On frequency splitting

[TDAF]

Exactly how and why does frequency splitting occur in tesla coils??
Also, why does the coupling coefficient influence it??

[Hydron]

See the link below for some info, talks about spark gap coils but the same principal applies:

https://web.archive.org/web/20171123202740/https://www.richieburnett.co.uk/operatn2.html#splitting

[TDAF]

Why does the primary and the secondary 'see' more capacitance on the other side??
What's exactly meant by this??

[Uspring]

Imagine 2 pendulums of the same length hanging beside each other. They both have the same oscillating frequency. Now connect the pendulums with a weak spring. The spring is a form of coupling. You will then have 2 oscillating modes, one mode, where the pendulums swing parallel and another mode, where they swing opposite to each other. The parallel mode has the original frequency, but the opposite mode has a somewhat higher frequency, dependent on the strength of the spring.

Coupled tanks in a TC show the same behaviour. The different modes and their frequencies can be characterised by the phases of the currents and voltages of the tanks relative to each other. For some phases the restoring forces (as in a pendulum) in the system become "stiffer", leading to a higher frequency and for other phases it becomes"looser", resulting in a lower frequency.

Generally both modes are excited and the mixture of 2 different frequencies shows up as beats.

[Teravolt]

TDAF hear is a page of physics java applets and you might find what he is talking about in the pendulums lab

http://www.cabrillo.edu/~jmccullough/Applets/oscillations.html

another one is

http://www.falstad.com/mathphysics.html

I found these on google under "java physics applet"

[Teravolt]

hear is another one

http://bugman123.com/Physics/index.html

[T3sl4co1l]

Simply, that's what happens in an overcoupled system.

There... really isn't a simple way to explain it.  In a word, math.  If that hasn't scared you away, read on...

FYI, it can be described in any number of ways... but not really explained meaningfully.  Any reference to circuitry or physics, is really just another description, not an explanation.  There are many equivalents: mechanical pendulums, acoustic resonators, even atomic energy levels; but none of these says why.

It has to do with polynomials.  You know, those equations of powers of x that you learned and forgot in high school, never to see again?  Surprise!

It goes several levels deep.  First, understand that: a system of resistors, capacitors and inductors, can be expressed through an equivalent polynomial.  The terms in the polynomial are given by ratios of the component values.

This is also the "characteristic" or "auxiliary" polynomial, which accompanies a differential equation.  That differential equation, of course, is also equivalent to the RLC system.  (A SPICE simulator solves this equation directly -- it's easier for a computer to just chug through it dumb, especially when diodes and transistors are involved.)

The frequency response of the system, is equivalent to the roots of the polynomial.  By another theorem, the frequency response and time-domain (waveform) response are also equivalent, so that wraps up everything you want to know about the system.

The act of changing coupling, is equivalent to changing the weight of some terms in that polynomial.  This changes the roots of the polynomial, in rather unexpected ways.  At least, unexpected without considerable analysis.

One more thing you need to know: roots are plotted on an X-Y plane.

If you have two roots, horizontally adjacent, and you have a parameter, that when increased, tends to bring the roots closer together, then at some point, they will overlap.  This is a repeated root.  For a coupled-resonator system, this is called critical coupling.  On further increase, the roots split up vertically (overcoupled).  (The horizontal condition is undercoupled.)

Why do the roots cross paths, vertical one way and horizontal the other?  Because complex numbers.  It is difficult to apply meaning to the sqrt(-1), but a very reasonable meaning is this: a 90 degree rotation.  So, by adjusting that parameter, you've pushed the roots from real values to complex values, and as a result, their path gets rotated by this much.  And the rotation doesn't just happen out of nowhere -- roots can't rotate arbitrarily, this can only be done in steps.  So, they must overlap before changing directions.

This is also the underlying problem with creating a system of certain characteristics -- factoring polynomials (solving roots) is notoriously hard!

Tim