# RE: K Factor & Mutual Inductance

```Subject:
RE: K Factor & Mutual Inductance
Date:
Sat, 12 Apr 1997 04:44:13 +0000
From:
"John H. Couture" <couturejh-at-worldnet.att-dot-net>
To:
Tesla List <tesla-at-pupman-dot-com>

At 11:54 PM 4/10/97 +0000, you wrote:
>
>
>Heinz, John, all,
>
>> John,
>>
>>         You state that the R is effective, not DC or AC. Why can't you
>> measure the R of the coil, calculate the XL, at the
>> expected frequency of operation, and use the result to find a ballpark
>> Q? Could you elaborate on effective R?
>>
>> Heinz
>>
>> >
>> >
>> >Hi John, All,
>> >Have you ever tried the formula Q = sqrt( L / C ) / R.
>> >
>> >Barry
>> >
>> > ----------------------------------------------------
>>
>>   Barry -
>>
>>   I have never seen the above Q factor equation before. What would you
>> use
>> for R? In the usual equation   Q = X/R   where X = 6.283 F L  the R is
>> an
>> effective resistance, not DC or AC.
>
>What???
>
>    The "R" in the equation is the ESR (effective series resistance)
>as it is for wL/R etc. ESR is measured at the frequency of operation
>since it is frequency dependent due to skin effect.
>
>Here is the derivation for the equation above:
>=> Q^2 = wL/R x 1/wCR
>=> Q^2 = L/C x 1/R^2
>Therefore Q = SQRT(L/C)/R
>
>(the => means "implies" for those without the math background)
>The above formula appears in The Radiotron Designer's Handbook among
>others.
>    Lastly, the ESR can be converted to an equivalent shunt resistance
>by: shunt R = (1+Q^2) x ESR
>
>Malcolm
><snip>
>
> ---------------------------------------------------------

Malcolm -

Thank you for the derivation of Q = sqrt(L/C)/R.  I lost my Radiotron
years
ago (a good book). I did find the derivation in Henney's Radio
Engineering
Handbook.
The sqrt(L/C) is shown in my TC Notebook to calculate the secondary
circuit
peak current. This is the equivalent of Zo in Ohms law. The Zo and Xo
are
consudered almost equal for these calculations.

Apparently we both agree that the R is not the DC or AC resistance. It
must
be determined by calcs after finding the Q and the X of the coil. The Q
is
found by Q = Fr/(F2-F1) where Fr is the resonant frequency and F2 and F1
are
the half power points. The X is easily found by solving  X = 6.283 Fr L.

John Couture

```