A basic AM modulation problem

[Highlander-SP]

Consider a AM signal:

φam(t) = ( 1 + A cos ωmt) . cos ωct

where the frequency of the information sinal wm = 5 KHz and the frequency of the carrier wc = 100 KHz. The constant A = 15. That signal may be demodulated by a envelope detector?
What should be the output of the envelop detector?
Find out the frequency spetrum of the envelop detector output.

 

[ramy gad]

it must contains the 5k message signal plus some high freq. as the envelope detector join the peaks of the AM signal to reconstract the the info signal
the cap charge then discharge until the next peak comes to charge again this generates hi frequences

if this does n't covince you can search the web
but i didn't find before any mathimatical prove for the spectrum for the output of the envelope detector

 

[Highlander-SP]

Then, what should br the amplituds of each frequency?

in that case, do I have those frequencies? :

frequency...............amplitud

wm.......................... A
wc - wm................... ?
wc........................... ?
wc + wm.................. ?

is that right above?

remembering that the envelope detector works also as a low-pass filter.

 

[nandopg]

The amplitude of each sideband is Ec*ma/2 , where ma=Em/Ec is the AM modulation index, Em is modulating signal amplitud and Ec the unmodulated carrier amplitude.

The amplitude of the carrier in the modulated waveform in frequency domain is equal to the amplitude of the unmodulated carrier and doesn't change with the modulation index.

NandoPG

 

[pthoppay]

Hi,


First i am not sure whether you could demodulate with envelope detector. As normal AM signal with kp*am<1 (in your case A<1)is demodulated by envelope.

When kp*am>1 (in your case A>1) it becomes DSBSC wave and guess should DSBSC demodulation.

Not sure though, just check it up.

Regards,
thoppay

 

[Highlander-SP]

I think that the pic should be the output of the envelop detector, but what sould be the frequency spetrum of the envelop detector output at the pic?

 

[VSMVDD]

Hi

if you have a 100Khz carrier modulated by a 5khz bandwidth to 100% modulation
envilope for a 1vpp input {line level}
then the freq spectra {bandwidth} of your recovered signal will still be 5Khz

there is no + and - you are thinking there is fm in the carrier


AM amplitude modulation is setup to have an acceptance bandwidth at the
transmiter for the reciever
whereas fm is restricted freq bandwidth so you need to compress the audio to make it fit {audio is 0-15khz or so }

{in your case 5khz bandwidth not much but plenty for inteligable signal about as good audio as an analogue phone line}

it is worth adding that most broudcast transmiters on AM dont use AM as such

they use double sideband slightly different
and sounds far better after detection and rectify back to audio


{so basicaly once its rectified by the detector it will have 5khz audio bandwidth
becouse this is what is being transmited


if i transmit 10khz of audio bandwidth at 100khz carrier i still get 10khz bandwidth back once rectified by the detector even on your reciever i will still get it

its then up to how you process the signal further to

1} clean it up
2} add enphasis or de-emphasis etc {mosty used in FM stuff}
3} compression or compandment {mostly ssb stuff}

 

[Highlander-SP]

isn`t there any kind of emptying of the carrier? is there a possibilty?

 

[Borber]

pathoppay was close.
This is a case of over modulation and the output signal from envelope detector is severely distorted. So the output spectrum is wider than 5kHz, consider harmonic components.