[sdiy] Re: linear FM

[Magnus Danielson]

From: jhaible at debitel.net
Subject: Re: [sdiy] Re: linear FM
Date: 6 Feb 2003 12:29:52 +0100,Thu,  6 Feb 2003 12:29:52 +0100

Jürgen,

> > > And given a certain ambiguity of triangle oscillator states (unlike a
> > > saw oscillator, a triangle oscillator has no clear mapping of a voltage
> > > to a phase),
> > 
> > It does. 
> [...]
> > My point was that you need to view both the voltage of the cap and the state
> > of
> > the schmitt-trigger to get the full phase.
> 
> Exactly what I tried to say. Looking just at the capacitor voltage leaves
> two possibilities for phase (phase in the traditional sense), and only
> the history (as stored in the schmitt trigger etc.) will make the mapping
> clear.

Exactly.

> If I understood Achim's mails right, he proposes an (alternative) definition
> of phase, where the mapping between current & voltage and phase & frequency
> is *always* clear (without looking at attitional information), and he does
> this by introducing a switching between pos and neg frequency (and alternating
> increase and decrease of phase). This is clearly different from the classic
> definition of phase (or so I thought), but I wanted to find out if it
> is a consistent alternative definition.

Then I haven't grasped the content in Achim's emails fully. But then, my brain
has been slightly out of tune lately due to a light touch of fever, so I blame
that in the meanwhile, OK? ;O)

Sounds interesting. Got to read up on it. It is however a bit hard since this
thread alone has become rather high volume... considering the topic at hand.

> > So, would changing the signs of a sine/cosine core be equalent to running it
> > backwards in time/at negative frequency?
> > Yes.
> 
> Certainly, but that's not the point, as in practical life you cannot decide
> between positive and negative frequency - you'll only notice if the
> sign *changes*. And I don't see something like that in any unmodulated
> oscillator - you must *force* the "natural" succession of states and
> voltages to *reverse* by an external modulation to achieve that.
> IMO this applies to any oscillator (it's only most clear for a sine
> oscillator). 

Not QUITE! For a quadrature oscillator like a cosine/sine oscillator you will
notice the difference between positive and negative frequencies in weither the
cosine peaks 90 degrees before (pos freq) or after (neg freq) the sine.
But, if you have an assymetric waveform you will also notice the sign of the
frequency depending on which waveform you get, the forward or backward
direction variant. This would also be apparent on the relative phase between
fundamental and various overtones.

For waveforms like sine and triangle you would not notice for a single
waveform, but for a sawtooth you would, since it would be rising for positive
and falling for negative frequency.

So, negative frequencies isn't that hard to detect in all cases.

> If you look at the triangle oscillator again, the schmitt trigger controlling
> the charge / discharge of the capacitor is mandatory to create an oscillator
> at all. Without it, you just have an infinite ramp, which will hardly
> count for "oscillation" at all. No oscillation, no frequeny. No oscillation,
> no phase. So the whole contraption that creates the oscillation in the
> first place is the black box that creates a _fixed_ frequency, regardless
> what internal switching takes place to achieve this goal. 
> Only if you add some *extra* contraption for modulation - thru-zero
> modulation even! - it makes sense to talk about a reversal of frequency
> or decreasing phase as well as increasing it. Unless you make entirely
> different definitions for "phase". IMO.

For a true static frequency for a single waveform being phase direction
insensitive, yes. But there are several buts in there and in practice will the
phase noise create the oppertunity for negative frequency even for fixed
frequency and non-modulated tones.

The concept of negative frequency isn't as easy to shake of onces shoulders as
one might wish.

Cheers,
Magnus