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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>
Thanks for the kind words. As with many aspects of coiling, it's
sometimes easier to build a system, and then measure certain parameters
after the fact. This appears to be the case with resonator proximity
effect losses and resonator base impedance. Terman's proximity effect
analysis assumes lumped behavior - that the same current flows through
all portions of the resonator. We also know that the resonator base
current is ultimately balanced by the displacement currents "flowing"
through the distributed capacitances of the resonator and topload - and
that these currents are not the same in all portions of the resonator.
This makes Terman's approach of estimating proximity effect of limited
use in base-driven resonators.
We can most likely assume that other resonator losses (such as coilform
and wire insulation dielectric loss, leakage currents, corona, or
radiation losses) are negligible compared to the resistive losses in a
well constructed resonator. However, if we wanted to accurately measure
proximity losses of the secondary itself, we'd need to directly drive it
as an inductor (horizontal orientation, same entry and exit current),
measure its L and Q, and then backfigure it's effective AC resistance.
We can then remove the DC resistance and the estimated skin effect
resistance, leaving proximity effect resistance. However, this only
tells us what the proximity effect losses would be if the secondary was
used AS AN INDUCTOR. However, since current is non-uniform in a
resonator, the value we obtain for the coil when used as a "lumped"
inductor will be of limited value when the coil is used as a base-driven
Let's suppose instead that we measured the base impedance when the
secondary is being used AS a resonator. In this case, we'll be
introducing grounding impedance into the RLC circuit, since the
resonator/topload displacement currents must ultimately make their way
back through the surrounding lossy grounding system in order to complete
the AC circuit back to the base of the resonator. Now, even if attempt
to remove the resonator's DC and skin effect contributions as we did in
the measurement above. We are still left with the combination of
grounding system and proximity effect losses in our measurement.
As Paul indicated, grounding losses can vary significantly with soil
type, moisture, the integrity of the grounding system, the phase of the
moon, etc... :^). A poor grounding system can easily introduce losses
which are much greater than those of the (pre-breakout) resonator alone.
>From a practical standpoint, it appears that base resonator impedance
may not be fully predictable, but must instead be measured after the
-- Bert --
Web Site: http://www.teslamania-dot-com
Tesla list wrote:
> Original poster: "Barton B. Anderson by way of Terry Fritz
> Hi Bert,
> Excellent write up of skin effect and proximity losses.
> Question about proximity losses:
> Assuming at resonance reactances cancel leaving the above losses, you
> mentioned there is no closed-form
> approach that can be used to estimate proximity effect. It seems to me that
> once calculating and removing
> skin effect losses, that what is left over can be attributed largely to
> proximity losses. Obviously a
> measurement is required to identify losses, then break down the losses into
> their respect catagories and
> lump the remaining to proximity losses. I'm sure eddy currents and misc.
> losses will be part of this
> value, but the largest contributor should be the proximity losses. It's not
> a "closed-form" method, but
> would this approach work?
> Tesla list wrote:
> > 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 --