ece 4710: lecture #19 1 bandpass review modulated bandpass signal where g (t) is complex envelope...

ECE 4710: Lecture #19 1

Bandpass Review

Modulated bandpass signal where g (t) is complex envelope of baseband signal

Desired modulated signal, s (t), obtained by:

1) Selection of appropriate modulation mapping function

g [m(t)] and

2) Multiplying g (t) by sinusoidal carrier with frequency fc

Modulating baseband signal m(t) can be analog or digital signal

tfj cetgts 2)(Re)(


Bandpass Review

Spectrum of bandpass signal is

Frequency translated version of baseband spectrum

PSD of bandpass signal is

Chapter 5 goals: Study g(t) and s(t) for various types of analog & digital modulation

methods» AM, DSB-SC, FM, OOK, BPSK, FSK, QPSK, MPSK, QAM

Evaluate spectrums and examine basic Tx and Rx structures

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ffGffGtsfS cc

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cgcgvffPffPfP


Amplitude Modulation

Complex AM envelope given by Ac is for the carrier power level m(t) is modulating source signal analog or digital

» For AM m(t) is normally considered to be analog audio signal

Bandpass AM signal is If m(t) -1 then amplitude of cos(2fc t) is always > 0

No negative values means complex envelope is purely real g(t) = x(t) + j y(t) = x(t) in-phase component only!!

Envelope of g(t) = | g(t) | = x(t) baseband signal information completely represented by AM signal envelope» No need for **carrier phase information** in s(t) to correctly recover m(t)» Primary advantage for AM

m(t) -1 is the normal case for AM (e.g., broadcast AM)

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tftmAtftgts ccc 2cos)](1[2cos)()(


AM Signal Waveform

m(t) assumed to be sinusoidal just for

demonstration purposes

Envelope of s(t) precisely represents m(t) if:

Amin 0 or m(t) -1

Carrier signal phase in s(t) is the same throughout all

amplitude variations of m(t)

Only in phase component of s(t) needed to recover and in-

phase signal = | g(t) | = baseband signal envelope


AM Signal Spectrum

AM Bandpass Spectrum )]([)( tsfS

)]()()()([)( 21

ccccc ffMffffMffAfS

LSB + USB = DSB

LC

RF BW = 2 baseband

signal BW = 2 B

RF BW


AM Modulation %

AM modulation percentage

100% modulation if: max[m(t)] = +1 & min[m(t)] = -1

If Mod % 100% then m(t) -1 and Ac [1 + m(t)] > 0» Required by FCC for AM broadcast radio

Overmodulation of AM signal (% Mod > 100%) causes AM signal BW to be much larger than baseband signal BW if standard 2 quadrant mixer is used in Tx

» Enables envelope detection in Rx for baseband signal recoveryVery simple and inexpensive Rx circuitry

1002

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2 % Modulation minmax tmtm

A

AA

c


AM Modulation %

If Mod % > 100% then m(t) < -1 and Ac[1 + m(t)] < 0 Overmodulation The carrier will have an instantaneous phase change of 180° :

Ac cos(2fc t) Ac cos(2fc t)

g(t) is now complex and envelope of s(t) is no longer m(t) If a two-quadrant multiplier is used for generating s(t) in Tx then

» Low values of m(t) are “clipped”» Distortion is introduced and signal BW is increased significantly» Not allowed by FCC for AM Broadcast

Four-quadrant multiplier could be used to successfully generate overmodulated AM signal» Must use product detector (mixer) NOT envelope detection in Rx to

properly recover m(t) Tx and Rx much more expensive

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tmtftmAts cc


AM Signal Power

If modulating signal m(t) has no DC then

Modulation Efficiency

Highest AM efficiency is only 50% best case!! Other power “wasted” on carrier

» Needed for envelope detection but it does NOT improve S/N @ Rx

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212 tmtmAtmtmAtsP ccAM

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21 tmAAP ccAM

CarrierPower

SidebandPower

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tm

tmE


Envelope Detection

Simple diode circuit that takes RF input s(t) and produces output envelope | g(t) |

1

2 3 1

2

3

Vin > Vout, Diode ON, C charges

Vin < Vout, Diode OFF, C

discharges slowly thru R

Vin > Vout, Diode turns back ON,

C charges again until Vin < Vout

Produces “noisy” representation of g(t) envelope carrier + m(t) !!


Simple AM Rx

)(ts )(ts )(tm

Antenna

EnvelopeDetector LPF

AnalogOutput )(tmHPF

)(ts )(ts )(ts

Modulated Signal at Rx input

Envelope Detector output has high frequency noise due to imperfect

diode-RC response

LPF produces smooth output by attenuating high frequency noise

HPF output eliminates DC

component due to carrier

envelope (Ac)

)(ts


Simple AM Rx Circuit

Antenna

EnvelopeDetector LPF

AnalogOutput )(tmHPF

)(ts )(ts )(ts

EnvelopeDetector

LPF HPF

)(ts

)(ts )(ts

)(tm

1C 2C3C

1R2R

3R


AM Signal Spectrum

f +fc

fc0

AM Spectrum@ Rx Input

f +fc fc 0

AM Spectrumafter

Envelope Detector

High Frequency

“Noise”

f0

AM Spectrumafter LPF

f

AM Spectrumafter HPF

0

Carrier DC removed but

low frequency distortion

introduced!!B

B

BB

B

B

cfRCB

21

LPF RC :


AM Signal Spectrum

AM Spectrum AFTER HPF Must remove DC component

caused by carrier (Ac) to recover m(t)

Distortion of low frequency portion of m(t) permanently introduced Consequence of AM and simple Rx circuitry which is main advantage

of AM Distortion is OK for audio signals (human speech has no energy < 300 Hz)

Distortion is NOT OK for most data signals causes ISI

f0 BB

1 1 0 1 0 0 1PSD for

Polar NRZ


AM Transmitter

AM is a linear modulation method Carrier envelope is linear representation of m(t)

AM Tx must preserve linearity of s(t) or signal will be distorted One approach:

Generate low power s(t) and then use Class A or B linear amplifier for Tx power amplifier (PA)» Not efficient in converting DC power supply to RF energy

Typically 40-60% efficient

» Energy lost to heat Expensive for high power broadcast AM (5-20 kW stations) Cooling of PA and other components also expensive

tftmAts cc 2cos)](1[)(


AM Transmitter

Better approach: Amplify carrier signal only to very high level using efficient Class C

or D power amplifiers » Typically 80-95% efficient

Amplitude modulate the high-power carrier by using m(t) to bias the DC supply of the PA» PA output signal will vary to “DC” supply signal

» “DC” signal is not really constant DC variable m(t)

One technique generates Pulse Width Modulating signal from m(t) » Pulse width is to signal amplitude

» Pass PWM through high power switch to generate high voltage signal

» Use LPF to generate “DC” signal for PA


AM Tx from PWM


Amplitude Modulation

Primary Advantages:1) Linear so that carrier envelope m(t) for mod % < 100

2) Envelope detection enables simple Rx circuit for baseband signal recovery

3) Low cost Rx’s built

4) Efficient use of bandwidth RF BW 2 B Primary Disadvantages:

1) Signal power “wasted” on carrier

2) Poor Rx performance for low S/N ratios

3) High power, expensive Tx’s required for good S/N at Rx

4) Simple Rx with envelope detector cannot be used for data signals where line code PSD’s have signal power @ low frequencies


AM Big Picture

Amplitude Modulation is:

1) Bandwidth Efficient

2) Power (S/N) Inefficient

3) Cannot be used for most digital/data signals

ece 4710: lecture #19 1 bandpass review modulated bandpass signal where g (t) is complex envelope...

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