The Water Fuel Cell

[eclipsed78]

Hi all,

I am defining the total inductance reacting within the resonant circuit of each type of VIC with either one or two cores...

The dual core VIC....

This type of VIC is used with closed magnetic path cores like toroids, completed E cores, completed C/U cores, etc.......basically, due to the closed magnetic path, the coefficient of coupling (k) should be very close to 1......It consists of two cores, one containing a step-up transformer, and the other core containing the resonant chokes...the core containing the resonant chokes are the only coils that are significantly reactive within the resonant circuit...therefore, if the fields are aiding, then the total inductance is simply...

L1 + L2 + (2 * M)

M = k * (L1 * L2)^(1/2)

k = (1-sigma)^(1/2)

sigma ={ L1 (while L2's leads are shorted) } / { L1 (while L2's leads are left open) }

but if a closed magnetic path core is used like toroids then k is about 1 so....

L(total) = L1 + L2 + [ 2 * (L1 *L2)^(1/2) ]

Or if the coils are wound the same number of turns on a closed magnetic path core then the total inductance that is within resonance is about:

L(total) = 4 * L1 OR 4 * L2

and if the toroids Al is known from the manufaturer, then the total inductance is now:

L(total) (H) = 4 * (N^2*Al)/10^9

where N = number of turns


The single core VIC.....

This type of VIC is used with an open magnetic path...like I cores....basically the coefficient of coupling between each coil is very important.....

As an example from the data I collected from B2 spice simulations of resonant frequency sweeps and reverse calculating the inductance in resonance...

A simple transformer's secondary will resonate with a series capacitor directly proportional to the coefficient of coupling shown in the equation below....

L(in resonance) = L(sec) * (-0.9860438 * (k)^2 - 0.0043922 * (k) + 0.990869)

This equation simply shows that a coil that that is not in either series or parallel relationship to the primary has a certain amount of inductance which is reactive within the secondary series resonant circuit, whether it is the secondary or the chokes of the single core VIC, and it can be calculated...

Whats important about this is that with coupling of close to 1, the total reactive inductance is close to 0, therefore closed magnetic path cores will not work as a single core VIC....

There are three coils aiding each other on the single core VIC...so the equation becomes:

L(total) = L1 + L2 + L3 + (2 * M1) + (2* M2) + (2 * M3)

where M1, M2, and M3 are mutual inductance between the series inductors which is reactive within the resonant circuit and can be reverse calculated by measuring the coupling between each pair of coils....

So it is a question of how much the coils are coupled that directly influences the amount of inductance that is reactive within the resonant circuit...but if the chokes are bifilar, I believe that they would have a greater amount of coupling due to their proximity...close to 1....therefore magnifying the amount of inductance within the resonant circuit...This theory would show that the single core VIC is the most efficient type of circuit to increase the amount of inductance that is reactive within a series resonant circuit......

Unfortunately, the calculation of the total inductance is too complex for a single equation to encompass all possible combinations of coupling...apparently, the amount of mutual inductance that is reacting within the series resonant circuit is a 3rd order polynomial, and the equation would change due to any change in the amount of coupling between each pair of coils...

But if you have measured the coupling, and if you would like to cheat, then in order to find the resonant frequency of the single core VIC without actually testing it on a capacitor that might pop, it is my advice to use the sweep function of B2 spice and measure the output response, and reverse calculate the total inductance that is reactant to the series resonant circuit from the frequency that has the highest voltage peak responce....

I have included the 4 simulation sweep experimental data and graphs are very interesting at lower couplings...

Notice that between the single core and the dual core VICs, each coil could be exactly the same inductance but the single core would have more inductance to be reactant within the series resonant circuit.....I use the dual core VIC because I think it is more efficient with the transfer of power, and it is easier to calculate the total inductance that is reacting to the series resonant circuit...

[longcat]

hello eclipsed, could you explain where the (2 * M) comes from in your first equation?

L1 + L2 + (2 * k * (L1 * L2)^(1/2)) looks to me like the binomial theorem, in which k would be always one. Is this information i can read about in books to find out more?

regards

[eclipsed78]

hi longcat,

Thats a good question....

The way I understand it is that each coil independently influences the other....so L1 independently influences L2, and L2 independently influences L1....therefore 2*M because the amount of mutual inductance is the same between both coil.....and can be calculated by the equation:

M = k * (L1 * L2)^(1/2)

Ref:

Timbie, William and bush, Vannevar "Principles of Electrical Engineering" 4 ed 1951 pgs. 345 - 346

Although it may not be apparent that k is a calculated ratio of the amount of coupling between two coils, "sigma" is the ratio of the amount of inductance that is leakage inductance / self inductance of one coil, the measurement of sigma will give a number between 0 and 1...and it can be used within the equation:

k = (1-sigma)^(1/2)

sigma = [ L1 (while L2's leads are shorted or together) ] / [ L1 (while L2's leads are open or not together) ]

Which then can calculate the amount of coupling between two coils...k will always be a number between 0 and 1 just like sigma if it is measured correctly...

After researching for the refs again I ran into a site that referenced a book that apparently states that the Q of the inductors can not be too low...so this measurement might not be "perfect" but I have measured the coupling of a toroid that I wound before and the measurement calculated to a coupling of .996...so that coefficient of coupling would make sence as the core is a closed magnetic path....so the measurement seems to work fine...but research to how high the Q must be should be understood further...

Refs:

http://en.wikipedia.org/wiki/Leakage_inductance

http://www.cliftonlaboratories.com/ferrite_transformers.htm

F.E. Terman's Electronics Measurements, 2nd Ed.
(refed within the site above)

[eclipsed78]

Hi,

After reviewing the equation which defines the amount of inductance that is reactive on a secondary resonant cirucit using the single core VIC, it simplifies to:

L(in resonance) = L(sec) * (1 - k^2)

or

L(in resonance) = L(sec) * sigma

where:

sigma = [ L1 (while L2's leads are shorted or together) ] / [ L1 (while L2's leads are open or not together) ]

or

sigma = [ L2 (while L1's leads are shorted or together) ] / [ L2 (while L1's leads are open or not together) ]


Which make sence because the inductance that is not coupled with the primary is what is reactive within the secondary resonant circuit...

This inductance that is not coupled though reacts with every other inducator on the core with the same equation...but how, I am not exactly sure....as the series mutal inductance equation does not model the data collected, there seems to be something else affecting the total inductance reacting within the resonant cirucit...