PI DAMPING EQUATION CHALLENGE

[moodz]

There is a fundamental priniciple at the heart of ( most ) PI technology and that is the damping of the coil.
I have seen almost endless discussion on how to improve it ... but what is it really ?

"That's easy" some will be saying .. you just calculate your critical damping resistance and off you go. .... well yessss ...

but what if I told you there is further improvement to be made ??
This is not a another PI circuit ... its the fundamental mathematics.

THE CHALLENGE .... What is the missing damping formula below ??? Its a a straight up formula that holds for all cases that the "classical" damping resistor holds for.
Its a much better damping method.

The trace for the standard damping is in top pane and the new formulat damping is in the lower trace pane.
Its not a trick question ... standard LTSPICE modelling.

[moodz]

.... negative resistances / subcircuits and other LTSPICE tricks not accepted by the judges.

[Teleno]

I don't know the formula but R5 must surely be variable and a function of Vb that results in a constant discharge current.

[Carl-NC]

The formula for a traditional damped flyback is



where i₀ is the peak coil current at turn-off and tau = 2R_DC_L; R_D is the damping resistor and C_L is the total parasitic capacitance. For critical damping we normally make R_D = 0.5*sqrt(L/C_L).

[moodz]

I don't know the formula but R5 must surely be variable and a function of Vb that results in a constant discharge current.

Ok that is ZP damping ( patent by me now expired ) .. unfortunately that is not the answer.

Just to demonstrate the improvement of "mathematical damping" here is a pic below ...

Classical damping in RED, ZP damping in BLUE and this method in GREEN.
All coil currents the same each time.

[Teleno]

This would be the formula for ZP: R = abs(V(Vb))*pi/1000*sqrt(L/C)+0.001

[Teleno]

R =if(I(L2)> 0.005,1Meg,1)

[moodz]

This would be the formula for ZP: R = abs(V(Vb))*pi/1000*sqrt(L/C)+0.001

I model the current sink for the ZP method .. so the formula is a bit different. But that seems to be good for ZP damping.

[moodz]

[QUOTE=Teleno;n419134]R =if(I(L2)> 0.005,1Meg,1)

/QUOTE]

The function I use is mathematically continuous however your step function looks good. Is the residual current in the coil falling to zero or sitting at some value post flyback ? ... cant quite see it in your plots.

[Teleno]

The function I use is mathematically continuous however your step function looks good. Is the residual current in the coil falling to zero or sitting at some value post flyback ? ... cant quite see it in your plots.

A sigmoid function perhaps?

The current stops a 5mA and then decays to zero through 1 ohm.

[Teleno]

R =10000*I(L2)+ 0.001

[Tinkerer]

R =10000*I(L2)+ 0.001

R =10000*I(L2)+ 0.001 This looks nearly perfect.

I look at it in a different way:

To discharge a pure inductor, a high resistance works the best.
Our PI coils are not pure inductors, there is also a certain amount of capacitance.
To discharge a pure capacitance, the lowest resistance works best.
To get a fast discharge of the PI coil, that has inductance and capacitance, the traditional way is a compromise called critical damping. As every compromise, it is a combination of good and bad.

A perfect impedance match for the fastest discharge of the PI coil is the coil's capacitance. It matches perfectly the impedance needed for the fastest discharge.
The perfect YIN and YANG.
I discharge the inductance of the coil into the capacitance of the coil.
Then I discharge the capacitance of the coil into the inductance of the coil. This is called resonance.

On the TX coil that I have on the bench now, the discharge of an inductance of about 2000uH, 60 turns, at about 1A takes 1.4us. About 60 Ampere-turns in 1.4us.

To represent the impedance of the inductance and the capacitance of the coil mathematically is beyond my capability, but the simulators are exactly doing that, because the simulation results perfectly match the bench results.

[Teleno]

A perfect impedance match for the fastest discharge of the PI coil is the coil's capacitance. It matches perfectly the impedance needed for the fastest discharge.
The perfect YIN and YANG.
I discharge the inductance of the coil into the capacitance of the coil.
Then I discharge the capacitance of the coil into the inductance of the coil. This is called resonance.

Si you just let the coil resonate? I don't understand how you end the process without oscillation. It could be done by shorting the coil when the current is near zero, by a comparator or at a fixed delay.

[Tinkerer]

Si you just let the coil resonate? I don't understand how you end the process without oscillation.

If we would just let it oscillate, it would be a perfect sine wave in the resonant frequency. However, there is also resistance in the circuit, so we need to replace the resistive losses. So we stop it and then restart it.

I will post the simulation.

Moodz asked for the mathematical formula. How would you mathematically represent the impedance of the capacitance of the coil? And the matching impedance of the inductance of the coil?

I guess that would be the answer to the challenge.

[Tinkerer]

Here is a simulation of nearly the same circuit I have on the bench. You have to let it run to the end. [ATTACH]n419164[/ATTACH]
I can also show you the real one functioning on the bench.