Barry, 

Re. Your recent question about increasing the gain of the VRDT
displacement detector. If the gain is too high, short period oscillations
will occur, sometimes strong enough to be visible. They will show up
in the MATHCAD model of the transfer function. Also with higher gain,
phase shift problems in the displacement amplifier will show up;
often changing the capacitor in the low-pass filter will cure them.

The value of "r" does not directly affect the zero stability of the 
VBB system, assuming the loop gain is reasonable. However, if it is
changed without adjusting the proportional damping resistor Rp, the
system will become undamped and will actually oscillate at the feedback
period of several tens of seconds. A partially damped condition would
seem to be a zero instability. Use the MATHCAD model to investigate
the damping change, and make sure it comes out greater than 0.707.

Regarding getting a copy of J. Steim's Harvard thesis: it is 160 pages;
It does say that it is copyrighted, so I really don't want to get involved.
Maybe Harvard has a way of providing a copy.

Regards,
Sean-Thomas

-----------------------------------------
For the reader, here is a review of what I wrote in April regarding using 
a vary large feedback capacitor with a low value of "r".

Regarding the question of using lower displacement gain "r" and a much larger
feedback capacitor Cp: Naturally, you can plug any range numbers into the 
transfer function and get any response you want. Decreasing "r" by 1/50
and increasing Cp by x50 and adjusting the damping can give a flat response.
However, lowering "r" really lowers the high frequency corner, and seismologists
really want something flat to above 50 hz., or at least well above the anti-
aliasing filters of the digitizer. Reducing "r" and increasing Cp causes a
serious reduction of the net output (k=1/(G*Cp), G=Gn/M). This means that an 
amplifier that adds noise and probably compromises the dynamic range needs 
to be put ahead of the digitizer.  One of the major plusses of a VBB 
instrument is that the passive-component feedback results in an inherent 
dynamic range of 120db or more which is not limited by amplifiers.

For reference, for the multi-period design I am using a VRDT with 
200 millivolts/micron, a 10x amplifier, for an "r" of 2 000 000 volts/meter.
With Cp set to 20 uf for all periods, the output is 2100 volts/meter/second,
and the -3db upper frequency corner is at 80hz.

Also, decreasing "r" really limits the sensitivity to detecting small 
accelerations, increasing the noise floor. And if Cp is too large, it
can cause short-period oscillations, which will be predicted by the
MATHCAD worksheet of the transfer function. Making the mass large doesn't help
either; the brownian noise of 0.3kg is below the low noise model for any
reasonable period and Q. Put as a simplistic concept, a smaller mass is 
"easier" for the feedback system to "control". Commercial VBB masses range
from 0.6 to less than 0.1 kg.

You have suggested that you are using 500ufarad with "r" = 42 000. Unless you 
have won the lottery, I assume that this is a pair of 1000 uf electrolytics.
The biggest problem in using a large Cp is that non-polarized electrolytics
are not acceptable for the feedback components. They are very temperature
sensitive in regard to value and leakage. Polypropolyne or polystyrene
are needed. The leakage of these is 10^5 megohm-microfarads or more;
electrolytics have a value as little as 1, and being electro-chemical
cells, are very temperature dependent. And since the dielectric layer is
formed by the imposition of voltage, it degrades with time, or the actual
capacitance varies with the voltage and frequency.

If you look under the hood of the feedback box of a Streckheisn, it is 
packed with an array of pricey cubical 10uf poly capacitors, all measured.
Years ago, I got into a discussion with Mr. Guralp about using tantalum
capacitors in the feedback.  THere was a problem with instability with 
temperature change as the Cp change made the feedback unstable. As far as
I can see, poly caps are used for both the feedback and the integrator C
in all the commercial instruments.

I mentioned the oscillations around 4hz. Aside from the above considerations,
a value we like to ignore is the presumably quite short time constant of 
the displacement detector amplifier. It naturally does have some low-pass 
filtering with associated phase shifts. My original VBB audibly hummed at 
about 400 hz until I added a small RC filter to the amplifier input. I used 
a decade resistor to tweak it until the oscillation stopped, with something 
like 1200 ohms into 4 uf, which I presume was making a phase correction. 

Regards,
Sean-THomas

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