Hi Bill
If you put two intergrators in a series loop, you'll find that over time,
they will dampen out. I've seen various explanations for this on the
web. One says that careful balancing is need while another says that
it needs more gain.
I tried fiddling with the balance and it mad no difference. The half time
was about the same. Then I tried input gain. It made a nice elipse
instead of a circle that would dampen out.
I then realized that both were wrong. It was phase error. We like
to think of intergrators as exactly 90 degrees but that isn't
true. The actual gain of the amplifier, not being infinity, means
that there will always be a small phase loss on each cycle.
It is like snipping a little off each cycle.
I found that adding one highly divided down inverter across
one of the intergrators was enough to compensate for the
lost energy on each cycle. On mine, unit, it uses transistor
opamps. These have a gain between 1000 and 10,000
someplace. I attenuate the signal with a large series resistor
and a gain pot attenuator until I just balance the loss.
Because I run a really long cycle for the main circle, I want
to make sure the faster cicle ( running about 50:1 ) will
not significantly dampen on one full loop around the large
slow circle. I use my Nicolet scope ( digital ) with a really
stretched out display to look for either increasing or descreasing.
Another way to deal with it, that works well with tube
opamps, is to use a diode in the feedback loop. This
works because of the nice high voltage swings.
First get a slighly increasing oscillation by the method
above. Then put two diodes in reverse parallel onto
a tap of the feedback used of the strait opamp.
In this case, it is recommended to put that attenuation
on the output of the straight opamp because you
want to get enough voltage to turn on the diodes.
If this doesn't make sense, I'll try to put together
a pdf.
Dwight
