[sdiy] Re: linear FM

[jhaible at debitel.net]

Z
> > 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. 


Or I haven't. I'm still not so sure. Achim ?





> > 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.


It's just a matter of definition. I can call the (voltage) node after
the first integrator "sin", and the second node "cos" - or the other
way round, and voila, I can call it oscillating backwards. But that
alone is nothing special. As you said, I could just invert one of
the voltages to get the same result.
Normally you would simply asume normal (positive) frequency and label
the nodes as sin and cos, respectively, to fit into normal (positive)
counting. Unless you're using both output pairs (sin, cos and sin, -cos)
at the same time - see the mechanical analogy below.


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

... and I don't claim I'd be that experienced in using it.

Visualizing a spinning wheel is most helpful. It moves in a circular motion,
and it moves forward in time. You can look at it from two sides, and you'll
see it either spinning clockwise or counterclockwise. Normally you will
discribe it as spinning with a certain number of cycles per second, and often
this is enough. If you also want to give information about the direction
in which it turns, it makes sense to say "it turns clockwise when I look at it
from the south". (Which is equivalent to saying "it turns counterclockwise
from the north.") Just saying "it turns clockwise" is not enough!

Only if you have a change of direction (be it from cw to cww, or from ccw
to cw, observed from S or N), and/or if you have several wheels that
spin in different directions, it's high time to introduce a concept
of "negative frequency".


JH.

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