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Re: AC coil resistance equation
James and all,
Calculating Rac ahead of time is not trivial, since there are many
effects at work that can make the AC resistance of a coil markedly
different than the DC resistance. Quite honestly, it's much easier to
simply measure it with a signal generator and oscilloscope AFTER you've
made the coil. For those who want to grind through the calculations and
charts, probably the best single reference is Frederick Terman's "Radio
Engineer's Handbook", McGraw-Hill Book Company, 1943, 1019pp. Refer to
the section dealing with copper losses for air-core coils, pages 74-80.
There appear to be no closed-form equations that cover all of these
losses. While this treasure is, unfortunately, out of print, it may
still be found in libraries and hamfests, and is available for sale on
the Web. Check out: http://www.mxbf-dot-com/ OR
http://www.bibliofind-dot-com/cgi-bin/texis.exe/search.vor
Physically measuring Rac is best done by connecting a non-inductive
resistive decade box in series with the base of your resonator (toroid
in place), and driving it with a low impedance sinusoidal RF signal
generator. A batch of low valued carbon resistors can also be used, or a
low resistance pot (with some loss of accuracy if it's wirewound). By
setting the signal generator to match the resonant frequency of the
resonator and toroid pair, you can then carefully adjust the series
resistance so that the voltage drop across the series resistance is
exactly HALF of the applied voltage.
At resonance, the impedance of the resonator drops to the AC resistance
(Rdc plus any additional AC resistance due to skin and proximity
effects). By adjusting the series resistance so that HALF of the applied
voltage is across the series resistance, you've now set Rseries = Rac.
BTW, do not try to measure the voltage at the top of the toroid, since
the loading will really mess up your other measurements. Now carefully
remove the series resistance and measure its value (or read it if using
a decade box). Depending upon the coil and operating frequency, Rac will
typically be in the range of 3-5X Rdc.
One other note: To get a better estimate of the non-breakout Q of your
secondary system, you'd need to add the groundpath resistance of your
resonator's base ground to the above value of Rac in order to get an
estimate of the overall "effective" Rac of the resonator/toroid/ground
system. Using this value in the denominator for the equation for Q will
get you much closer. A poor grounding system will significantly reduce
Q, AND your system's performance.
Safe coilin' to you!
-- Bert --
Tesla List wrote:
>
> Original Poster: "bmack" <bmack-at-frontiernet-dot-net>
>
> From: "bmack" <bmack-at-frontiernet-dot-net>
>
> ----------
> > From: Tesla List <tesla-at-pupman-dot-com>
> > To: tesla-at-pupman-dot-com
> > Subject: Re: AC coil resistance equation
> > Date: Thursday, August 27, 1998 9:46 PM
> >
> >
> > From: "James" <elgersmad-at-email.msn-dot-com>
> > "JAMES" wrote:
> >" I thought the AC resistance equation for coils was 2 pi freq(in Hertz)
> H(in
> > Henrys)."
> >
> > James:
>
> You have the equation for inductive reactance, Not the resistance!
> They are very different. I don't know how to explain it without going
> into a long disertation that may only confuse you.
> Resistance and reactance combined is called impedance.
> Impedance is the pathagrean sum of the two.
>
> Z=sqrt(R^2+X^2)
>
> Z= impedance
> R=resistance
> X=reactance
>
> Unloaded Q, Qu=X/Rac -This determines the Quality factor of the coil.
> Energy is lost via heat due to the Rac ( real, resistive part).
>
> An impedance also will cause a phase shift between E and I
>
> But then there's conjugates and resonance ....etc.
>
> Like I said, it can get involved. I suggest you curl up with a
> basic electronics book to fill in the blanks. Then we can help
> take the rough edges off the experience
>
> Jim McVey