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Re: 50%

Tesla List wrote:
> 
> > Subject: 50%
> 
> >From bert.hickman-at-aquila-dot-comTue Oct 29 22:57:35 1996
> Date: Tue, 29 Oct 1996 20:44:19 -0800
> From: Bert Hickman <bert.hickman-at-aquila-dot-com>
> To: tesla-at-pupman-dot-com
> Subject: 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 --
> 

Bert,

I just have to disagree, inspite of your 100% perfect component thought 
experiment.  I can't see a transient functioning link coupled resonant 
scenario transfering more enrgy between two identical capacitors than a 
direct wire connection. (which is %50)  Work has to be done on the 
dielectric in the uncharged capacitor regardless!  50% of the orignal 
energy contained in the charged cap is required to do this. Regardless of 
any other reactive components.  The losses are all heat related 
(resistive, if you will).

It is important to remember that even in a direct wire transfer between 
the two caps, we will have a true, ring up, resonant circuit also, 
complete with damped wave! The wires are our inductor and the caps are 
our capacitive agents.  A directly coupled resonant circuit.

Richard Hull, TCBOR