How does an amplifier inadvertently demodulate a radio signal?

[Merlin3189]

It is he. I was looking for a hand-waving hero. That's why I also put the odd little fellow at the end: he's not exactly waving, but as near as I could find.

 

[musichascolors]

None of the above examples of "tremolo" are free of some frequency mod at the same time.
A tremolo arm / 'whammy' bar on a guitar stretch the strings so no well justified 'A.M. Only' example for a tremolo.

Yeah, Fender calls their whammy bars tremolo and their tremolo effects vibrato, they just have them switched up.

Anyway, I started experimenting using a plugin/program called Mondomod. I generated a sine wave, and then used AM modulation on it, I was able to see the side bands Then, I rectified it, and the frequency displayed was the rate of modulation.

 

[sophiecentaur]

That sounds to us like AM.

Yes, it has the sound of varying amplitude but 'modulated by what? I was just being picky at the use of "A.M." which is, to my mind, a special term and not to be used in other contexts if we want to avoid newcomers being confused in their search for understanding of AM radio etc.. When they see the scope trace of two close sine waves (which would appear the same as DSBSCAM - with that grotty phase inversion at the zero crossing) and the real AM signal where the envelope is clearly the same as the modulating signal. One big difference between the two effects is that two beating signals can be produced with two perfectly linear generators whereas AM requires a non linear process in the modulator. There is also the issue of the beat frequency with two tones being at twice the frequency that would correspond to AM (with suppressed carrier).
. . . . . or have I been too immersed with this in the past to have a healthy view?

 

[musichascolors]

I think I get it now...

The rectifier basically converts the signal to DC/a flat line. So obviously alternating the amplitude of DC in the shape of the original signal recreates that signal (since the DC is a straight line). (I know it's actually the opposite order, but I think that's the idea)

And then the low-pass filter just cleans up the noise and distortion (from the DC and AM)

 

[jim hardy]

The rectifier basically converts the signal to DC/a flat line. So obviously alternating the amplitude of DC in the shape of the original signal recreates that signal (since the DC is a straight line). (I know it's actually the opposite order, but I think that's the idea)

And then the low-pass filter just cleans up the noise and distortion (from the DC and AM)

You're getting there.
Back to post 5

Then you remove the DC offset with the simple coupling capacitor at input of first audio stage..

old jim

 

[the_emi_guy]

Yes, it has the sound of varying amplitude but 'modulated by what?

I think what Baluncore is eluding to is that AM can be viewed either as a linear sum or non-linear mixing depending on your point of view.

Consider a 1MHz carrier and a 1KHz message signal. We can multiply these, using a mixer for example, to obtain AM.

In the frequency domain we have produced 1.001MHz upper sideband, and a 0.999MHz lower sideband CW signals.

Nothing prevents us from synthesizing the same AM signal by starting with 1.001MHz and 0.999MHz CW signals and summing them linearly.

We generally don't do this because it is often impractical to generate a physical signal in this manner. However, it is it is often easier to *analyze* modulation by viewing modulation as this linear sum. This is how we analyze phase noise for example. We consider the carrier to be a long rotating vector (phasor), and the noise to be a small vector with its tail sitting on the the head of the carrier vector. The net signal+noise is the vector sum.

The attached image shows how AM is produced when the two modulation sidebands are rotating relative to the carrier in such as way that they do not change the phase of the carrier. It also shows why the sideband amplitudes are half of the AM amplitude. By simply shifting the phase of the same two sidebands, we can produce PM, where the sideband phases are arranged so that their amplitudes cancel but phase deviations add.

 

[sophiecentaur]

To produce 'AM' by adding three tones would require a particular set of tones that would have to be phase related in a specific way. I have a feeling that producing those those tones would, in itself, require some non linear phase detection / locking process. A beat can be obtained with any old pair of tones.
Now, I don't feel particularly strongly about this but the difference between the those two ideas sounds 'significant' enough to cause confusion for the uninitiated. People are only too willing to get the wrong ends of sticks.

 

[Baluncore]

I think what Baluncore is eluding to is that AM can be viewed either as a linear sum or non-linear mixing depending on your point of view.

I agree with sophiecentaur that the sum of two close tones are strictly not AM.

In a wide channel, they can be modeled as an independent sideband signal with suppressed carrier. If the two tones had identical amplitudes then there will be a hypothetical carrier frequency and phase that could make it a double sideband suppressed carrier signal. The two tones are actually a two tone test signal in a wide channel.

But as humans with real ears, we do not resolve the two close sinewaves. They are too close in frequency to be separated in our cochlea. Even if they were demodulated, the difference frequency would be sub-audible. We hear the linear sum, or constructive / destructive interference of the two tones as a slow variation in amplitude. We cannot tell the difference without a narrow RB analyser. That is why, to our imperfect ears, it sounds like a single audible sinewave, amplitude modulated by a sub-sonic sinewave.

 

[the_emi_guy]

I agree with sophiecentaur that the sum of two close tones are strictly not AM.

[A + Mcos(ω_mt)]sin(ω_ct) = Asin(ω_ct) + M/2(sin(ω_c+ω_m)t) + M/2(sin(ω_c-ω_m)t)

So multiplying the stuff on the LHS produces AM, but adding the stuff on the RHS does not?

 

[Baluncore]

The trig identity you originally posted; sin(m) * sin(c) = ½ cos(c–m) – ½ cos(c+m) only holds for the special case of AM with 100% modulation, where the amplitude of the carrier and modulation are equal. It is a simple identity because the complexity has cancelled.

Your edited version involves three sine wave terms on the RHS.

[A + Mcos(ωmt)]sin(ωct) = Asin(ωct) + M/2(sin(ωc+ωm)t) + M/2(sin(ωc-ωm)t)
So multiplying the stuff on the LHS produces AM, but adding the stuff on the RHS does not?

With three terms, it requires one more precise term be created than is available when adding only two audio tones.
It also requires that the two tones being summed will have exactly the same amplitude.

I maintain my assertion that the sum of two close tones are strictly not the same as AM.

 

[the_emi_guy]

My diagrams show the sum of three vectors, the carrier and the two sidebands, which, I think, matches the trig.

I guess I was mistaken when I assumed that this was direction you were heading when you brought up adding close freqs and obtaining beat freqs.

Sorry.

 

[Baluncore]

Sorry.

Emi_guy; don't be sorry for asking difficult questions. It wakes me up. Sorting out misunderstandings due to the inadequacies of the English language and it's users is a necessity. I have to agree with Fourier et al, that a real signal is the vector sum of all it's frequency component phasors.

It is interesting that the trigonometric identity sin(m) * sin(c) = ½ cos(c–m) – ½ cos(c+m) appears at first to be simple AM because on the LHS it is the product of the carrier by the modulation. But the equivalenced signal is synthesised from the linear combination of only two cosinewaves on the RHS. The truth is that this identity actually represents a double sideband signal with a suppressed carrier, DSB SC. The carrier must be reinserted by linear addition before it is possible to use a simple envelope detector to demodulate the signal.

The simple? broadcast AM that can be detected immediately with an envelope detector is represented by the_emi_guy's posted equation;
[A + M cos( ωm t )] sin( ωc t ) = A sin( ωc t ) + M/2( sin( ωc + ωm ) t) + M/2( sin( ωc – ωm ) t )
The difference here from DSB SC, is that the modulation is offset by A, sufficiently so that the modulation term [A + M cos( ωm t )] never crosses zero.

Getting back to the topic. It takes a non-linear component to make an envelope detector that might inadvertently demodulate an AM broadcast signal. That non-linear component could be the junction of an amplifier input transistor, zinc oxide on a galvanised iron roof, copper oxide between crimped wires, or germanium condensed and crystallised in the metal flue of a coal burning stove.

 

[sophiecentaur]

[A + Mcos(ωmt)]sin(ωct) = Asin(ωct) + M/2(sin(ωc+ωm)t) + M/2(sin(ωc-ωm)t)

So multiplying the stuff on the LHS produces AM, but adding the stuff on the RHS does not?

There is a hidden requirement in the two sideband phases that means you need them to be taylor made. Otherwise you could be getting phase modulation or an AM PM mixture.

 

[the_emi_guy]

There is a hidden requirement in the two sideband phases that means you need them to be taylor made. Otherwise you could be getting phase modulation or an AM PM mixture.

That is exactly what the diagrams that I attached were highlighting.

I also mentioned that this is not necessarily the practical way of generating modulation, but is a common method of *analyzing* modulation. phase noise in particular.

Unfortunately I took the thread a little off topic in the process.

 

[sophiecentaur]

Yep. The devil is in the phase detail. Fourier rules. [emoji846]