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Resonance but with current and voltage out of phase....

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si2030

Wed Jul 23 2008, 04:52AM

Registered Member #1571 Joined: Wed Jul 02 2008, 03:26AM
Location: Bendigo Victoria Australia
Posts: 44

Hi there,

My questions relate to LCR resonance, the application of which is applied to a Cockcroft Walton Multiplier.

I have done many LTSpice simulations with this concept and at the heart of the topology, I am using a CD4046B PLL.

My issues are with the phase of the resulting "resonant" voltage and the series LCR circuit current feeding the multiplier.

The idea is similar to the SSTC topologies that use a PLL - in particluar Steve Wards PLL SSTC driver topology => here is my schematic..

in that you want to hunt and lock resonance even with ground strikes. With a multiplier, as the multiplier fills it modfies the total of the resonance capacitance. Once filled the system stabilises at a frequence (barring any discharge).

I have found that with this 4046 feedback mechanism - using a current sense tertiary coil - my simulations do hunt resonance and lock on the current phase. I can therefore conclude that the system is in resonance.

My problem: CURRENT lags VOLTAGE in resonant mode. I am coming to understand that this is a SIDE EFFECT of the secondaries resistance and Q - that is - an imperfect resonant state... so it will never be completely in phase... this next trace shows my simulation in resonance but even so no true phase alignment...

My questions:

1) Is it a true assumption that the phase of the current will never truely be in phase with the voltage even at a "resonant" point?

and more importantly...

2) with the current lagging in phase from the voltage, can I still run a full bridge and what effect on the IGBTs can I expect... its in resonance but the phase is still out.

Hoping someone can shed some light on this and also let me know re the IGBT effect..

Simon

Ken M.

Wed Jul 23 2008, 09:37AM

Registered Member #618 Joined: Sat Mar 31 2007, 04:15AM
Location: Us-Great Lakes
Posts: 628

That looks "kinda" normal since current or voltage lags the other I can't remember.

GeordieBoy

Wed Jul 23 2008, 12:17PM

Registered Member #1232 Joined: Wed Jan 16 2008, 10:53PM
Location: Doon tha Toon!
Posts: 881

> Is it a true assumption that the phase of the current will never truely be in phase with the voltage even at a "resonant" point?

The phase of which voltage? and which current?

Do you mean the inverter's output voltage, the inverter's load current, the base current of the resonator, the voltage on the toroid!!???

Remember: CIVIL For a (C)apacitor I comes before V. For an (I)nductor V comes before I.

For a series resonant circuit connected across a voltage-fed inverter, the current draw is in-phase with the fundamental of the inverter's output voltage when driven at resonance. The voltages across the individual L and C components lag and lead this current by -90 and +90 degrees respectively. So taking the phase of the inverter's fundamental frequency as the reference point, the load current is in phase at resonance, and the voltages across the L and C are at 90 degrees to it.

I hope that helps,

-Richie,

si2030

Thu Jul 24 2008, 05:37AM

Registered Member #1571 Joined: Wed Jul 02 2008, 03:26AM
Location: Bendigo Victoria Australia
Posts: 44

Hi Richie, others,

Thankyou for replying - it really helps.

It seems the simulation was doing the right things and it was me who was struggling to understand it.

I am feeling a little ignorant here for asking what are basic questions but could you clarify a few more things for me. I have included another trace of the simulation of the above circuit....

First of all in my topology would you refer to the inverter as the primary inductor and full bridge and secondary inductor?

When you say the inverter's output voltage are you referring to the voltage across the primary inductor of this air core transformer? I am assuming so as they are pretty much in phase (bottom pane - the square wave is the drive signal to the IGBTs (one leg), the sine wave - blue is the current across the primary - this is at 200ms - at 600ms its perfect... so soft switching).

..and secondly, the voltage between the secondary inductor and the capacitor is 90 degrees leading. This must be the voltage through the capacitor(its clearly working). I can find nowhere though where the voltage is lagging for the inductor. One side of the secondary inductor is connected to ground the other side of it connected to the capacitor and also the multiplier and then the other side of the capacitor is then connected to ground. The multiplier gets a 90 degrees leading voltage signal (working) but the lagging voltage through the inductor?..

I feel a lot more confident that this circuit is actually working well in sim now but I want to understand this as much as I can and this is fundamental to the intention of this circuit.

Hope you can assist.

Simon

GeordieBoy

Thu Jul 24 2008, 10:23AM

Registered Member #1232 Joined: Wed Jan 16 2008, 10:53PM
Location: Doon tha Toon!
Posts: 881

> First of all in my topology would you refer to the inverter as the primary inductor and full bridge and secondary inductor?

Perhaps my use of the term "Inverter" is misleading you here. An Inverter in this case is a device that converts DC power into AC power, (the oposite of rectification) and _IS_ your full-bridge (H-bridge).

> When you say the inverter's output voltage are you referring to the voltage across the primary inductor of this air core transformer?

Yes. The voltage between the mid-points of each leg in the H-bridge.

> the sine wave - blue is the current across the primary - this is at 200ms - at 600ms its perfect... so soft switching).

Currents flow THROUGH things. Comments about the waveshape below...

> ...and secondly, the voltage between the secondary inductor and the capacitor is 90 degrees leading. This must be the voltage through the capacitor...

Voltages go ACROSS things.

The current waveform in the bottom trace is composed of two components. A sinusoidal current that will be in-phase with the output voltage from your H-bridge at resonance. AND a triangular current waveform that is the magnetising current of the primary winding. The magnetising current lags the applied voltage by 90 degrees. These two different waveshapes add together to give you the "almost sinewave shaped" current waveform that is "almost perfectly in phase" with the H-bridge output voltage.

Hope this helps,

-Richie,

si2030

Thu Jul 24 2008, 10:54AM

Registered Member #1571 Joined: Wed Jul 02 2008, 03:26AM
Location: Bendigo Victoria Australia
Posts: 44

Richie, This is helping alot thankyou.

One last thing about this topology, why is the voltage (top pane - pink trace) between the secondary inductor and the resonant capacitor 90 degrees leading. Why isnt it aligned with the other wave forms?

With regard to the H bridge and triangle wave, the current travels through the primary first one way and then the other. Is there a triangle wave that is the magnetising current lagging 90 degrees for each leg? That is - a sine wave for the current and TWO triangle waves - one at 90 degrees before and the other 90 degrees after, producing the near perfect sine wave result?

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