From obxwindsurf@yahoo.com Thu Oct 02 09:00:09 2003
Subject:Re: Solid State scanner project - warning: very geeky discussion follows!

Steffan,

That was the thought train I was entertaining yesterday morning,
however when I drew a timing diagram I realized that you would get
the overlap when the two sines half-wave-rectified (HWR), would be
both off delivering an interruption in the signal. In addition, 90
degrees shift (if phase shift was a viable option) is probably too
short (too much overlap) and it would be more like 120 or 135
degrees, however, even with 120 or 135 degrees there would still be
a "both-off" time lapse in which no taps were sounding.

What I realized was that you need two sinewaves 180 degrees out of
phase, and each one HWR. The positive haves of the first one control
VCA 1's gain and the positive halves of the second one (which occur
at the zero output of the first one), would control VCA 2. In
addition you need some way of making the beginnings of those HWR
alterations overlap with the signals are increasing to full peak as
well as decreasing back to zero.

Bear with me for a moment because the next few paragraphs get a
little more geeky than ANY of my previous discussions :)

I have not worked this out mathematically but based on experience
with these sorts of things in my career the following explanation
seems most intuitively obvious.

This (simple out-of-phase non-overlapping HWR) does not approximate
the transfer function of the actual scanner since there is a time
when one set of fixed plates (FP) is fully transferring signal to the
rotor, and as the rotor swings to the next set of FP, the signal from
FPn is fading while the signal from FPn+1 is increasing until the
signal from FPn+1 is fully transferring signal to the rotor and the
process repeats with subsequent plate pairs. Because of the rotor's
mechanical design there is never a time when only one plate's
contribution is heard (if I'm understanding the picture of the open
scanner correctly)

Since the rotor swings in a circular motion, and a sinewave is a time-
domain representation of the angular position on a circle, a
simplified model can be considered where any single set of FP can be
loosely viewed as representing the 180 degrees of the circle and the
rotor passing through in a circular motion scanning 0 to 180
degrees.

As the rotor begins coming through a FP set its transfer gain
increases from zero (at 0 degrees of our model) towards full transfer
when the plate set exactly coincides with the rotor (90 degrees of
our model) and decreases back to zero (at 180 degrees of our model)
as it swings through the plate set and inter-FP gap. An adjacent set
of plates repeats the process, but since the rotor can be in
proximity of two plate simultaneously there is a complex interplay
between the signal on FP1 and the signal on FP2. It seems intuitive
to me that this might be something like:

Rsig = K*(sin(FP1_angle + gap_angle)) + K*(sin(FP2_angle + gap_angle))

Where K is some gain constant resulting from interelectrode
capacitance, dielectric effect of the air and insulators, and
frequency of the signal on the FP, and FP2_angle in the case of 2
sine waves 180 degrees apart and each of them HWR, is approximately
equal to 180 + FP1_angle.

Because of the gap and the fact that the moving rotor has a
constantly changing overlap as it passes from the first to the second
set of plates, there would always be a case where FPn and FPn+1 would
contribute to the rotor signal simultaneously until the rotor had
left FPn completely (as the trailing edge was passing through the
gap). At this particular instant the transfer gain of the rotor and
FPn+1 would be very near full with very little CHANGE in gain
resulting from changes in rotation angle.

I would imagine that if you had a butchered scanner with only two
plate sets on it, and placed a positive voltage on one plate and a
negative voltage on the other and observed the output of the rotor
with an oscilloscope, it would look very close to one cycle of a sine
wave as the rotor swings through the FP sets.

Now back to the original discussion: since both plates of an adjacent
set contribute to the sound at the rotor, mimicking this
electronically is accomplished by shifting the baseline of the
signals from zero BEFORE HWR, thereby creating the overlap (I wish I
could post a picture to illustrate this - a picture is definitely
worth a thousand words!), and cancelling this baseline shift AFTER
HWR, so that zero volts represented zero VCA gain.

This results in a transfer function that very closely approximates
the interplay between any two FP sets and the rotor in the mechanical
scanner.

Regards,
Kevin