Re: 2-Coil Tuning

To: tesla-at-pupman-dot-com
Subject: Re: 2-Coil Tuning
From: MSR7-at-PO.CWRU.EDU
Date: Tue, 28 May 1996 07:54:48 -0400
>>From MALCOLM-at-directorate.wnp.ac.nzMon May 27 21:56:04 1996
>Date: Tue, 28 May 1996 09:31:55 +1200
>             I was moved to conduct some scope experiments in the 
>weekend due to the fact that my coils are working at peak performance
>with considerably more Lp than is required to tune the primary to the
>secondary fr. I used to think that the higher Lp was offsetting the
>ion cloud/corona capacitance. I still think that is an important oper-
>ational mechanism, but something else also happens.
>     With the coils tuned to the same frequency and coupled to a 
>working degree (say about 0.1 or so), the double-humped frequencies
>are around equal amplitude. But by lowering the primary frequency
>beyond this, the higher of the two split frequencies diminishes in 
>amplitude considerably while at the same time, the lower of the
>frequencies rises in amplitude. It seems that by so tuning, the coil 
>output is tending to single frequency operation at the lower of the 
>two split frequencies with a much greater concentration of energy at 
>just one frequency.

Hello Malcolm and other coilers,
        I took a look at Terman's text (Radio Engineers' Handbook,
McGraw-Hill, 1943, pp 154-163) to see what he said about this.  I, too, have
wondered if one should drive a coil at one of the split frequencies, for
example.
        In discussing the double humped appearance in inductively coupled
double tuned circuits, Terman states: "In cases where unsymmetrical peaks
are obtained, the low-frequency peak will be depressed when the secondary is
tuned to a higher frequency than the primary and the secondary Q is higher,
or when the secondary is tuned to a lower frequency and the secondary Q is
lower."
        Observation:  This may provide a mechanism for identifying the
relative Q's of the primary and secondary in a dynamic mode of operation.
        Terman also states that the secondary current is a maximum when
K=Kc, if the two coils are tuned to the same frequency, and driven at that
frequency.  Any change in operating frequency or coupling causes a falloff
in maximum possible current.  He also states that operating the coil pair
off resonance will reduce the ratio of the output voltage to input voltage.
Terman does not consider the case for maximum energy transfer, however,
which is probably more interesting to us.
        Terman goes on to discuss the impedance matching necessary to
maximize the current in the secondary.  He says that the maximum secondary
current is achieved when:
Rp=(w x M)^2 x Rs / (Rs^2 +Xs^2) and Xp=(w x M)^2 x Xs / (Rs^2 +Xs^2)
where:
w = 2 x pi x F
M = mutual inductance
Xp=primary reactance component = w x Lp
Xs=secondary reactance component = w x Ls
Rp=primary resistance component
Rs=secondary resistance component
This can only occurr is w x M is greater than or equal to the square root of
Rp x Rs.  Now, if I could just measure Rs and Rp accurately while producing
sparks!

Regards,
Mark S. Rzeszotarski, Ph.D.