Could we use frequency modulation in the current AM band?

[rorban]

Still, if you amplitude modulate a purely sinusoidal RF carrier with a purely sinusoidal audio signal (and do not exceed--or even quite equal 100% modulation on negative peaks), the frequency spectrum of the modulated RF carrier includes components at the sum and difference frequencies. No such components exist in the spectra of the separate RF and audio signals. Doesn't this suggest that a nonlinear operation has taken place? Also, the most straightforward (note that I said straightforward--no intention to pass judgment on practicality in real-world situations) purely analog technique for mixing the audio and RF signals to produce a modulated RF carrier is the use of a transconductance multiplier, which the baseband analog folks consider to be the quintessential NONLINEAR active-circuit element. No question that FM is--if you will--MORE nonlinear than AM, but is AM PURELY a linear operation?

It has been more than half a century since I was an EE undergrad, but I vaguely recall being told that AM could not be implemented using purely linear circuit techniques. For sure it can't be implemented using purely passive circuit elements (in Prof Guillemin's terminology, LLFPB--lumped, linear, finite, passive, and bilateral). In practical terms, that came down to resistors, capacitors, and inductors without ferromagnetic cores. Electrolytic capacitors (and ultracapacitors, which didn't exist back then), should also be eliminated.

What is linear in AM is the modulation, which is where the information lies. Yes, AM is created by a multiplication process, which is arguably nonlinear. However, the sidebands obey the scaling and superposition principles required for a system to be linear. This is even true when the carrier is not suppressed because the carrier can be considered to be a DC term in the modulation.

One might think of the superposition and scaling behavior AM modulation as a example of the distributive law of algebra, as illustrated by

a (b + c) = a b + a c

a (2 b) = 2 (a b)

In this case, "a" would be the carrier and "b" and "c" would be two Fourier components of the modulation. The essential reason why AM modulation is linear is that the carrier, a, has constant amplitude and frequency.

 

[PTBoardOp94]

Multiplication is mathematically a linear operation. Multiplying two signals with real analog circuitry is not.

I believe it was DanStrassberg who wrote that multiplication was not linear because multiplying a function by itself produces the square of that function. Let's take a closer look at this.

There are actually two situations he could be discussing. The first is where the two inputs of a multiplier are tied together to produce the square of a function. Does the rule of superposition hold? No. (It is not possible to turn off one of the inputs without disabling the other) Therefore the system is not linear.

But if you leave the two inputs independent (but initially equal), you get a different result. The rule of superposition holds, as does the rule of scaling, so the multiplication is theoretically linear.

Really enjoying this topic - I like the theory of signal transmission quite a bit.

 

[Tom Wells]

Still, if you amplitude modulate a purely sinusoidal RF carrier with a purely sinusoidal audio signal (and do not exceed--or even quite equal 100% modulation on negative peaks), the frequency spectrum of the modulated RF carrier includes components at the sum and difference frequencies. No such components exist in the spectra of the separate RF and audio signals. Doesn't this suggest that a nonlinear operation has taken place? Also, the most straightforward (note that I said straightforward--no intention to pass judgment on practicality in real-world situations) purely analog technique for mixing the audio and RF signals to produce a modulated RF carrier is the use of a transconductance multiplier, which the baseband analog folks consider to be the quintessential NONLINEAR active-circuit element. No question that FM is--if you will--MORE nonlinear than AM, but is AM PURELY a linear operation?

It has been more than half a century since I was an EE undergrad, but I vaguely recall being told that AM could not be implemented using purely linear circuit techniques. For sure it can't be implemented using purely passive circuit elements (in Prof Guillemin's terminology, LLFPB--lumped, linear, finite, passive, and bilateral). In practical terms, that came down to resistors, capacitors, and inductors without ferromagnetic cores. Electrolytic capacitors (and ultracapacitors, which didn't exist back then), should also be eliminated.

What is linear in AM is the modulation, which is where the information lies. Yes, AM is created by a multiplication process, which is arguably nonlinear. However, the sidebands obey the scaling and superposition principles required for a system to be linear. This is even true when the carrier is not suppressed because the carrier can be considered to be a DC term in the modulation.

One might think of the superposition and scaling behavior AM modulation as a example of the distributive law of algebra, as illustrated by

a (b + c) = a b + a c

a (2 b) = 2 (a b)

In this case, "a" would be the carrier and "b" and "c" would be two Fourier components of the modulation. The essential reason why AM modulation is linear is that the carrier, a, has constant amplitude and frequency.

Graphically, I guess then, the "line" we are modulating would be the line formed by the upper and lower edges of our AM waveform envelope.
Which ideally, with no modulation, form straight lines, as its "Amplitude" is then constant.

This calls up the issue of "carrier control" and 100%+ and above modulation.
I have read that while carrier control seemed like a good idea to everyone, in the real world, AGC circuits did not like to play well
with a changing level of carrier. Wouldn't either carrier control or over 100%+ modulation be clearly nonlinear, since
we're changing carrier level? I suspect it is non-linear but if done carefully the ear doesn't mind.
I have definitely noticed that most of my radios work well with 150% pos mod, but some sound awful.

 

[rrsounds]

This calls up the issue of "carrier control" and 100%+ and above modulation.
I have read that while carrier control seemed like a good idea to everyone, in the real world, AGC circuits did not like to play well
with a changing level of carrier. Wouldn't either carrier control or over 100%+ modulation be clearly nonlinear, since
we're changing carrier level? I suspect it is non-linear but if done carefully the ear doesn't mind.
I have definitely noticed that most of my radios work well with 150% pos mod, but some sound awful.

Assymetrical modulation simply means that the positive-going peak is higher than the negative one.

The 'area under the curve' must be identical for both polarities, or there will be a DC component in the audio. In the case of AM, that is called "carrier shift."
A minimal variation in the carrier shift spec results in a more linear modulation and thus a less distorted sound.

You could make it so the carrier level increases at what would normally be 100+% modulation...approaching, eventually, what would then be "DSB-reduced carrier."

But really, since the carrier is what creates the quiet background during moments of low or no modulation (which is a good thing), THAT is when you need a stronger carrier.

So, if you want more carrier with lower levels... AND more carrier with higher levels? At that point, we're simply talking more carrier altogether, IOW, higher power...There is no free lunch in AM!

Kind Regards,
David

 

[DanStrassberg]

Assymetrical modulation simply means that the positive-going peak is higher than the negative one.
David

If you compress the negative peaks, the result OUGHT to be audible distortion. But if you allow the carrier level to increase slowly so that it is not necessary to clip the negative peaks (and then let the carrier level decrease slowly after the peaks are over), maybe the instances of distortion will occur seldom enough that they go unnoticed. I never heard "greater than 100% modulation on positive peaks" explained, but I always thought that was how it must work. OTOH, the systems were designed by people who are a lot smarter than I am. Cyril Brennan (I think that was his name--WAPE, WVOK, WQYK, to name a few), for example.

 

[Tom Wells]

I'm using Breakaway Broadcast processor, set up for 150% pos, and it's fun to watch the envelope get wider on a scope, while still not pinching off beyond minus 100%. In the 1930s-50s amatuer radio operators experimented with swing inductors and other methods to
vary the carrier level via an AGC-like bias on one grid or another of their AMs. Most found it could be some improvement as far as reducing
carriers "loading up" a frequency, but required careful manual RF gain adjustment on the part of the receiver.
Those who tried to use AGC on reception found no improvement, as David notes, since the quieting effect was absent, and the AGC then brought up the noise when the carrier was reduced.

I could never get any decent mod over positive 100% until I was using BBP. How it does this with no detrimental artifacts is
still amazing to the ears. Unless I listen on a radio with square wave down-conversion, and then its...pretty bad, actually.