Why we do that in AM demodulation?

[idmond]

Hey all,

"In AM synchronous demodulation, Why we don't divide m(t)coswt by cos(wt)
instead of multiplying by cos(wt), since this can be easily implemented by a simple divider circuit?"



If it's all about thinking mathematically, then it seems like it's more intuitive and a whole lot easier if we just divide by coswt, why we go through all the trouble and multiply then we have to know the trig identity of (cos(a)cos(b)) and then put a LPF after the output...

I asked this question to two professors and I got different answers:

#Professor 1 Reply:
"For your scheme to work you must know exactly what the frequency w is that the transmitter is using, which tends to drift. So try your scheme with dividing by cos (w+delta)t and see whether you can recover the signal."


#Professor 2 reply was:
"we don't use the division scheme for two reasons:

a- In the real world, noise is added to the received signal and it is going to look like this, m(t)coswt+n(t). If you then divide by coswt, you will get, m(t)+n(t)/coswt, and since the cosine function ranges from -1 to 1, thus for values of cosine less than 1, the noise term will be amplified instead of being attenuated , so you will get poor SNR.

b- When the cosine function goes to zero, you will divide by zero and this will cause amplitude spikes which leads to circuit saturation."



I am now confused more than ever which one is true?

 

[Harald Kapp]

These answers don't contradict, they complement each other.

 

[idmond]

they complement each other.

well, it seems like you really understand the first one, which is:
"For your scheme to work you must know exactly what the frequency w is that the transmitter is using, which tends to drift. So try your scheme with dividing by cos (w+delta)t and see whether you can recover the signal."

because, frankly i don't understand what the frequency shift has anything to do with choosing the multiplication scheme over the division scheme. after he told me that, I started analyzing the problem mathematically just like he told me, but again it was a dead end:

1- if we used the usual multiplication scheme for demodulation:

if the received AM modulated, frequency-shifted signal was something like this:

then the demodulated signal would be:

2- if we used the division scheme for demodulation:

if the received AM modulated, frequency-shifted signal was something like this:

and if we pass through a low pass filter, we get the output signal:

In both schemes, the spectrum of the message signal m(t) is shifted by an amount of . So if we had a PLL, it would track the frequency of the received carrier as it drifts and the frequency shift would be zero in both schemes, so we get:




1- for the division scheme :

2- for the multiplication scheme:

so in both schemes the problem is solved, the message signal is received.
what's the problem then?