## PSN-L Email List Message

Subject: Re: Etc.
From: Karl Cunningham karlc@.......
Date: Sat, 22 Jan 2000 10:47:08 -0800

```At 06:29 PM 1/21/2000 -0500, you wrote:
>All one has to do is pass a sample of that error voltage through a high
>pass filter (only dynamic elements with a period LESS than say 300
>seconds are measured) and on to the signal processing circuittry.
>After one or two integrations (this always seems to kick up a few
>postings...let's see.  The first integration of acceleration
>would give velocity and then integrating velocity gives
>displacement...I think.  But there again, is the high pass filter
>actually the first integration? I think so, so the >signal at
>that point would be velocity. See what I mean? ).

I guess I'll have to start going to those meetings again... Poster's
Anonymous.  I thought I was strong and could resist posting a reply about
integration.  But alas, I've succumbed to temptation...

Integrating the signal is not always as easy as it seems, especially twice.
Sure, the integrators can be built, but the gain of an integrator is
inversely proportional to frequency.  So, using your example, to obtain a
range of period from 300 seconds to 0.2 seconds (5Hz) requires a range of
1500:1 in the gain of the stage.  That means any
low-frequency instability in stages before the integrator will be
multiplied by as much as 1500 on the way to the output.  Integrate a
second time and it's the square of that value -- 2.25 million.  That's bad
news.  I tried this one time and found out the hard way -- after I had
constructed the circuits.

Also, I don't think the high-pass filter is the same as integration.  It's
closer
to a derivative function over some range of frequencies (gain increases with
frequency), but still isn't really that either.

I think there is an answer to this problem, though.  The VBB design puts
a derivative function in the feedback, in the path to the feedback coil.
And since (in the bandwidth of interest) the current in the feedback coil
is proportional to acceleration (guaranteed by the mechanical dynamics, and
the fact that loop gain is kept fairly high), the signal ahead of the
derivative function has to be velocity.  You can then integrate this
function once to get displacement.

Karl

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Larry Cochrane <cochrane@..............>