Re: Resonator base impedance (help needed)

```Original poster: "Bert Hickman by way of Terry Fritz <twftesla-at-uswest-dot-net>" <bert.hickman-at-aquila-dot-net>

Richie and all,

At 1/4 wave resonance an RLC model will work quite well as long as the
impact of skin effect and proximity effects) are factored into computing
Q. These losses, while frequency and geometry dependent, show up as an
additional resistive loss above and beyond the simple DC resistance of
the resonator. For resonators that are "short" compared to wavelength,
radiation losses are very minor and can safely be ignored. And as you
indicate, at resonance the inductive and capacitive reactances should
cancel leaving only the real AC resistance as the effective input
impedance. Approaches that reduce DC resistance and skin and proximity
losses without proportionally reducing inductance will increase the
pre-breakout Q.

Since skin effect is mainly a function of the wire's conductivity,
diameter, and operating frequency, skin effect losses can be reduced by
using larger diameter copper (or silver plated copper) wire, multiple
overlapping layers of wire connected in parallel, Litz wire, and by
operating at a lower resonant frequency. Skin effect can be fairly
easily estimated using a closed-form equation if you know the wire's
diameter, conductivity, operating frequency, and magnetic permeability
(usually 1).

Proximity effect further reduces the region of conduction in the wires
formed into a coil. Proximity effect is caused by the effect of magnetic
fields from adjacent conductors, and it further increases the observed
AC resistance of the wire. Unfortunately, proximity effect is also
considerably more difficult to reduce without also reducing the
inductance of the resonator (using techniques such as space winding).
Further complicating practical before-hand estimation is that there
appears to be no closed-form approach that can be used to estimate
proximity effect, although the losses can be as large, or even larger,
than those stemming from skin effect alone. The only text that I'm aware
of that covers practical estimation of both skin and proximity effects
for single-layer and multi-layer inductors is Terman's excellent 1019pp
tome, the "Radio Engineers Handbook, McGraw-Hill, 1943.

-- Bert --
--
Bert Hickman
Stoneridge Engineering
Email:    bert.hickman-at-aquila-dot-net
Web Site: http://www.teslamania-dot-com

Tesla list wrote:
>
> Original poster: "R.E.Burnett by way of Terry Fritz
<twftesla-at-uswest-dot-net>" <R.E.Burnett-at-newcastle.ac.uk>
>
> Hi all,
>
> I have a question for those in the know about resonators:
>
> How can I calculate the input impedance at the base of a Tesla Coil
> at resonance,  before breakout ???
>
> I know how to measure the base impedance using an RF source with
> voltage and current probes.  However,  I would like to know if I can
> estimate the base impedance at the design stage before winding the
> actual resonator.
>
> Gut feeling suggests that the impedance should depend on Ls and Cs.
> However it seems that the H/D ratio and wire size may also play a
> significant part in determining Zbase ???
>
> Also,  since a resonator can be modelled as a series RLC circuit in
> which Xl and Xc cancel out at resonance,  then the input impedance
> would seem to be a pure resistance equal to R ???  Does this mean
> that the usual measures taken to increase Q factor (minimise R) will
> also decrease the base impedance of a given resonator ???
>
> I have only seen mention of base impedance in Gary Johnsons paper.
> This refers to DC resistance,  skin effect,  radiation resistance,
> etc..  but does not give an explanation for the measured Zbase.
>