Amplitude Modulation Modulation Index, Envelopes, Envelope Recovery

Prepared by: Keyur Desai Department of Electrical Engineering Michigan State University ECE458 Spring 2007 Recall DSBSC ● Double sideband suppressed carrier ●

● ● 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)}|

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● ● In the message add DC ●

● ● 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