[sdiy] analog through zero FM dummy

[Martin Czech]

SNIPED

:::So far I agree, but we want a carrier of 0Hz. 
:::Your maths is just too general. ;-)
:::
:::That in mind I'd say:
:::tri(M/wm*cos(wm*t)+p0)

Oh, really? The recent thread was about zero carrier, but sometimes
a non zero carrier is also nice, e.g. you start with a sine wave
that gets more and more side partials.


:::>This gives a current like:
:::>
:::>i(t)=(i0+M*sin(wm*t))*exp{C*U/Ut}
:::
:::Here is where I start to disagree:
:::i(t)=i0*M*sin(wm*t)*exp{C*U/Ut} 
:::
:::I.e. in these TZ circuits the reference current is multiplied (not added as
:::it might look) along with the modulation signal, which is here assumed to
:::be sinusodual.
:::
:::That multiplication takes place in the OTA in my circuit, and it takes
:::place by making the reference current of the expo proportional to the
:::modulating input in the EN circuit. (Iout = Iref * exp {...}, substitute
:::Iref with i0*M*sin(wm*t) and you're there. This works only for one quadrant
:::hence the rectification and sign restoration.) 
:::Lets look at the TZVCOs, for 0V at the linear input: there is no current
:::fed into the timing cap! In my circuit OTA is then off. And there is no
:::reference current fed into the expo in the EN circuit. Without modulation
:::signal the output signal is 0Hz (or DC)!


Ok, I aggree if wc=0 is given. If wc !=0 i disagree, because then (the
circuit must be changed a little bit) and we come to my additive
solution, I think.


:::This is where you started, just that M' is a function of the voltage on the 
:::expo input now, and the carrier is 0Hz.

:::>So I claim: analog TZFM is not the same as "theoretical FM".
:::
:::Depends on the definition of "theoretical FM" i guess ;-)

Yes, this sentence was rubbish, we have to be more specific:

Usual analog TZFM circuits seem not to include wc != 0, which is perhaps
the more interesting case.

:::Some remarks here: one must track the modulation frequency along with the
:::carrier frequency, only then you get constant peak freq deviation, i.e.
:::constant timbre. (To modulate the timbre dynamically you can use the expo
:::input of the TZFM-VCO, varying the PFD.)

How does this come together with your first remark saying wc == 0?

:::And, there is one other thing one should notice, when applying waveshaping
:::to the generated tzfm-triangle (to get sinusodial output) one gets a
:::different result than with a generic tzfm-sinusodial oscillator.

? I don't think so. As long as the tri wave represents the phase in a correct
manner (and I believe it does) it will "point" to the right entry in
our "sine table" (shaper).

:::I still wonder if a real sinewave oscillator can be made running back and
:::forth?

It should be possible. The usual quadrature oscillator with instant amplitude
stabilisation (reference signal cos(x)^2+sin(x)^2 == const) should
be ok. Only the direction of integration must be switched (observing
stability) , like in the Haiblesian version of Tietze/Schenk tri wave
oscillator. Juergen choose the way to generate tri waves with 
waveshaping to sine thereafter.

m.c.