Amplitude ModulationModulation Index, Envelopes, Envelope Recovery

Prepared by: Keyur DesaiDepartment of Electrical Engineering

Michigan State UniversityECE458 Spring 2007

Recall DSBSC● Double sideband suppressed carrier●

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● In the spectrum no carrier

What is AM?● AM signal = DSBSC + Carrier● = m(t) cos(wt) + V cos(wt)● = (V + m(t)) cos(wt)● = V(1 + m(t)/V)cos(wt)● 1 + m(t)/V > 0 => min{m(t)}/V > -1 => |min{m(t)}|<V● AM = amplitude modulation●

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● In the message add DC●

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● Add DC such that a(t) >= 0, then perfect recovery with a simple demodulator

Spectrum of AM signal● Note the component at carrier frequency● Now you know why DSBSC was called suppressed carrier

What is Modulation index?● Proportion of negative change in the carrier amplitude● Amount of modulation is 0, because it's only carrier ● Hence modulation index is also 0

What is Modulation index?● The minimum carrier amplitude is 0.75● When there is no signal the carrier amplitude is 3● Proportion of negative change in carrier amplitude = (3 – 0.75)/3=?● The modulation index = 0.75 = 75%

AM signal generation

AM signal generation● g + Gsin(ut)● g[1+ G/g sin(ut)]● Modulation index = G/g

Significance of modulation index● For m < 1 the boundary of AM signal has the shape of the message ● For m > 1 not true● There are techniques that can extract the boundary and hence

recover the message: called envelope detection

How to measure modulation index● For simple signals like sin(ut) its easy to measure modulation index● For complicated signals like speech you have to use more

complicated techniques● One such technique is to use oscilloscope in X-Y mode● On X axis apply the message on Y axis apply the AM signal● Follow the procedure in the lab handout

The envelope of AM signal● AM signal =

The envelope of AM signal● AM signal =

The envelope of DSBSC signal● DSBSC = A [0 + m(t)] c(t)● a(t) = m(t)● e(t) = |m(t)|● Thats why envelope recovery cannot work on DSBSC signal● Then what is a good thing about DSBSC?

Types of signals● Narrowband (f2 – f1) / (f2 + f1) << 1● Wideband (f2 – f1) / (f2 + f1) >>1● Where f2 is the highest frequency component in the signal● Where f1 is the ???? frequency component in the signal●

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● In Experiment 2 you will try to understand the how the envelopes of wideband and narrowband signals look like

Demodulation● Also called envelope recovery in AM signal case● Recall:●

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● How to get message back?● All you have to do is to extract the envelope

Demodulation● Ideal envelope detector●

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● What is the circuit that gives the absolute value of the input waveform?

Demodulation● How you do it in TIMS?

Demodulation● Didode detector

Effect of overmodulation

Spectra of AM