# Re: More ISSTC theory stuff (l o n g)

```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>

> But did you do this simulation assuming a fixed frequency drive, at the

This circuit has actually two resonances. The driving frequency for the
loaded case is between them. I just kept the same frequency while
changing
the parameters.

> We are now using self-resonant and PLL drive
> circuits that adjust the inverter frequency to keep the primary current in
> phase with the voltage. The reason being that our IGBTs like zero-current
> turn-off.

This makes some difference, but the current still increases if the
keep the voltage and current in phase. This happens because of the
mistuning of the primary and secondary circuits changes the impedance
conversion factor.

> I _think_ that with one of these drive circuits, the reactive component
> would just be forced to go away. Unless the circuit was in a state such that
> there was _no_ frequency at which the input impedance was purely resistive,
> in which case I have no idea what would happen, but it would probably be
> spectacular and expensive.

There is always a frequency where the input impedance is resistive.
Actually,
if the load resistance increases, there are three frequencies where this
happens. The normal one, and others at both sides of it. The maximally
flat design is the limit case between just one frequency and three where
the input impedance is resistive.

> I mentioned the L-match thing to Richie Burnett and he tried base-feeding a
> resonator straight from the inverter, through a L-match network. His setup
> is like an ISSTC in that it shows the desirable dual resonant behaviour (no
> "magnetizing current") but also like one of your directly-coupled spark-gap
> coils in that the voltage gain n=1. However it seems to perform just as well
> as an ordinary SSTC.

Yes, it's possible to design the coil in this way. But in this case it's
not possible to obtain a maximally flat characteristic on the input
impedance ("maximally resistive"). The exact design would be based on a
Chebyshev bandpass filter, that also makes the impedance conversion.

> I think the inductively coupled ISSTC might still have the advantage for
> high powered coils though, since it has an extra untuned transformer (n) to
> help with the impedance matching, thus the primary "L-match" can have a
> lower loaded Q and hence lower losses.

Yes, the required Qs are lower in this case (with transformer).

>  >I get: In 200 us: 2.4 J
>
> whoops, it looks like I missed out a 1/sqrt(2)

Another way to make this calculation:
Consider a square wave with peak amplitude Vmax and a sinusoidal current
with peak amplitude Imax:
Average power = (1/Pi)*Integral (0, Pi) of Vmax*Imax*sin(x) dx
= (2/Pi)*Vmax*Imax.
The result is the same of when only the fundamental sinusoids are
considered
and their rms values are multiplied:
Average power = (4/Pi)*Vmax/sqrt(2) * Imax/sqrt(2) = (2/Pi)*Vmax*Imax

Antonio Carlos M. de Queiroz

```