Multiphase Resonant Circuits

gyulasun · March 30, 2019, 01:58:36 PM

Hi sourcecharge,

Thanks for returning to this project of yours again. I would like to learn about some more details on your circuit if you do not mind.

The best would be if you made a Print Screen on your schematic while in b2Spice, then I could possible understand it more readily because it is not clear.

Basically do you have a square wave generator which drives some (up to say 20) separate series LC circuits? And you use MOSFET switches to define the ON sequences for the series LC circuits? No magnetic coupling between the separate coils, right?

When you defined the R resistance in your Reply #2, as

[R = total series resistance of the series resonant circuit, including, ESR(cap), and of the coil, R(dc), R(ac), R(di), R(core)...not to mention the dc resistance of the mosfets and the connecting wire...]

all of these sound ok but I do not see the generator internal resistance included? Does not a square wave generator drive then any one of the series LC circuits? And how is an output load connected?

How do you create the multi phases? By using several MOSFET switches controlled in sequence by a multiphase pulse generator? Or it is simpler? What do you mean on EPRR ? Some kind of power ratio?

I am surprised a little that you consider the resistance of a ferromagnetic core. Is such data not covered in the eddy current specification or that is not enough?

Sorry for so many questions... Thanks for any details you are willing to share.

Gyula

sourcecharge · March 30, 2019, 05:41:43 PM

Quote from: gyulasun on March 30, 2019, 01:58:36 PM
Hi sourcecharge,

Thanks for returning to this project of yours again. I would like to learn about some more details on your circuit if you do not mind.

The best would be if you made a Print Screen on your schematic while in b2Spice, then I could possible understand it more readily because it is not clear.

Basically do you have a square wave generator which drives some (up to say 20) separate series LC circuits? And you use MOSFET switches to define the ON sequences for the series LC circuits? No magnetic coupling between the separate coils, right?

When you defined the R resistance in your Reply #2, as

[R = total series resistance of the series resonant circuit, including, ESR(cap), and of the coil, R(dc), R(ac), R(di), R(core)...not to mention the dc resistance of the mosfets and the connecting wire...]

all of these sound ok but I do not see the generator internal resistance included? Does not a square wave generator drive then any one of the series LC circuits? And how is an output load connected?

How do you create the multi phases? By using several MOSFET switches controlled in sequence by a multiphase pulse generator? Or it is simpler? What do you mean on EPRR ? Some kind of power ratio?

I am surprised a little that you consider the resistance of a ferromagnetic core. Is such data not covered in the eddy current specification or that is not enough?

Sorry for so many questions... Thanks for any details you are willing to share.

Gyula

Hi,

The digital logic of the multiphase driver logic consists of series to parallel registers, 2 mosfets and 4 nor gates which are powered by a reference voltage from +/- 10V. It took me a long time to figure out how to make a circuit that can vary in frequency, # of phases, duty factor, and voltage output from 0V to +/- 10V. This circuit is expensive and requires a professional function generator (to know exactly what frequency you are using down to the hertz) that is driven at a multiplied frequency equal to the number of digital logic multiphase dual output for direct mosfet driving. Each dual output is connected directly to a N and P channel mosfet's gate. This type of driver circuit is commonly known as a half bridge. Referencing the exact chips for this circuit would be too much information, but there are MANY series to parallel registers, nor gates, and mosfets that anyone can get. All phases of the circuit can be turned on and off with a debounced SPST switch.

The logic circuit does turn on and off the half bridge(s), and can vary in duty factor which is the on/off time of the period of the frequency. A duty factor of an AC square wave is defined as the total time on of the N and P channel mosfets divided by the total period time. The duty factor (as well as power factor and dissipation factor) can be expressed as a percentage, or a number between 0 and 1. Anything outside of these perimeters is nonsensical.

There is no magnetic coupling between the multiple coils. The coils are simple toriodal inductors wound progressively, one time around without the ends touching.

The generator of the square waves are multiple half bridge drivers. The digital logic as well as the function generator do not introduce resistance as they are only gating the mosfets. The half bridge drivers consist of small signal mosfets which have Rd(on) resistance. Usually, the N and P channel mosfets do not have the same Rd(on), and must be averaged. The 2N7000, and BS250 are cheap and easy to find, although the exact 2N7000 and BS250 from way back may not be available as there are always differences in the Rd(on) and current capabilities from different manufacturers. This should not be that important as simply finding mosfets that suit your needs and to include the Rd(on) in the calculations. The connection wire from the linear power supplies are also part of the the series resistance but should be limited by simply using low gauge connection wire.

The power supplies do not introduce extra series resistance. I thought this might be the case, so I bought Maxwell super capacitors, and used them as the power supply. The output voltage peak of a single phase series LC circuit did not change between the linear power supply and the super capacitors. The super capacitors have a rated ESR (Equivalent Series Resistance) from the manufacturer, so therefore the linear power supplies do not introduce any significant series resistance up to the ESR of the super capacitor.

This brings up another point I would like to address before moving on to the rest of your questions. The measurement of the voltage peak of a series LC resonant circuit can be measured by multimeter, or by oscilloscope. The multimeter and oscilloscope do not measure exactly the same as newer oscilloscopes only have a automatic calibration that never works. Previous oscilloscopes had the capability to manually adjust the volts per division but now, most digital Oscopes do not. Calibration between each measurement device is necessary. Meaning, I have a 10V reference chip that is 0.0002% variance at 23 degrees C and this was used to calibrate my multimeters. The multimeters have AC and DC measurements, but the AC measurements are frequency dependent and the error only increases as frequency increases. The DC measurements are the most accurate way of measuring voltage as they have the least amount of error and are not frequency dependent. So in order to measure an AC output voltage peak, I have put together a simple voltage multiplier type of circuit, able to generate up to about 500V DC. I used the multimeter to read the DC output voltage and use the oscilloscope to visually line up one channel measuring the voltage multiplier DC to the second channel measuring the peak of series LC resonant circuit. This is done by increasing and decreasing the voltage multiplier's output. Note that if the capacitor in the series LC resonant circuit is less than about 10nF, the probe of the Oscope can decrease the voltage peak measurement. This occurs because of the EPR (Equivalent Parallel Resistance) of the capacitance of the probe in parallel to the EPR of the capacitor in the series LC resonant circuit.

Moving on.

The output load(s) are easy to understand. A single phase series LC resonant circuit's unrectified output across a load is defined as a physical resistor that is connected in parallel to the capacitor of the series LC resonant circuit. The EPR of the capacitor is now in parallel with the physical resistor and adds like resistors in parallel. In order to use multiphases, imagine the same single phase series LC resonant circuit, but using rectifiers to polarize the output. By rectifying the positive and negative output of the AC signal from the series LC resonant circuit, two exactly the same resistance of physical resistors can be placed in parallel to the capacitor. This essentially is the same circuit as far as the series LC resonant circuit is concerned. Multiphase output is simply rectifying the outputs of multiple phase resonant circuits and connecting all positive rectification to one physical resistor, and all negative rectification to a second physical resistor. The load can also be a single resistor in a multiphase circuit by connecting the positive outputs to one side of a resistor, while connecting the negative outputs to the other side of the same resistor. This resistance has a virtual ground and it is actually calculated to be half the resistance of the single phase example, so to have the same voltage peak output as two polarized resistors, the single resistor must by two times the resistance to calculate it's equivalence.

ESR = [ DF^2 / (1+DF^2) ]x EPR

EPR = 1 / ( 2 x pi x F x C x DF )

DF = dissipation factor, which can be measured by LCR meter. It is usually given by manufacturer datasheets, and I have found the metalized polyester have the least dissipation factor (0.0003) in regards to cost. V-caps (Teflon and copper) I would theorize that they are the best but they are way too expensive to even bother checking compared to the metalized polyester type you can find at digikey.

EPRR (Equivalent Parallel Resistance Ratio)

EPR x 1/EPRR = an adjusted EPR

example:

5k ohm loads, or 10k ohm load.

5k ohm (EPR) x 1/5.3 = 26.5k ohm EPR

DF = 1 / ( 2 x pi x F x C x 26.5k ohm )

ESR = ( 1 / ( 2 x pi x F x C x 26.5k ohm ))^2/(1+( 1 / ( 2 x pi x F x C x 26.5k ohm ))^2) x (1 / ( 2 x pi x F x C x 26.5k ohm ))

This results in a lower ESR that each resonant circuit calculates to, meaning the voltage output is higher as EPRR increases.

EPRR / # phases = 2nd ratio that theoretically cannot go above 1, and B2 spice calculates that no matter how many phases are used, it never calculates above 0.25 .

Lastly, core resistance is real and is approximated by Legg's equation, but further study is needed as I have outlined my original problem regarding core resistance. All real resistance must be accounted for when calculating the output of multiphase resonant circuits.

Hope that helps....

gyulasun · March 30, 2019, 07:08:54 PM

Hi sourcecharge,

Oh, you certainly gave answers...

thanks for your time and efforts. I go through it and digest and when have further questions, will ask.

Thanks,
Gyula