cycles, cycling and cyclical structures

[Martin Czech]

Time to throw a new idea into the dungeon...


>BTW. All that cycling isn't good for you, you need to get into the lab, inhale
>some sane soldering fumes like the rest of us ;)

That's what my mom always told me...  No serious, as long as the pulse
is not above 165 bpm I'm still able to think, and some great ideas were
born riding through the black forrest.  

Recently I thought about test structures for delay measurements.
You may know that ring oscillators are used for this purpose. This
means a ring of inverters, of course an odd number. It is not so easy
to determine the speed of CMOS integrated logic from static parameters,
so an inverter chain or ring is still a good idea.

OTOH there are still hundreds of attempts to patent such ring oscillators,
it is very hard not to jump out of the window if you look into the actual
patent surveys...

All right, what is it all about? As long as you have an odd number of
inverters in the ring, it should start oscillating as soon as power is
switched on.  I say it should, but we all know that amplifiers oscillate
, whereas oscillators always get stuck ;->. Old saying. Well, they do
run most of the time, but if you take a lot of inverters, say 21, the
pattern which is running arround in circles is not exactly determined.

Now, this is a pain in the @ss for parameter measurement people,
why bother with that, we are set for music. Exactly we are, and this
undetermined behaviour is something interesting. Inverters were used
before, just think of J.H.'s WASP clone. E.N. has a great deal of digital
pseudorandom cycling stuff, but AFAIK it is all clocked logic.

This proposal is different, because it is analog. It remembers me of the
modes that a resonator like a church organ pipe can have. You need a ring
of inverters, the slower they are, the better. (I can't hear 1MHz). We
can regulate the speed via Vdd and or by controling the current for each
individual inverter.  You know the "clocked inverter", totem pole which
has two PMOST in series and two NMOST.  The outer MOST can be used for
switching or current throtteling.  We can use other elements as well,
there are single CMOS inverters in SMD, or we can use OTAs, op-amps...


There are a lot of possibilities to create such a cyclic resonator in the
audio range, it is like a organ pipe that is bend into a torus.  We can
tap the ring, mix the taps. We can apply a forced initial condition
via set transistors. We can apply an external signal. Finally we can
go completely linear, using integrators and avoiding input overdrive.
This last option may have noise problems, however. Also the frequency band
is limited due to the inverters. Better use phase shifters instead.

The most interesting things will of course happen, if the ring is
long, i.e.  if the individual section delay time is much shorter then
the total ring time.  Because only then a complex pattern other then a
sine wave can exist in the ring.

There are interesting questions:

-Once a pattern has settled in the ring, will it survive a voltage
controlled ring mode tuning?

-Will the pattern survive at all, or will it alter infinitely due to
amplification of noise? Or will it lock into a natural mode of the device
due to parasitics?

-Will it be possible to force an initial state, and will this state
circulate for a longer time?

-How will an external signal interact with the resonance modes, and how
will the nonlinearity act upon that?

-This is a nonlinear resonance system. Is it possible to find a route
to chaos?  

-Anyone been there?

-How will this sound like? Can we get away from the usuall
sine-tri-sqa-saw stew?

Lots of questions. Ihave no answers for. That makes life interesting!
Now, who is biting the worm? I guess a software simulation will not do,
because of the very nonlinear nature of the device.


As you may see, cycling is not totally useless for diy. (I sometimes see
Jan Ulrich and other Telekom staff rushing on the other side of the road
which is kind of funny... makes me feel infinitely small)

m.c.