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Re: 50%
Richard and all,
Well... I disagree. This is one of those areas where the commonly
accepted theory may need to be more closely examined. I'm going to open
myself up to MAJOR flamitude and claim that we_can_ break the 50% energy
transfer limitation! The thought experiment below describes how this is
theoretically possible. I also believe its possible in practice as well.
I've verified this via PSPICE simulations, and it could be verified at
low voltages using a MOSFET "gap". I've also done an estimate on my 10"
coil in single-shot mode in a previous post to Robert Stephen which
seems to indicate an ouput:input ratio of 56%.
The Thought Experiment:
Assume we start out with a pair of LC circuits, tuned to the same
natural frequency (Fo). We use "perfect" components having no dielectric
leakage, no AC or DC coil resistance, and no EM radiation losses. In
series with the primary LC circuit we place a perfect switch, initially
OPEN, that we can close and open at precise times. Assume we initially
charge the primary cap to some voltage Vp. The initial energy in the
system is Eo=0.5CpVp^2. Lets look at two cases:
Case 1: The coils are so far removed from each other that k=0.
In this case, once we close the switch, we get the familiar oscillating
current and voltage of an LC circuit. Since we've specified perfect
components, the oscillations continue indefinately as energy is
exchanged between the cap and inductor. The sum of the energies in the
coil and cap at any instant are always equal to Eo.
Case 2A: We loosely-couple the second LC circuit to the first with k<<1.
A. Now when we close the switch, the behavior is much different. The
oscillations die down in the primary circuit and build in the secondary
circuit as energy is coupled to the secondary. The "beat" frequency of
this energy interchange is approximated by k*Fo. At the end of the first
beat, _all_ of the primary's energy has been transferred to the
secondary. At this point Es = Eo!
This process then reverses, and all the energy in the secondary
circuit now transfers back to the primary. Since we've specified perfect
components, this energy exchange process continues indefinately. At the
end of the 2nd beat, we'll have the initial energy Eo back in the
primary circuit. Although the amount of time required to complete energy
transfers increases with smaller coupling, the total amount of energy
transferred is still the same at the end of the transfer!
Case 2B. Same as 2A above, but we close the switch for exactly ONE
beat, and then re-open it. At the end of the first beat, NO energy
remains in the primary circuit, ALL the energy now resides in the
secondary
circuit. Once we open the switch, we've blocked the path of energy
transfer back to the primary. The secondary now continues to ring with
total energy Es = 0.5CsVs^2 = Eo. We've achieved 100% energy transfer
from the primary cap to the secondary cap, even though "in theory" the
best we can do is 50%.
What gives?
If you look at case 2A above, the total energy in the primary:secondary
system remains Eo, and _on the average_ the energy in the system is
shared on a 50:50 basis between primary and secondary circuits. However,
the commonly accepted limit of 50% transfer efficiency ultimately comes
from a steady-state CW model and analysis, NOT from the transient case
we actually have in a disruptively-excited, properly-quenched Tesla
coil.
The steady-state model doesn't handle step functions, and can't handle
opening the primary circuit in the middle of the analysis! The
difference between steady-state and transient conditions is also at the
root of why we get _much_ better results with k's that are MUCH larger
than the CW
"critical coupling" coefficients. It also hints that we could do a
similar trick with tube and solid state coils to increase the peak
energy transfer ratios (like John Freau's pulsed tube coil that Richard
described on an earlier post).
Now practically speaking, we don't have perfect components, and the
sparkgap is far from being a perfect switch. Suppose we maximize k to
quickly couple power to the secondary or tertiary resonator, minimizing
gap
losses, and then quench the gap at the appropriate time. In fact, if
breakout is controlled, and we use "real world" gaps, we may _still_ see
output:input energy transfer ratios exceeding 50% for efficient 2-coil
systems. I'd be willing to bet that its the NORM for well-tuned
maggies!
Well... I anticipate MUCHO flaming and a deluge of over-ripe plant
material for posting this heresy - my umbrella's raised and my
firesuit's on... fire away, gang!
Safe coilin' to ya!
-- Bert --
Tesla List wrote:
>
> >From hullr-at-whitlock-dot-comMon Oct 28 21:48:14 1996
> Date: Mon, 28 Oct 1996 12:43:40 -0800
> From: Richard Hull <hullr-at-whitlock-dot-com>
> To: tesla-at-pupman-dot-com
> Subject: 50%
>
> All,
>
> In theory, We should never be more than 50% efficient in energy transfer
> from one capacitor to another! i.e. the Cprimary to the Csecondary
> Usually the resonator load capacitance plus Ion cloud loading. This
> assumes 100% coupling and zero other losses! If fact, we are much lower
> than that with the finest system in operation.
>
> 50% of the capacitively stored energy always disappears in circuit loses
> (resistive and magnetic) even with direct wired connections. There is a
> lot of additional wasteful garbage going on in between the primary and
> secondary capacitors.
>
> Richard Hull, TCBOR