# Re: Frequency splitting and measuring Q

• To: tesla-at-grendel.objinc-dot-com
• Subject: Re: Frequency splitting and measuring Q
• From: "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
• Date: Tue, 2 Apr 1996 13:45:47 +1200
• >Received: from rata.vuw.ac.nz (root-at-rata.vuw.ac.nz [130.195.2.11]) by uucp-1.csn-dot-net (8.6.12/8.6.12) with ESMTP id SAA26835 for <tesla-at-grendel.objinc-dot-com>; Mon, 1 Apr 1996 18:46:15 -0700

```Skip Greiner writes...

> Richard Quick and Richard Hull have both mentioned frequency spliting
> when the primary and secondary are overcoupled. I would appreciate it
> very much if someone could explain exactly what splitting is and how it
> exhibits itself.

When you have a double-tuned circuit having the property that kc < k
(critical coefficient of coupling < coupling constant), the system
resonates at 2 frequencies, one at either side of the "real" resonant
frequency. k is fixed in a system, but kc is related to the Q's of
the two coils by : kc = 1/SQRT(Qp x Qs). It is caused by the mutual
inductance reflected into the primary and secondary coils. The split
disappears when kc = k and this happens when the coils are sparking
(Q drops dramatically - see recent posts by Richard Hull, myself
and others). When kc=k, the system is said to be critically coupled
and power throughput hits a maximum. You can see the effects when
scoping a coupled system single-shot. The scope shows a DSBSC envelope
characteristic of the two frequencies produced. The frequencies beat
together and reach in-phase coincidence in the primary and secondary
You can also see the twin frequencies by attaching a sig. gen. to
the primary circuit via a high impedance and scoping the secondary.
In this case, you get two response peaks and a null between them
(where the correct frequency would occur).

> I suppose if the phenomenom is present then the solution
> is to decouple until it goes away... right?

The twin frequencies will merge when the system is
sufficiently heavily loaded (Qs drops as the secondary spark grows
while Qp is very low anyway due to primary spark). If you arrange
k = kc under non-sparking conditions, you will never get any power
through the system. You will find that the high Q of the coils makes
kc an incredibly small value and that setting k to match this
requires that the coils be separated by several feet.

> With regard to measuring Q. It seems to me that someplace I have seen a
> formula for Q as follows:  Q = fc / (f1 - f2).  Where fc is the resonant
> frequency of a coil, f1 and f2 are the higher and lower frequencies above
> and below fr where the voltage drops to .707 of the value at fr. Is this
> valid or have I got something wrong ?

Exactly right IMO.

Malcolm

```