Re: [TCML] VSWR, Q factor, Loads and Impedances

["DC Cox" <resonance@xxxxxxxxxxxx>]

Interesting comment.

But, you made the initial assumption the loads are purely resistive, and I'm
not sure that's the case especially with
large coils.

Dr. Resonance




On Tue, Dec 23, 2008 at 5:52 PM, Paul Nicholson <tcml87@xxxxxxxxxxx> wrote:

> From another thread:
> > Low VSWR can assure more radiation than a high VSWR which
> > insures large sparks.
>
> > I'm not sure that the concept of VSWR is even applicable
> > to Tesla coils.
>
> VSWR doesn't have any great meaning here.
>
> It would start to apply if you broke the connection between coil
> base and ground and inserted an RF source.   Then the VSWR would
> be the ratio of top volts to base volts once the steady state
> condition has been reached - ie once the resonator has 'rung up' and
> the continuous power coming in from the source balances the power
> dissipated in the resonator's losses and load.
>
> Consider a loss-free resonator with some load Zload applied.  If
> the resonator has characteristic impedance Zc, then the input
> (base) impedance seen by the source is
>
>  Zbase = Zc^2 / Zload
>
> This is the impedance 'inversion' effect of a quarter-wave resonator.
>
> If the power passing from source to load is P, and all the
> impedances are purely resistive, then
>
>   P = Vbase^2 / Zbase
> and
>   P = Vtop^2/ Zload
>
> (since no power is lost in the loss-free resonator)
>
> Equating these, we get
>
>   Vtop/Vbase = sqrt( Zload / Zbase) = VSWR
>
> and pulling in the 'inversion' equation,
>
>   VSWR = Vtop/Vbase = Zload / Zc = Zc / Zbase
>
> Suppose now another case, this time a lossy unloaded resonator
> having Q-factor Q.  In steady state we have
>
>   Zbase = Zc / Q
> and
>   Vtop = Zc * Ibase
> and
>   Vbase = Zbase * Ibase
>
> Putting these together gives VSWR = Vtop/Vbase = Zc / Zbase = Q
>
> So the VSWR here has the same value as the Q factor, although they're
> distinct quantities with different definitions.
>
> When our RF source is removed and the base is grounded again, we
> can no longer use the ratio Vtop/Vbase since Vbase is now clamped
> to zero.  The VSWR becomes undefined and we must use instead the
> Q factor.
>
> --
> Paul Nicholson
> --
>
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