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Re: Neumann's integral for mutual inductance
Subject:
Re: Neumann's integral for mutual inductance
Date:
Wed, 26 Mar 1997 04:03:08 -0700
From:
"DR.RESONANCE" <DR.RESONANCE-at-next-wave-dot-net>
To:
"Tesla List" <tesla-at-pupman-dot-com>
To: Dr. Rzeszotarski:
Found your comments on the 4:1 ratio interesting. We have constructed a
number of loose coupled classical resonators and found the 4:1 ratio
also
to be very effective with resonators in the 18 to 36 inch dia. We
usually shoot for 900-1000 turns on the secondary inductor as an optimum
value with loose coupling. With smaller dia. resonators such as 2-3
inch
dia. a ratio of 6:1 to 7:1 seems to optimize. Again with loose coupling
in
the classic pri-sec coil configuration (non-magnifier).
If time permits please post a short example of using Neumann's line
integral in the calculation for a classic coil configuration. I thought
this was interesting. We have measured mutual inductance of several
resonators but are unfamilar with this integral application. Please
post
some information so we can test this theory against our practical
measurements.
DR.RESONANCE-at-next-wave-dot-net
----------
> From: Tesla List <tesla-at-pupman-dot-com>
> To: tesla-at-poodle.pupman-dot-com
> Subject: Re: Primary field size
> Date: Monday,March 24,1997 7:41 PM
>
> Subject:
> Re: Primary field size
> Date:
> Mon, 24 Mar 1997 09:08:57 -0500 (EST)
> From:
> msr7-at-po.cwru.edu (Mark S. Rzeszotarski, Ph.D.)
> To:
> Tesla List <tesla-at-pupman-dot-com>
>
>
> Hello All,
> Kevin M. Conkey said:
> >How can you determine the useful field size that a given primary puts
> >out?
> You can determine it by calculating the mutual inductance
> between
> the primary and secondary, using Neumann's formula for the line
> integration.
> Having said that (and having calculated quite a few), you really don't
> need
> to. Whether you use a flat spiral or an inverted cone geometry, most of
> the
> coupling will be close to turns near the base of the coil. If you have
> a
> specific geometry you want to evaluate, send me private E-mail and I can
> do
> the calcs for you.
>
> >How did someone come up with the aspect ratios of pri/sec? Was it
> >strictly through trial and error, or can you figure it out?
> The general rule of thumb of using a primary height/diameter
> ratio
> of between 3:1 and 4:1 for diameters larger than 3 inches or so was
> developed empirically by a number of experimenters. Smaller coil
> diameters
> may necessitate higher ratios, in order to increase the inductance.
> I have investigated the secondary using a helical resonator
> model
> similar to that employed by the Corum brothers, with additional more
> realistic component values, and have found similar results. There is
> little
> to be gained by using H/D ratios in excess of 4:1. I build all of my
> conventional coils using a 3.5:1 ratio now.
> Most of the primary energy couples to the secondary near the
> base of
> the coil. ( I have posted graphs of this, available in the archives.)
> As a
> result, coil height is unimportant from a mutual inductance standpoint.
> Resonant rise is what you want to optimize, and the tradeoff between
> resonant rise and coil losses (due to A.C. coil resistance and
> distributed
> capacitance) limits the optimal ratio to around 4:1 or so.
>
> Flames, comments welcomed,
> Mark S. Rzeszotarski, Ph.D.