LC resonant circuit for voltage amplification

[toyonline]

Hi, I recently have built a LC circuit for voltage amplification purpose. The circuit is shown in the attachment. Through frequency sweep, I observed resonance behavior of the circuit. The problem is the voltage increase is only ~8 times larger than the original input voltage, which is not enough for my purpose. And through Spice I know the simulated increase of voltage of this circuit is 50dB, i.e. 300 times larger.

I know Q factor maybe a parameter that influence voltage increase of my circuit. So maybe the limited amplification is due to low Q factor of some of electronic components in my circuit? If my hypothesis was right, maybe I need to change some old components in my circuit with brand new components.

Would any one help me to point out other possibilities? and suggestions to improve that voltage increase?

Thanks so much.

 

[FvM]

Estimate the Q factor of involved inductors and calculate equivalent inductor series resistances at the resonance frequency to repeat the simulation under realistic conditions.

 

[WimRFP]

The voltage multiplication of your network is because of that the series circuit is inductive and the parallel resonant circuit is capacitive (LC L-match). Other option can be capacitive series circuit and inductive parallel circuit (CL L-match).

The loaded Q-factor almost equals the multiplication factor. So if you want a factor of 300, the loaded Q factor of the L and C in the LC L-match is 300. To have low loss, the Q factor of the components itself should be >>300.

When using LC circuits to make the inductive and capacitive behavior, the component Q factor must be even higher. If you want relative low loss, this is not the way to go as practical components will not have sufficient Q-factor.

You could do the transformation in steps. For example a cascade of two networks that do factor 17 each. I would go for a transfomer option. If it is a high voltage application, a two stage approach can be useful. First stage via transformer, the last stage via LC resonance.

The choice of circuit also depends on the source and the behavior of the load (can it be a short circuited load, or an open load, etc).

 

[toyonline]

I estimated the Q factor of my inductor is around 1000~1500, while Q of capacitor are manufactured by Q~100,000. I think the problem is due to the inductor. As you mentioned, Q should >>300.

Could you explain more about the cascade network? or any reference recommend to me? Thanks a lot.

The voltage multiplication of your network is because of that the series circuit is inductive and the parallel resonant circuit is capacitive (LC L-match). Other option can be capacitive series circuit and inductive parallel circuit (CL L-match).

The loaded Q-factor almost equals the multiplication factor. So if you want a factor of 300, the loaded Q factor of the L and C in the LC L-match is 300. To have low loss, the Q factor of the components itself should be >>300.

When using LC circuits to make the inductive and capacitive behavior, the component Q factor must be even higher. If you want relative low loss, this is not the way to go as practical components will not have sufficient Q-factor.

You could do the transformation in steps. For example a cascade of two networks that do factor 17 each. I would go for a transfomer option. If it is a high voltage application, a two stage approach can be useful. First stage via transformer, the last stage via LC resonance.

The choice of circuit also depends on the source and the behavior of the load (can it be a short circuited load, or an open load, etc).

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The resistance of the inductor is estimated to be 1 ohm. So, I estimated the Q of inductance should be 1000~1500. Does that sounds rational?

Estimate the Q factor of involved inductors and calculate equivalent inductor series resistances at the resonance frequency to repeat the simulation under realistic conditions.

 

[FvM]

The resistance of the inductor is estimated to be 1 ohm. So, I estimated the Q of inductance should be 1000~1500. Does that sounds rational?

Not at all. AC resistance will be considerably higher than DC resistance due to skin and proximity effects and there will be core losses in any inductor with magnetic core. Even an air core inductor has some additional eddy current losses.

What's your inductor type?

In addition, you're assuming an ideal voltage source driving the circuit. Something that's rarely found in real electronics.

 

[WimRFP]

Your Q factor estimates seem very optimistic (you should measure Q at the operating frequency). Only physically very large coils will reach Q>1000. Miniature inductors have Q<100.

Also your capacitor Q estimate is too optimistic. You need an air dielectric capacitor to have Q > 5000.

For an LC L-network (L in series with source, C parallel to load):

Zload/Zin = rt(Vout/Vin). Qloaded = rt(Zload/Zin - 1 ), XL = Zin*Q, XC = Zload/Q.

an example:
you want a 1 to 20 voltage step and the load is 10 kOhms, all at 5 MHz. Because of conservation of energy, Zin = 10k/20^2 = 25 Ohms (and this is a real impedance).

So Qloaded = rt(10k/25 - 1) = 20.0, hence

XL = 25*20 = 500 -> L = 15.9 uH,
XC = 10k/20 = 500 -> C = 64.0 pF.

when the capacitor Q factor is 500, you lose 100%*20/500 = 4% in the capacitor.
Same formula is valid for the inductor.

The circuit is a low pass filter, with a very high peak (20 times) around the LC resonance frequency.

The two step approach uses two LC filters behind each other.

Your application is a mistery for me, but you may explore other schemes to get voltage multiplication factor of 300.

 

[toyonline]

Thank you. I now understand that skin effect. And my inductor should have higher resistance at high frequency. The Q value is something like several hundred, or even 10-100.

My inductor was fabricated with copper wire #24 wound on iron powder cores.

I just simple wind the wire onto the core, doesn't consider any effects from winding manner. But I do measure inductance, which is the same as I designed.

I dont know whether different winding manner will affect Q of inductor significantly?

Not at all. AC resistance will be considerably higher than DC resistance due to skin and proximity effects and there will be core losses in any inductor with magnetic core. Even an air core inductor has some additional eddy current losses.

What's your inductor type?

In addition, you're assuming an ideal voltage source driving the circuit. Something that's rarely found in real electronics.

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Thank you.

I have read from appnotes, which indicate my inductor should have a Qmax= ~300. In real case, I do not expect it will reach 300. And according to my experiment, I would expect a corresponding series resistance of the inductor of 500 ohms or even higher.

Now, the problem is clear, the Q of inductor limits my voltage amplification. So I wonder if any improvement could be made to improve Q value of my inductor? without changing topology of the original LC network, since I need two frequencies from the LC circuit.

Your Q factor estimates seem very optimistic (you should measure Q at the operating frequency). Only physically very large coils will reach Q>1000. Miniature inductors have Q<100.

Also your capacitor Q estimate is too optimistic. You need an air dielectric capacitor to have Q > 5000.

For an LC L-network (L in series with source, C parallel to load):

Zload/Zin = rt(Vout/Vin). Qloaded = rt(Zload/Zin - 1 ), XL = Zin*Q, XC = Zload/Q.

an example:
you want a 1 to 20 voltage step and the load is 10 kOhms, all at 5 MHz. Because of conservation of energy, Zin = 10k/20^2 = 25 Ohms (and this is a real impedance).

So Qloaded = rt(10k/25 - 1) = 20.0, hence

XL = 25*20 = 500 -> L = 15.9 uH,
XC = 10k/20 = 500 -> C = 64.0 pF.

when the capacitor Q factor is 500, you lose 100%*20/500 = 4% in the capacitor.
Same formula is valid for the inductor.

The circuit is a low pass filter, with a very high peak (20 times) around the LC resonance frequency.

The two step approach uses two LC filters behind each other.

Your application is a mistery for me, but you may explore other schemes to get voltage multiplication factor of 300.

 

[WimRFP]

You can use an LC circuit in series with the source and an LC parallel resonant circuit parallel with the load to get a double peak response. If these frequencies are relatively close together, you need very high component Q, or you may need even three stages. In my opinion such an approach with three stages is close to technically impossible.

If you tell us something about power level, voltage level, the two frequencies and maximum physical size, we might be able to help you better.

 

[FvM]

Realistic Q numbers of cored inductors have been discussed in this previous thread. https://www.edaboard.com/threads/220098/

 

[WimRFP]

@toyonline: When using large air gaps (to get good temperature stability, high power, or low intermodulation), winding topology affects Q-factor. An example is copper in the fringe field zone of the air gap.

 

[toyonline]

Thank you for the suggestion. Could you provide me some links or reference on this?

I know the circuit I used was named as double tuned LC circuit. But I don't know other circuit that could provide double frequencies.

You can use an LC circuit in series with the source and an LC parallel resonant circuit parallel with the load to get a double peak response. If these frequencies are relatively close together, you need very high component Q, or you may need even three stages. In my opinion such an approach with three stages is close to technically impossible.

If you tell us something about power level, voltage level, the two frequencies and maximum physical size, we might be able to help you better.

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Thank you. That's useful.

Realistic Q numbers of cored inductors have been discussed in this previous thread. https://www.edaboard.com/threads/220098/

 

[toyonline]

I have changed my winding geometry, with more winding core angle. I found that winding geometry gives me a improved voltage magnification, 3 times larger than original. That's amazing. Maybe I could improve more by increasing unwinding cores.

@toyonline: When using large air gaps (to get good temperature stability, high power, or low intermodulation), winding topology affects Q-factor. An example is copper in the fringe field zone of the air gap.

 

[WimRFP]

Regarding other solutions: frequencies, power, voltage, etc?

 

[toyonline]

The most convenient way to me is to change inductors in order to have a better Q for tuning purpose.

Regarding other solutions: frequencies, power, voltage, etc?

 

[Orson Cart]

it is very hard to get Q higher than 100 unless you use good litz wire and low loss ferrites with suitable gaps, iron powder cores will give losses at moderate to high frequencies which will limit the real Q, run your flux density lower than 40mT peak in your ferrite also when you design your chokes, even better litz wire on air core toroids gives a practical method for high Q.

 

[toyonline]

Thanks for your suggestion.:-D

it is very hard to get Q higher than 100 unless you use good litz wire and low loss ferrites with suitable gaps, iron powder cores will give losses at moderate to high frequencies which will limit the real Q, run your flux density lower than 40mT peak in your ferrite also when you design your chokes, even better litz wire on air core toroids gives a practical method for high Q.