New frequency generation in AM signal

[DaveE]

And now you have done it.

What's the point here? You do know that the 3 of us all understand this, right? It's not "rocket science" for analog EEs after all. My apologies for getting involved. I have been duly chastised.

 

[Swamp Thing]

It sometimes happens that members find it hard to see "where the OP is coming from", as they say these days. This could be because the experts don't remember grappling with the question from that particular perspective -- a perspective which, in the big picture, may not be not very useful. Or it could be because their specific gifts made it easy for them as students to sail through easily. So then you have threads like this one where the OP remains dissatisfied with the replies until the thread fizzles out or gets locked.

In this particular case I remember asking questions along nearly the same lines as the OP, which is why I found this pretty interesting:

It was thought by most people until about 1920 that the side frequencies were just a mathematical artifact ... Carson in the USA experimented with narrow quartz crystal filters and found that the side frequencies do exist.

As a student I wanted to know exactly why and how a filter (like one of Carson's filters in the quote) would produce an output when the input is an AM carrier centered somewhere far away from the filter's bandwidth. The answer that I finally figured out was something like this...

It's easier to start with a suppressed carrier AM signal that contains only the sidebands and no component at the carrier frequency. The thing about this signal is that its phase is zero degrees for one half of the modulation cycle and 180 degrees for the other half of the modulation cycle. If you apply this to a filter that is centered on the carrier frequency, the filter will build up an output during one half cycle, only to ramp down its output during the second half cycle as the opposing phase input drives it down. Think of a swing that is subjected to little pushes at its resonant frequency for a certain time, followed by the same number of pulls for the same time, and so on. So a filter of infinite Q will not build up significant output over many modulation cycles.

Now, what if the filter is centered around the carrier frequency plus the modulation frequency? Imagine that the filter is already "ringing" ("swinging") at its own resonance frequency. This ringing output is sometimes be in phase with the carrier frequency, and sometimes out of phase. It alternates between 0 and 180 according to the modulation half-cycle, if we take the carrier as our phase reference. But if we look at the suppressed carrier AM, its phase is also alternating between 0 and 180. Thus the input can keep on driving the filter's resonances to higher and higher levels -- theoretically infinite output if the Q is infinite.

Adding the carrier frequency back to get conventional AM won't affect this output, a la superposition.

QED, sort of, I think.

I am not sure if this will address the OP's concern, but there you go.

 

[Averagesupernova]

I think what the OP is looking for can be summed up most simply by saying that you cannot change a sine wave in any manner without generating new frequencies.

 

[sophiecentaur]

A snag is that the whole topic is more complicated than this thread is suggesting and we're trying to sum things up too simply.

I think what the OP is looking for can be summed up most simply by saying that you cannot change a sine wave in any manner without generating new frequencies.

"any form" is an overstatement. Phase and amplitude changes are linear.

Because, the phrase "time constant" implies a linear response, which can't make more DC than whatever it gets.

Another overstatement. A rectifier circuit will be operating with different charge and discharge time constants. A 'good' transformer with loads of copper and iron will produce a fast charge slope and a high resistance load will produce a slow discharge slope. The mean (DC) Voltage will be affected by both time constants. Without some regulation, audio amp psu's have to be over-engineered to reduce hum.

The best answer here is to appreciate how frequency and time domain descriptions can be interchanged by the FT and forget the nuts and bolts of the circuit involved.

 

[Averagesupernova]

"any form" is an overstatement. Phase and amplitude changes are linear.

Linear relative to what? Any change made to a sine wave will put energy in a different part of the spectrum than the original carrier during said change.

 

[Baluncore]

"any form" is an overstatement. Phase and amplitude changes are linear.

No, they are nonlinear.
There may be no sidebands before or after the change, but sidebands are present during the change.

That is where phase modulation and amplitude modulation come from.

AM is one dimensional, the product of a sinewave and one changing transmission coefficient.

PM is two dimensional, the separate AM, of separated sine and a cosine waves, that are linearly added.

If the phasor points a different way, or has a different magnitude, that requires a non-linear change to the signal path.

The change over time, of a linear parameter, must be interpreted as the product of two signals over time. One is the parameter that changes. When you turn a light switch on, or off, you modulate the light.

 

[sophiecentaur]

No, they are nonlinear.

Yes you are strictly right but it involved a second varying (modulating) signal. I put it badly but I was assuming a non varying parameter - like the gain of a fixed attenuator. That is very different from the effect of a diode etc where the input signal can 'affect itself' without the need for a modulating signal or any changing parameter.

But, as has been mentioned above, we are chasing our tales. The basic theory is perfectly secure and, in our individual ways, we are trying to provide short cut answers which is risky and can sound like an argument about basics.

 

[Averagesupernova]

Two signals (or more), one signal with a non-linear device in the signal path, it doesn't matter. Both examples involve changing the carrier which generated sidebands. I believe we are in agreement there. The math says it's so, so it has to hold in the real world.
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Discussion of what the transistors, diodes, poor connection on an antenna wire, etc do when encountering a carrier is a different area of discussion and if the op asks this specifically we should try to answer. But the basic has been said. Change a carrier, get new frequencies.

 

[Baluncore]

But, as has been mentioned above, we are chasing our tales.

It is difficult trying to follow your tall tales, but I am not chasing my tail.

If only the addition of variables is involved, it is linear.
If the multiplication of variables is involved, it is non-linear.

 

[sophiecentaur]

No, they are nonlinear.

Yes you are strictly right but it involves a second varying (modulating) signal. I put it badly but I was assuming a non varying parameter - like the gain of a fixed attenuator. That is very different from the effect of a diode etc where the input signal can 'modulate itself' without the need for a modulating signal or any changing parameter.
We know a linear device when we see one.

 

[Baluncore]

It does not matter if a variable is a signal or a circuit parameter.
Nor does it matter what makes any variable change.
Multiplication of variables is non-linear.
Addition of variables, or multiplication by a constant, is linear.

We know a linear device when we see one.

It is too easy to hope something that looks linear is linear.
To be safe, we know a non-linear device when we see new frequencies appearing.
We must then take the time to identify the variables and the source of the multiplication.

 

[sophiecentaur]

It is too easy to hope something that looks linear is linear.

This is getting a bit daft. A 3dB attenuator, made with metal resistors 'looks; linear and it behaves linearly. I was merely trying to contrast this with a resistor network which has a diode nestling in there somewhere. I reckon we could tell the two circuits apart with a simple spectrum analyser. In one case there will be detectable products and not in the other. Why are you bothering to argue with this? Is it a "tall tail"?

 

[Averagesupernova]

A 3dB attenuator, made with metal resistors 'looks; linear and it behaves linearly. I was merely trying to contrast this with a resistor network which has a diode nestling in there somewhere.

If you include what the quoted above network does as part of my statement about changing a sine wave will always create new frequencies then I guess I stand corrected. But I think you know better than to suggest I'm saying that. If you truly believe I would suggest such a thing then why not take it a step farther and suggest I am claiming the same thing when a carrier signal is completely dissipated in a load resistor?
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You said it yourself:

We know a linear device when we see one.

But yet it seems you claim that @Baluncore and I do not see the difference.

 

[sophiecentaur]

But yet it seems you claim that @Baluncore and I do not see the difference.

I know you guys know all this and also the definition of a linear medium. Where components are concerned, you have to look at both Current and Voltage to decide on the linearity. Saying that the "carrier signal" is completely dissipated in a load resistor requires the concept of matching and this is going much further than necessary. We're only choosing to use different words to partially describe a situation. We'd have no argument if we wrote the Maths out.

 

[Averagesupernova]

Saying that the "carrier signal" is completely dissipated in a load resistor requires the concept of matching and this is going much further than necessary.

Right here. What you just said is the basis of the issue I am having with your posts. It is just more confusion added for no good reason (in my opinion). We can impedance match or not match. Any sidebands generated due to this is not relevant to the basics of this thread.
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I believe I should have been more careful with my words. Attenuating a carrier in a network of resistors is technically 'changing' the carrier and someone not as familiar with all of this could assume sidebands would be generated when the are not with fixed attenuation.

 

[sophiecentaur]

It is just more confusion added for no good reason (in my opinion).

That's the most common problem with PF threads. Someone asks a question to which there is either a hand waving answer or a full one. In actual fact, the wording of a basically simple answer can be a minefield but otoh, the mathematical answer can confuse the questioner. Then the chat on the sidelines gets even more confusing and our use of terms can get very loose.

Can't win.

 

[Baluncore]

I agree, you cannot win.

The problem with this thread was two early false assumptions, that electronic components were involved, and that an optical chopper was a linear component.
A chopper, or a switch, is non-linear because it has a variable transmission coefficient.

The Fourier Transform is mathematics. There is no need to discuss, the components of electronic technology, if the linear addition of variables, or the non-linear multiplication of variables, can explain it so simply.

 

[Averagesupernova]

What I took away from the original post was this:

If new frequencies are actually generated, what is the physical mechanism that generates these new frequencies?

There are only thousands of ways to accomplish this. It's not practical to answer all of them. Don't expect perfection. Keep it as simple as possible. If related questions arise, they can be answered or the op can be shown links that lead to answers.