Re: More ISSTC theory stuff

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Antonio Carlos M. de Queiroz" <acmdq-at-uol-dot-com.br> 

Tesla list wrote:
 >
 > Original poster: "Steve Conner" <steve.conner-at-optosci-dot-com>
 >
 >  >This structure can be designed exactly to have any bandwidth,
 >  >and any voltage gain or any input resistance, by using the same
 >  >procedures used in the classical design of passive filters.
 >
 > OK... cool... I agree totally. But what I am trying to find out is the magic
 > values of bandwidth, voltage gain, and input resistance, that will give
 > biggest streamer output from a given set of IGBTs, with reasonable tolerance
 > to detuning by streamer load.

The input resistance is determined by the amount of power that you have
available, and your switching devices. The voltage gain, is as
mysterious
as in a conventional coil. I guess that anything that produces more
than about 80 kV will work. The bandwidth affects mainly the coupling
coefficient between the coils, and the sensitivity to mistuning.
The big problem is to guarantee good matching for any load, what seems
impossible. Another problem is that the load is not purely resistive,
but has a small capacitance in series with it. No big problem, as
this can be converted to a parallel equivalent, with the capacitance
absorbed by the terminal+secondary coil capacitance.

 >  >It's also possible to make approximate designs by considering the
 >  >network as a series of two L-match impedance matching networks,
 >  >one C-L and the other L-C.
 >
 > I like this approach. I think that a lot of the design choices we _could_
 > make in the full bandpass filter network approach are constrained by other
 > things. For instance the coupling will be limited due to clearances for
 > primary-secondary flashover, and the voltage gain achievable in the primary
 > will be limited (I imagine) by such things as flashovers between primary
 > turns.

Surely. Most of the constraints are determined by proper insulation.

 > With the L-match approach, the problem is reduced to matching the real part
 > of the streamer load (several hundred kOhm) to the inverter output impedance
 > (around 1 ohm) The inverter doesn't have an output impedance as such, but
 > you can express the maximum current you want to draw as an impedance.

Yes.

 > (fundamental of inverter output voltage /(peak IGBT current you
 > want/sqrt(2))

Maybe: R=(4/Pi)*peak inverter voltage/peak current. This takes the
fundamental
of a square wave voltage waveform and the current as peak values.

 > I say fundamental because the inverter output voltage is a square wave but
 > our analysis will assume a sine wave. The current is a sine wave anyway.

What I assume above.

 > So my plan is to design the secondary according to good HV practice, choose
 > the highest coupling I can without any risk of flashovers, then choose the
 > primary L and C by treating it as an L-match. What do you think?

I was deriving a set of exact design equations.
Not so complicated at the end, using the filter approach.

Start with the specifications:
R = input resistance, Ohms
w0 = 2*pi*operating frequency in Hz, rad/s
B = 3 dB Bandwidth in rads/s (2*pi*bandwidth in Hz)
n = Voltage gain

Design a bandpass Butterworth (maximally flat) filter:

.    o--C1---L1--+----+----+---o
.                |    |    |
. +->            L2   C2   R2
. |              |    |    |
. R1 o-----------+----+----+---o

R1=R2=R
C1=B/(w0^2*sqrt(2)*R)
L1=sqrt(2)*R/B
L2=B*R/(w0^2*sqrt(2))
C2=sqrt(2)/(B*R)

Convert it to the final structure:

                 kab
.    o----Ca---+   +----+----+---o
.              |   |    |    |
. +->          La  Lb   Cb   Rb
. |            |   |    |    |
. Ra o---------+   + ---+----+---o

Ca=C1
La=L1+L2
Lb=n^2*L2
Cb=C2/n^2
Rb=R*n^2
kab=sqrt(L2/(L1+L2))

Note that the relation La*Ca=Lb*Cb holds, as in a capacitor discharge
coil.

Ex:
With 180 V of input voltage (a full bridge from 127 V rectified and
filtered)
and peak current of 100 A:
R=2.29 Ohms
With n=500, operating frequency of 300 kHz, and a bandwidth of 50 kHz,
the final elements result as:

Ra:  2.29 Ohms
Ca:  27.3 nF
La:  10.5 uH
Lb:  35.8 mH
kab: 0.117
Cb:  7.86 pF
Rb:  573 kOhms

Not very different from the usual for a capacitor discharge coil. This
coil
presents a constant resistance to the driver of 2.29 Ohms at 300 kHz,
with
little deviation for errors up to 25 kHz to each side. It remains to be
seen
what is the effect of different loads, and what happens before breakout,
and
if something can be done to improve the characteristics in these cases.

Antonio Carlos M. de Queiroz