sideband of a DSB AM
signal. - We may pass the DSB AM signal through a highpass
filter whose transfer function is given by - Obviously H(f) can be written as
31(No Transcript)
32- The spectrum of the USSB AM signal is given by
- Taking the inverse Fourier transform of both
sides, we obtain
33(No Transcript)
34- For lower sideband (LSSB) AM signal, notice
- We have
- Finally, we have proved
USSB AM
LSSB AM
35- To recover the message signal from SSB AM signal,
we require a phase coherent or synchronous
demodulator. - First multiply the received signal with the local
generated carrier , we have
- By passing the above signal through an ideal
lowpass filter, we have the output - For perfect demodulation, we must have .
desired signal
interference
363.2.4 Vestigial-Sideband AM
- Relaxing the SSB AM by allowing a part called
vestige to appear at the output of the modulator.
The resulting signal is called vestigial-sideband
(VSB) AM. - Generation of VSB AM
- generate a DSB-SC AM signal
- pass the DSB-SC AM signal through a sideband
filter with frequency response H(f)
37- In the time-domain the VSB signal may be
expressed as - impulse response of the VSB
filter - In frequency domain
- Consider the demodulation of the VSB signal
38- We have the product signal
- The lowpass filter rejects the double-frequency
terms and pass only the components in the
frequency range - The signal spectrum at the output of the lowpass
filter is - Undistirtion requirement
39(No Transcript)
403.2.5 Implementation of AM Modulator and
Demodulator
- Power-Law Modulation
- Nonliear device
- voltage-current characteristic of P-N diode
- input is the sum of the message signal and the
carrier - Let be the input signal. The output of
the nonlinear device can be expressed as
41- Power-Law AM modulator
- Suppose that the nonlinear device is approximated
by a second order polynomial.
42- Input to the nonlinear device
- Output of the nonlinear device
- The band pass filter with bandwidth 2W centered
at yields - where by design
43 44- Assume that
- Let
- The diode will turn on if and will
turn off if - The output across the load resistor is
- Since s(t) is a periodic rectangular function,
the Fourier series is
45- Hence
- Passing through a bandpass filter, we
have
46- Balanced Modulator for DSB-SC AM signal
47- Ring modulator for DSB-SC AM
- If c(t) gt 0, 1, 4 on, and 2, 3 off,
- If c(t) lt 0, 1,4 off, and 2,3 on,
1
2
3
4
C(t)
48- Therefore, we have
- Since c(t) is a periodic function, the Fourier
series can be expressed as - The desired DSB-SC AM signal is obtained by
passing through a bandpass filter with center
frequency and bandwidth 2W.
49- Demodulation of DSB-SC AM Signals
50- Demodulation of SSB Signals with pilot tone
513.2.6 Signal Multiplexing
- Multiplexing The process of combining a number
of separate message signals into a composite
signal for transmission over a common channel. - All message signals can be recovered at the
receivers. - Three common methods
- Time-division multiplexing (TDM)
- Frequency-division multiplexing (FDM)
- Code-division multiplexing (CDM)
52 53- Quadrature-Carrier Multiplexing
- Two message signal and .
- Transmit two message signals on the same carrier
frequency - Two signals are modulated into u(t) by
- The two message signals are demodulated by
-
54(No Transcript)
553.3 ANGLE MODULATION
- Angle modulation
- Frequency modulation (FM) Frequency is changed
by the message signal. - Phase modulation (PM) Phase is changed by the
message signal. - High degree of noise immunity by bandwidth
expansion. - They are widely used in high-fidelity music
broadcasting.
563.3.1 Presentation of FM and PM Signal
- An angle-modulated signal
- the phase of the signal.
- Instantaneous frequency is given by
- Since u(t) is a bandpass signal, it can be
represented as
57- If m(t) is the message signal, then in a PM
system we have - In an FM system
- From the above relationships we have
- On the other hand
phase deviation constant
frequency deviation constant
58(No Transcript)
59(No Transcript)
60- The maximum phase deviation in a PM system
- The maximum frequency-deviation in an FM system
61- The message signal
is used to either FM or PM for the carrier
. Find the modulated signal in
each case. - Solution
- we have
- Modulation index for a general m(t)
PM
FM
Modulation index
62- Narrowband Angle Modulation If for all , we
have - then we can use the approximation
- The modulation is very similar to conventional AM
63(No Transcript)
643.3.2 Spectral Characteristics of Angle-Modulated
Signals
- Assume that the message is a sinusoidal signal
- The signal is periodic with
period . The same is also true
for the complex exponential signal - Fourier series representation
Bessel function of the first kind of
order n
65- Therefore, we have
- Finally we obtain
- The actual bandwidth of the modulated signal is
infinite. However, the amplitude of the
sinusoidal components of frequencies
for large n is very small. - Property
66(No Transcript)
67- Example
- Find the expression for the modulated signal
and determine how many harmonics should be
selected to contain 99 of the modulated signal
power. - Solution The total power
- The modulated signal
68- The modulation index is given by
- Therefore
- We have to choose k large enough such that
- The solution k6.
69(No Transcript)
70- In general the effective bandwidth of an
anglr-modulated signal, which contains at least
98 of the signal power, is given by - Let the message signal be given by
- The bandwidth of the modulated signal is given by
- FM occupies less bandwidth then PM .
- Carsons rule For general message signal, the
bandwidth of the angle-modulated signal is given
by
71(No Transcript)
723.3.3 Implementation of Angle Modulators and
Demodulators
- Design an oscillator whose frequency changes with
the input voltage. - Voltage-controlled oscillator
- Varactor diode - capacitance changed with the
applied voltage. - A inductor with the varactor diode is used
in the oscillator circuit.
73- Let the capacitance of the varactor diode is
given by - When m(t) 0, the frequency of the tuned circuit
is given by - In general for nonzero m(t), we have
- Assuming that
- We have
74- Indirect method for generation of FM and PM
signals - generate a narrow a narrow band angle-modulated
signal - change the narrow band signal to wideband signal
75- Generate wideband angle-modulated signals from
narrow band angle-modulated signals - frequency multiplier
- implemented by nonlinear device and bandpass
filters - Using down converter
76- FM demodulation
- generate an AM signal
- use AM demodulator to recover the message signal
- Pass the FM signal through an filter with
response - If the input to the system is
- the output
- The above signal is an AM signal.
77- Balanced discriminator
- use two tuned circuits
- connect in series to form a linear frequency
response region.
78- FM demodulator with feedback
79- FM demodulator with phase-locked loop (PLL)
- Input
- VCO output
- Phase Comparator
80- Linearized model of the PLL
- or
-
81- By taking the Fourier transform
- Suppose that we design G(f) such that
-
v(t) is the demodulated signal
823.4 RADIO AND TELEVISION BROADCASTING
- AM Radio
- FM Radio
- Television
833.4.1 AM Radio Broadcasting
- AM Radio Broadcasting
- 535-1605 kHz
- 10kHz spacing
- bandwidth of m(t) is 5kHz.
- Superheterodyne receiver with intermediate
frequency - two frequency components and
are produced after the mixer
84- Rejection of the radio signal at the image
frequency - Assume there are two received signal
- The mixer output consists of the two signals
- The RF amplifier bandwidth is designed to be
sufficiently narrow so that the image frequency
signal is rejected - The IF amplifier has bandwidth of 10kHz to reject
signal from adjacent channels.
Desired signal
Interference from image channel
853.4.2 FM Radio Broadcasting
- FM Radio Broadcasting
- 88 - 108 MHz
- 100kHz spacing
- peak-frequency deviation 75kHz
- Superheterodyne receiver with intermediate
frequency
86(No Transcript)
87FM Stereo Transmitter
88FM Stereo Receiver
893.4.3 Television Broadcasting
- 1936 BBC black-and-white picture transmission
- Black-and-white TV Signal.
- The two dimensional image is converted to a
one-dimensional electrical signal by sequentially
scanning the image. - The scanning of the electron beam in the CRT is
controlled by two voltage applied across the
horizontal and vertical deflection plates. - In commercial TV broadcasting, the bandwidth of
the video signal is is limited to W 4.2Mhz. - VSB modulation is employed, the total
transmission bandwidth is around 6Mhz.
90(No Transcript)
91Interlaced pattern with rate 1/60 sec
92A typical video signal
93(No Transcript)
94(No Transcript)
95(No Transcript)
963.5 Mobile Radio Systems