TSSP: List Archives

From: Paul
Date: Sat, 06 Jul 2002 15:00:13 +0100
Subject: Re: [TSSP] Re: Top V Probe Design

Terry wrote:

> http://hot-streamer.com/temp/Jennings-JP-325/Diagram.jpg

Thanks, your annotations make things a lot clearer. Are you
planning to try this unit inside a TC?  Wonder how conservative
Jennings are with their ratings.

By way of a recap on all this

1/ We want to know how much charge flows into/out of the streamer
load on each cycle of the beat, and how much energy is dissipated
in the process.  We want to see how much, and how sharply this
limits the topvolts rise below the value predicted without
breakout.  We also wish to see just what the breakout voltages
are in order to see if a particular surface field strength 
threshold is involved.

2/ All of the above can be obtained quite accurately by
simultaneously recording the top voltage and the base current,
through a dual trace scope into a data file.

3/ We must ensure that we record a signal proportional to the
top voltage rather than the top charge,  otherwise we discard
the very effects we want to examine.

4/ The top voltage pickup must not be sensitive to coil charge.

5/ The top voltage, capacitance, and total charge are related
by   

   Q = C V

We have to treat all three quantities as functions of time, so
the differential is 

   dQ/dt = C dV/dt + V dC/dt

We get at dQ/dt by noting that the coil base current is the sum
of the displacement currents dQ/dt of the topload, and Ces dV/dt
of the coil itself,

    Ib = dQ/dt + Ces dV/dt

The Ces dV/dt term is calculated from the V trace and subtracted
from the Ib trace to obtain dQ/dt.  So far the only approximation
involved is to assume Ces is constant with time.

6/ Then, since dQ/dt, dV/dt, and V are all measured,

   dQ/dt = C dV/dt + V dC/dt

becomes a differential equation in C which we can solve.  This
would involve a least-squares curve fit and the error introduced
here will depend on how clean the waveform capture is.  This gives
us C as a function of time.

7/  Applying Q = CV, and taking C(t) to be Ctop + Cstreamer(t),
we can then calculate Cstreamer and its charge as a function of
time during the whole firing event.

8/ There are three sources of error,
   a) Absolute error of the V and Ib measurements.
   b) Approximation of Ces as constant.
   c) Trace noise and limited information content
      (10K points by 8 bits).
(a) can be calibrated out, say to 1%
(b) can be estimated by computing Ces for a range of estimated
streamer loads, and revised once a real streamer load is 
measured.
(c) we have to live with.  We cannot expect to average multiple
shots because the fine detail of the streamer loading will not
be coherent from one shot to the next.

9/  The modeling software is only involved as far as calculating
values of Ces and Ctop.

Well, there's some notes to be thinking about.  Anyone spot any 
problems?  It seems to me that once we crack this top-V measurement
problem, it opens up quite a pandoras box.

--
Paul Nicholson,
--


Maintainer Paul Nicholson, paul@abelian.demon.co.uk.