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COMS3100/7100Introduction toIntroduction to Communications
Lecture 15: Pulse Modulation
This lecture:
Pulse‐Amplitude Modulation
Pulse‐Time ModulationPulse‐Duration and Pulse‐Position Modulation
Ref: Carlson, Chapter 6.2‐6.3; Haykin, Chapter 3.3‐3.4
Pulse Modulation
2Pulse modulation (PM) offers two potential advantages over CW modulation
Th t itt d b t t d i t h t b tThe transmitted power can be concentrated into short bursts instead of being generated continuously. This enables the use of devices which operate better in pulse regime than in CW regime, mostly due to thermal reasons (e.g. semiconductor lasers, microwave active devices)
Time between pulses can be filled by sampled signal form otherTime between pulses can be filled by sampled signal form other sources – a scheme termed time‐division multiplexing.
Analogue PM has a disadvantage of requiring large bandwidth d t b d idthcompared to message bandwidth
Lecture 15COMS3100
Pulse Amplitude Modulation (PAM)
3If a message waveform is adequately described by periodic sample values, it can be transmitted using analogue pulse mod lation herein the sample al es mod late themodulation wherein the sample values modulate the amplitude of pulse train.Therefore, the amplitudes of regularly spaced pulses areTherefore, the amplitudes of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous message signal x(t).This technique is termed Pulse Amplitude Modulation
Lecture 15COMS3100
Generation of the PAM signal
4There are two operations involved in the generation of the PAM signal:
1. Instantaneous sampling of the message signal x(t) every Ts seconds, where the sampling rate fs = 1/Ts is chosen in
d h h l haccordance with the sampling theorem
2. Lengthening the duration of each sample so obtained to t t l ( l d h ld)some constant value τ (sample‐and‐hold)
)(tx)(ts
)(tx
τT
Lecture 15COMS3100
sT
Flat‐top Sampling and PAM
5Practical method for obtaining PAM (or implementing the steps 1. and 2. is the sample‐and‐hold (S/H) technique.
This method produces flat‐top pulses
sample‐and‐hold circuit
waveform obtainedf
Lecture 15COMS3100
Generation of PAM – holding network impulse response
6The finite width pulse obtained by the sample‐and‐holdcircuit can be interpreted mathematically using the following holding network.
Impulse response of holding network
)(tp
)(⎥⎦⎤
⎢⎣⎡ −
Π=ττ 2/)( ttp
)(tp
)( fP)](arg[ fP )](arg[ fP
Amplitude response of holding network
Phase response ofPhase response of holding network
ττ ffP sinc)( =
Lecture 15COMS3100
Flat‐top Sampling and PAM – sampled wave
7Periodic gating of the S/H circuit generates the sampled waveSampling pulse train, p(t)
Signal value at kTS
So far we have not yet specified th “ h ” f th (t) P(f)
Lecture 15COMS3100
the “shape” of the p(t) or P(f)
PAM
8Flat‐top sampling is equivalent to passing an ideal sampled wavethrough a network having transfer function P( f ) = [p(t)] Loss of high frequency content is called aperture effectLoss of high frequency content is called aperture effectThe larger the pulse duration or aperture τ, the larger the effectCan be corrected using equalizerNo equalization is needed if t/Ts<<1
Spectrum for ideal sampling when X( f ) = Π( f/2W )
WW−
aperture effect in flat‐top sampling ττ ffP sinc)( =
WW−⎥⎦⎤
⎢⎣⎡ −
Π=ττ 2/)( ttp
fj
Lecture 15COMS3100
)()()( fXfPfXp δ=fjeftpfP πτττ −== sinc)]([)( F
PAM
9
Lecture 15COMS3100
PAM
10There are many similarities between PAM and AM CW modulation
Modulation index
Spectral impulsesSpectral impulses
DC block
PAM spectrum extends from DC up through several harmonics of fsRequired transmission bandwidth can be estimated based on time‐domain considerations
Assuming small pulse duration compared to time between pulsesAssuming small pulse duration compared to time between pulses
Adequate pulse resolution then requires
Lecture 15COMS3100
Pulse‐Time Modulation
11The sample values of a message can also modulate the time parameters of a pulse train:
1. Pulse width – pulse‐duration modulation (PDM)
2. Pulse position – pulse‐position modulation (PPM)
The pulse width or pulse position varies in direct proportion to the sample values of x(t)p ( )
Lecture 15COMS3100
Pulse‐Duration and Pulse‐Position Modulation
12In both cases a time parameter of the pulse is being modulated
In both cases amplitude remains constant
Methods for producing PDM and PPM are similar
Lecture 15COMS3100
Generation of PDM and PPM
13When x(t) exceeds the sawtooth wave ‐ comparator output is a positive constant AOtherwise comparator output is zero
This is an example of PDM with trailing edgemodulation of the pulsemodulation of the pulse duration
For PPM signal, the PDM signal triggers a monostable pulse generator (triggers on p g ( ggtrailing edge and produces short pulse of fixed duration
Lecture 15COMS3100
Generation of PDM and PPM
14Sample values are nonuniformly spaced
This can be tolerated if tk- kTs<<Ts.For nearly uniform sampling the duration of the k‐th pulse in the PDM signal is
where the unmodulated duration τ0 represents x(kTs) = 00 p ( s)PPM pulses have fixed duration and amplitude ‐> there can be no potential missing pulses. k‐th pulse begins at time
where the unmodulated position kT +t represents x(kT ) = 0 andwhere the unmodulated position kTs+td represents x(kTs) = 0 and the constant t0 controls the displacement of the modulated pulse
Lecture 15COMS3100
Generation of PDM
15An approximation for the PDM can be formulated if we assume rectangular pulses centred at t = kTs and assuming tk varies slowly from pulse to pulseslowly from pulse to pulse
where
PDM signal contains the message signal plus a dc component and phase modulated signal at the harmonics of fss
Lecture 15COMS3100
PTM to PAM conversion
16Message can be reconstructed by first converting PDD/PPM to PAM.
Middle waveform is produced by a ramp generator that starts at time kT d t t tkTs and stops at tk
Demodulation requires received pulses with short risetime to preserve accurate message information
Lecture 15COMS3100
preserve accurate message information