[sdiy] Fwd: FM math question

[Magnus Danielson]

Dear Ian,

> At 06:34 AM 10/16/2008, Magnus Danielson wrote:
>> >
>> > I'm not seeing anything like that, but perhaps I don't understand what
>> you
>> > mean.  Please tell me in exact detail how to set up to see that.
>>
>>If you trigger your scope at the sawtooth reset, the output sine will
>>suddenly make a phase-jump at that point. if you adjust the phase
>>modulation depth correctly you force extra cycles (for positive ramp) or
>>less cycles (for negative ramp) to appear.
>
> You choose to not answer my request.  That's fine.  But I have looked
> extensively and I can't find any conditions where the modulated output is
> a pure sine wave (no sidebands) as you are suggesting.

I think you overinterprent what I said and what I did not say, and why.
I just didn't have the time to collect thoughts enought to express what
you where actually asking and was unhappy about it.

> Triggering at the sawtooth reset is meaningless, since there is no
> sawtooth when modulation applied.

I was assuming you where using a sawtooth waveform to phase modulate your
signal with, as opposed to modulating it with a sine. If this is not what
you are attempting to do, then of course my comment is totally
meaningless.

> There is no point discussing this further if you are not willing to say
> exactly how to set the system up to see what you are claiming.

I have only a very conceptual idea of how your system looks. I haven't had
time to look at any schematics or anything. Thus, I can't give you
indication to voltage levels etc. and I don't know what limits in
modulation depth you have. I just don't.

The condition I am talking about requires the ability to do a through zero
modulation of the range -PI to +PI radians of phase (360 degrees). The
sawtooth needs to cover exactly this range. When it does that, theory
gives that you can add or remove cycles. For a 1 kHz tone with a 10 Hz
saw, you can thus achieve 1010 Hz or 990 Hz. It is fairly straightforward
to analyze this from the way that the phase adds or subtracts to the
accumulated phase prior to the sine-function/sine-waveshaper.

If you can achieve this or not in your realization I can't tell, but you
will have to find it out. You should be able to if you have sufficient
phase range.

Notice, the carrier and modulation frequencies does not have to be locked.

The triggering on sawtooth that I was talking about was on the modulation
sawtooth, when looking at the modulated sine signal. It is the waveform
shaping at that point which will be most drastic on a scope. Regardless of
modulation depth, this is the place to look and ponder whatever that does
to the waveform and overtone spectra.

I can give more elaborate descriptions etc. if I actually have some
quality time on it. I did quite a bit of analysis yesterday evening and is
now more
familiar with the properties of the overtone spectra.

I am sorry if my replies have not held the quality you expect. There is
things happening on my laptop and my paper and pen is also at work, so
there is also work in progress. I am sorry if my daytime job and other
activities prohibits the high speed and quality reply that you expect.

Cheers,
Magnus