Re: [TCML] DRSSTC ring-up

["Udo Lenz" <udo_lenz@xxxxxxxxxxxxxx>]

   Hi Steve,

> > The reason for this has to do with the location of the poles. If the
> > primary
> > is tuned lower than the secondary, the lower pole will be located somewhat
> > below the primaries resonant frequency. The upper pole will lie a bit
> > above the
> > secondary resonance.
> > The upper pole is much closer to the secondary resonance than the lower
> > pole,
> > so running at the upper pole frequency will make your coil much more
> > efficient.
>
> This is something i suspected but still have difficulty proving.  Have you
> done any formal analysis to share on the subject?  My subjective view was
> simply that spark performance remained similar to the lower pole design
> (which had the same operating frequency) but the primary current went from
> ~300A to ~200A in my case.  But i still cant come up with a proof that says
> one pole is better than the other in a general sense.  This is something i
> should work on :-).

Probably the most interesting equation is the one that
describes the dependency of primary current on input voltage.
The expression for the current is quite complicated, but it becomes
much simpler, if we require, that the input voltage is in phase
with the current. That is the case, if the bridge switches at zero
current. I've also assumed, that the input voltage is sinusoidal.
This is obviously incorrect, but due to the high Q of the primary tank,
it will respond with an almost sinusoidal current. I don't believe
that this makes much difference in terms of a TC model.

If you supply a sinusoidal input voltage and have no phase difference,
then the input will just look like a resistor. Its resistance is given
by:

                     k^2 * w^2 * L1 * L2 / R2
R  =      -------------------------------------------
            (1 - w^2/w2^2)^2  +  (w * L2 / R2)^2  

where, L1, C1 and L2, C2 are the primary and secondary tank parameters.
R2 is the streamer load. Its capacitive part can be lumped into C2.
w is the input circular frequency and w2 that of the secondary resonance.

The value of R describes

a) The current the primary will ramp up to. Actually you will have some
resistance losses in your primary. These can be simply added to R in order
to calculate max current.

b) The amount of power transferred to the secondary. The power is

P = Iprimary^2 * R.

A bigger R will increase the coils efficiency but will also limit
the amount of current, you can get into it.

Basically R has the shape of a resonance curve with respect to
the frequency w. It peaks at the secondary resonance, i.e. w = w2.
The largest possible value is then (w at secondary resonance)

Rmax = k^2 *  L1 / L2  * R2

This is reminiscent of a standard transformer, when the secondary
is loaded with R2. That is "transformed" into a primary resistance
of  L1 /L2 *R2.

The secondary resonance is usually the most desirable frequency of operation,
but remember, that we have the requirement of zero current switching. This allows
only 3 possible frequencies, the lower and the upper pole and one
frequency in the middle. The pole frequencies never coincide with the
tanks resonant frequencies, so all we can do is to try to get close.
I find it interesting, that in the equation for R there is no explicit reference
to the pole frequencies or even the primary resonance.

The power potential of a bridge could be used optimally, if R is just the maximum
load, that the bridge can handle, i.e. Imax = Vbus / R. R is a moving target, though,
since it changes with arc load. The expression for R does give some hints on what to do,
if either R is to small (too high currents). You could then try to tune closer, increase coupling
or increase L1.
In the case of R being too large, which would throttle your primary current, you could go the
other way, i.e. detune, decrease coupling, decrease L1.

Antonio de Queiroz wrote:

> This is a text that I wrote earlier this year about drsstc tuning, poles,
> etc:
> http://www.coe.ufrj.br/~acmq/tesla/drsstcexcitation.pdf
> I design the system assuming no losses, aiming for complete energy transfer
> after a given number of cycles, leaving no energy in the system except in
> the output capacitance, the same idea of the conventional Tesla coil.

It depends on the burst length used. In a system with no losses, primary current
will rise without limit, so you will have to shut down the bridge at some time.
I believe some DRSSTCs are run with short bursts because of this.
Arc loading will limit primary current, though, which allows using longer bursts
and correspondingly more bang energy.
(Well, sort of, since the IGBT's are mostly driven beyond specs and can handle that
only for a short time)

Udo


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