Voltage Monitor for an LC circuit

[Paul Colby]

Hi,

I have an air wound 0.736 mH coil in series with a 3.5pF capacitor being driven with a function generator. Ideally the series resonant frequency should be around 3.13 MHz. The internal impedance of the function generator is 50 ohms or so. At resonance the voltage across the cap should be

$V_c = \frac{1}{R}\sqrt{\frac{L}{C}}V_o$​

where R is 50 ohm plus whatever additional resistive losses creep in and $V_o$ is the voltage across the L C pair.

I would like to maximize $V_c$ and monitor it's value at the same time. The problem is the capacitance of the scope probe or coax swamp out the 3.3pF. Even with this problem the $V_c$ is at 500V at 10V applied and I would like more[1]. My question is what approach would one suggest to monitor the voltage while operating at peak voltage without adding undue additional capacitance. The exact resonant frequency isn't that much of a concern.

[1] above a MHz this isn't a shock hazard and getting close to a burn hazard isn't feasible or desired. With my divide by 10 scope probe I get $V_c/V_o = 54$ at 1MHz.

 

[Tom.G]

What you seem to be after is higher Q. That entails reducing the losses in the circuit. With three circuit elements that leaves:

• Use heavier wire (or Litz wire) in the inductor
• Use a lower loss capacitor dielectric, like vacuum or air or Quartz
• Reduce the driving impedance

For less intrusive sensing try this Google search:
https://www.google.com/search?&q=fiber+optic+voltage+sensor

 

[Paul Colby]

What you seem to be after is higher Q. That entails reducing the losses in the circuit. With three circuit elements that leaves:

• Use heavier wire (or Litz wire) in the inductor
• Use a lower loss capacitor dielectric, like vacuum or air or Quartz
• Reduce the driving impedance

The Q I'm getting is actually a personal best. By my estimate (the funny formula thingy your browser doesn't display right if I recall) the voltage gain is proportional to one over the root of the capacitance. Switching to shorter cables raises the resonance frequency and the voltage gain quite a bit. The real question is how to I read a 1kV voltage without adding significantly to the capacitance?

So, while you're here, how does one reduce the driving impedance? Transformer might work?

 

[berkeman]

Are you trying to build something, or is this mainly for learning purposes?

 

[Paul Colby]

Are you trying to build something, or is this mainly for learning purposes?

Mostly exploratory learning by building and measuring. Running a quick experiment to see what I might achieve for how much effort.

 

[Tom.G]

Edits in Blue[/color]

the voltage gain is proportional to one over the root of the capacitance.

Sorry, the voltage gain across a reactive component[/color] in a series resonant circuit is equal to Q.
And at resonance, Q is the Reactance/Resistance, or 2πƒL/R.

(In a parallel resonant circuit, it's the current thru a reactive component[/color] that is multiplied by Q.)

So, while you're here, how does one reduce the driving impedance? Transformer might work?

Yeah, a transformer could work. So could an Emitter Follower transistor driver, whose output impedance is set mainly by the Emitter resistor.

If you assume perfect, lossless, L and C, your present configuration works out to a Q = 290; not likely in reality.
At 3.13MHz, due to the Skin Effect, the current in a wire travels in a surface layer only about 0.0015 inches deep (37um). This effective wire size leads to a greatly increased resistance, reducing the circuit Q. That would also explain your different readings with different lead lengths.

The other thing that can limit the ultimate voltage achieved is the voltage rating of the capacitor and the breakdown voltage of the inductor.

(Isn't it amazing how reality ambushes the best laid plans?)

Cheers,
Tom

 

[Paul Colby]

It may take some effort to break this down.

 

[Tom.G]

Both physically and electrically! (also, edits done in my earlier post for clarity)

 

[Paul Colby]

at resonance, Q is the Reactance/Resistance, or 2πƒL/R.

Yes, this is the same expression with at resonance 2pif = 1/sqrt(LC) being substituted. This leaves a 1/sqrt(C) in the expression. Certainly one may reduce R as you suggest however one may also reduce C. The cabled and probes I've used in my measurements swamp out C making it much larger. Since it's only the voltage drop across the capacitor that matters minimizing capacitance made sense to me.

 

[Tom.G]

Yes, this is the same expression with at resonance 2pif = 1/sqrt(LC) being substituted. This leaves a 1/sqrt(C)

Ahh, so it does, with frequency being the dependent variable.

Out of curiosity, why do you want a specific voltage across the capacitor if you can not measure it?

 

[Paul Colby]

Out of curiosity, why do you want a specific voltage across the capacitor if you can not measure it?

This is part/continuation of the thread(s) I had a while back on evanescent gravitational waves. It's unclear what the best approach is. Using standard quartz crystals has the advantage of high-Q yielding high mechanical stress in the crystal. The down side is the active volume of a standard crystal is ~mm^3 In the approach I'm taking here, the induced stress is proportional to the applied electric field while the active volume is cm^3 or 1000 times bigger. So, if I were to immerse the above device in oil I could in principle run it at 10s of kV or more. At a 0.75 inch thick crystal that's 1.5 kJ/m^3 over a cm^3. The question is how does this compare with what I can get with standard components. Anyway, playing about with this helps gain a feel for the numbers.

 

[sophiecentaur]

Why not use a small, remote loop probe to measure the nearby field and calibrate it to your scope probe when off-resonance, when loading is not a problem? I imagine that you would not be too short of signal to use a relatively remote measurement.

 

[Paul Colby]

The air wound coil is on a PVC (ABS maybe?) sewer pipe coupler so there is ample space for a sense coil. Thanks, that's a good suggestion.

 

[tech99]

In order to obtain maximum voltage across the inductor, we require maximum current through it. This requires the source resistance of the signal generator to equal the loss resistance of the coil. It is possible that this has occurred fortuitously. One method of obtaining a transformation from 50 Ohms down to the few Ohms of the coil is to shunt the generator with a capacitor. It is possible that the capacitance of the cable is performing this function. Other methods are to use a coupling winding or a tap. I should mention, incidentally, that 3.5pF is extremely small and it is likely that the self capacitance of the coil will be greater.

 

[Paul Colby]

Here's my understanding of where a parasitic coil capacitance would go in the circuit. I should be able to find a parallel resonance frequency and infer it's value. As it stands the $C_L$ may be benign as far as the series resonance is concerned?

 

[Paul Colby]

So, basically at high enough frequency the non-ideal inductor is shunted by the parasitic cap. What I need to check is that the inductor behaves like an inductor over the frequency range I choose to work in.

 

[tech99]

CL is not benign as far as the series resonance is concerned because below resonance it has the effect of inflating the inductance.
If you want the coil to be inductive, you must operate below the resonant frequency of 1 MHz which you mention.


.

 

[sophiecentaur]

At 3.13MHz, due to the Skin Effect, the current in a wire travels in a surface layer only about 0.0015 inches deep (37um)

HF broadcast transmitters use large bore copper tubing for the matching inductors to improve the resistive losses.

 

[Paul Colby]

The coil I'm using is tight wound single layer 80 some odd turns of #18 copper wire if I recall. Just set it up with a 15 ohm resistor in series. I put the voltage drop across the resistor on the scope and step the frequency through 100kH to 10MHz or so. Looks very inductive below 2MHz and there are sighs of some small bumps above 2 MHz.

Anyway, the 3.5pF cap is 23 kOhms at 2MHz. The power at 1kV would be 44 watts which is exceeds my abilities by a good measure. So, I'll need to manage my expectations. Going down in frequency looks attractive. Like all things it's a trade and this is the kind of data I need to proceed.

 

[berkeman]

step the frequency through 100kH to 10MHz

Be a little careful of putting too much power into this circuit at the higher frequencies. You run the risk of interfering with local radio receivers if you happen to couple into something that has any radiating efficiency. The AM broadcast band is around 1MHz in the US, for example.

As long as you keep the power of the circuit low, you should probably be okay.

 

[sophiecentaur]

Be a little careful of putting too much power into this circuit at the higher frequencies. You run the risk of interfering with local radio receivers if you happen to couple into something that has any radiating efficiency. The AM broadcast band is around 1MHz in the US, for example.

As long as you keep the power of the circuit low, you should probably be okay.

The inherent power of your RF source (what is it btw?) can ensure that things don't get too bad and also I presume you won't be connecting the gear to any long wire which could potentially be a good radiator. Nonetheless experimenters can be struggling to get anything at all out of an apparatus they have made but, suddenly, when all the tuning and circuit layout is right, it bursts into life and gives you ten times what they expected.
As well as there is the possibility of RF burns which can be produced with comparatively low powers. These burns can appear as little white spots on fingers and take weeks to heal up sometimes.
I haven't cottoned on to what you actually want to do with this resonant circuit. I assume that you want high RF volts across the plates of a capacitor? Do you need the C to be so low?
I would suggest that a parallel tuned circuit (same sort of components) with the Inductor fed from your source, connected to a tap across the 'lowest' few turns would produce stepped up volts on the C at resonance. I'm describing an auto transformer really. That arrangement reduces damping due to the amplifier resistance and the parallel parasitic C contributes to the tuning that you want. Tapped inductors are pretty common for antenna matching.

 

[Paul Colby]

If this ever gets to the experimental stage with extended run times the entire device will be in a Faraday cage for more reasons than one. I have a commercial cage of solid brass about 1 foot square. The picture of the capacitor shown above is similar to the device to be driven. If voltages are high enough I'm considering immersing the cap in insulating oil (mineral oil looks like it might be a good non-toxic choice?). Again, much depends on link calculation which are still be worked. For many reasons I would not want to exceed 1 or 2Watts of RF power.

 

[Paul Colby]

Tapped inductors are pretty common for antenna matching.

These are used as transformers, right?

 

[sophiecentaur]

These are used as transformers, right?

As auto transformers, in fact. There is less wire and fewer 'constructional details' to get right. It's particularly good for stepping up impedance and volts - which is what you seem to need- as there's no extra coils needed.
Is there any reason why you want to use such a high impedance? What would be 'ideal' for the Capacitor dimensions? (I assume that's the bit that counts.)
Do you have a reference to the actual experiment you are planning? I was wondering about the effect of g waves on the Inductor. Would the actual layout make a difference? e.g. having the inductor axis normal or parallel to the planes of the C plates.

 

[Paul Colby]

As auto transformers, in fact. There is less wire and fewer 'constructional details' to get right. It's particularly good for stepping up impedance and volts - which is what you seem to need- as there's no extra coils needed.

Yes, this is great thought, thanks. I could even make a sliding tap by sanding off the insulation along a vertical stripe. A step up transformer will transform the cap by the square of the ratio of the turns mod flux leakage and stray coupling etc.

Is there any reason why you want to use such a high impedance? What would be 'ideal' for the Capacitor dimensions? (I assume that's the bit that counts.)

Well, the insulator of the cap must be a single crystal of quartz. Multiple crystals can be used if they all have the same handedness (comes in left and right handed crystalline forms and there is an annoying sign flip between them). Also, the active volume counts with bigger being better within obvious limits. Quartz may be artificially grown but I assume at some non-negligable cost. Crystalline quartz is piezoelectric which means it obeys a system of constitutive relations,

$T_{nm} = C_{nmkl}S_{kl} - d_{nmk}E_k$​

$D_k = d_{nmk}S_{nm} + \epsilon_{kl}E_l$​

where all indices run over x, y, and z, repeated indices summed. $T_{nm}$ is the mechanical stress, $S_{nm}$ the mechanical strain, $E_k$ the electric field, $D_k$ the electric displacement. In the non-resonant high frequency limit $S_{nm}\approx 0$ over most the volume of the crystal. In this limit $T_{nm} = -d_{nmk}E_k$ where the relevant component of $d_{xyy} = 0.3 C/m^2$. So, bigger $E_y$, bigger $T_{xy}$. Bigger cap area, bigger current, $D_y$ on detection. Bigger cap plate separation, bigger voltage developed on detection. Detection is a complicated discussion.

Here is a link to the root discussion #1. I've learned several things since posting this and there are issues with some of my ramblings that I may understand somewhat better now. One of them is the role of crystal Q on receive I had reversed in the thread, basically double counting in the original discussions.

Do you have a reference to the actual experiment you are planning? I was wondering about the effect of g waves on the Inductor. Would the actual layout make a difference? e.g. having the inductor axis normal or parallel to the planes of the C plates.

I have no good references. There is a (very fine) group in Australia that has done some work proposing using ultra cold Quartz resonators for the detection of GW. They achieve enormous Q values. There is a reference if people are interested in the linked thread somewhere. For what I'm attempting I'm not convinced extreme Q values are helpful.

The effect of GW on garden variety circuit components is where I started in 2011. Did a lot of thinking on charged coaxial cables as GW antennas. As a notion this can work at high enough frequencies but for realistic operating voltages (I was considering Mega volts dc) the sensitivity is still zip. It's hard to beat the interatomic fields in bulk piezoelectric materials.

 

[Paul Colby]

Added a coil tap as recommended. I also tried a 1nF full scale variable cap in parallel with the "primary" or small winding count coil. I get a voltage boost of about 13.2 (about the turns ratio) at resonance which is 497kH. The variable cap was added to tune the resonant frequency. It has a very small effect on the resonant frequency ~5% to 10% maybe. Even smaller effect on the voltage output.

 

[sophiecentaur]

I found this link with an image of a similar coil. But, for antenna tuning, you don't expect a high Q because you want to match the Energy out of the resonator.
What sort of Q do you get for your resonator? What source impedance is your sig generator? Does adding a hefty series R make a difference to the Q? Do you have a schematic diagram of the setup? I always started with one of those to help my brain. What is the theoretical Inductance of the coil - about 100uH or less?

 

[Paul Colby]

First of all, thanks for the help. In graduate school I was the guy in the circuits class who never quite got it.

I'm using an hp3325B function generator which has (by spec) a 50 ohm output. A schematic of the setup is essential.

Prior to adding the tap and using the 3.5 pF cap Q ~ 57 or so based on the voltage developed across the cap (as dominated by scope probe). Operating as shown in the schematic with tap it's very low Q (I'll need to measure it but it's less than 2 is my bet.) Also the schematic doesn't contain the 3.5pF cap which will go where the scope is currently.

The coil dimensions are 5 inches in diameter and the length is 3 inches. It's 80 turn (roughly)

 

[Paul Colby]

Okay, ran a inductance calculator on line and I get 762 uH (very close to what my hand held L meter says) http://www.66pacific.com/calculators/coil-inductance-calculator.aspx

 

[Tom.G]

I hope the 'scope probe is an X10 probe, else the capacitance will have a major effect.

Try putting the scope probe across the tuning capacitor, leaving the 70-turn winding open.
If I got this right...
With 1nF, my calcs show the resonant frequency in such a case to be 1MHz and Q≅4.
With 100pF, I get ≅3.16MHz and Q≅0.07.

 

[Paul Colby]

Tom, things look pretty flat. With the probe x10 set the voltage across the tuning cap look pretty flat at a little below the applied voltage. I really don't know the internal impedance of the hp3325B other than what's printed in the spec. Could it be that the internal impedance is kept low and is guaranteed by spec to drive a 50 ohm or greater load? Tuning the cap has a small effect. at 1nF at 1Mhz is 160 ohms. If I prorate the inductance by length the 10 turn coil is about 0.07mH or 440 ohms. You'd think changing the cap would have a big effect not a small one?? Maybe I should degrading the sources impedance with 1k resistor in series.

 

[berkeman]

I really don't know the internal impedance of the hp3325B other than what's printed in the spec. Could it be that the internal impedance is kept low and is guaranteed by spec to drive a 50 ohm or greater load?

(I haven't been following the thread for a few days, so apologies if this has been said before). An HP 3325B signal generator has an output impedance of 50 Ohms. It is calibrated to put out the set voltage when driving a 50 Ohm load. If you drive a high impedance load instead, you get about 2x the set drive voltage.

 

[Paul Colby]

Okay, this gives a sharp resonance at 1Mhz

 

[Paul Colby]

If you drive a high impedance load instead, you get about 2x the set drive voltage.

Thanks, this may clear up some real mysteries it's like the flying Dutchman of factors...

 

[Tom.G]

BTW, according to the on line calculator you posted, the 10-turn winding is about 24 uH, which yields the 1MHz resonance.

Since you are after a high voltage at the secondary with negligible power, series resonance may work better on the primary... or series resonance on the secondary as your original design and an un-tuned primary impedance matched to the source.

Maybe we can get a Ham Radio operator interested here. They may be able to better approach this in an Impedace Matching context.

 

[Paul Colby]

series resonance may work better on the primary...

Yes, agreed. This might put more current into the primary.

I've been thinking that a power mosfet might make a good class C or D drive for the primary. Basically use the hp function generator to switch a current off and on at the desired frequency. If the Q is reasonable the voltage at the crystal will be near sinusoid? Anyway, I'm out of town for a week and this will have to wait till I return. Thanks all for the help.

 

[Baluncore]

Try this tapped coupling. Trigger on Channel 1, adjust frequency for zero phase between scope channels.

 

[sophiecentaur]

Okay, ran a inductance calculator on line and I get 762 uH (very close to what my hand held L meter says) http://www.66pacific.com/calculators/coil-inductance-calculator.aspx

I think you need the resonance to be across the whole coil, tuned with the intended load capacitance across it. The resonance of the bottom section will always be low Q because it has 50Ω to ground (the generator source) or a series R which uses up your available volts. The 50Ω in the bottom end would (I think) be transformed by the turns ratio squared( =5k) for the full length resonance. I would be inclined to look at that with a really high impedance take-off (a high resistor or, my suggested loop probe. A higher turns ratio could be worth trying - easy to implement. The Capacitor 'cell' should be connected by a short rigid 'L' of wire to the top terminal and the bottom end, nice and tidy with short wires to the tap. Personally, I would always use soldered joints and arrange things like the construction in that link I gave you.
Was there a reason for the cell to have such a low capacitance? Strays have a lot less effect if the C could be ten times that value. Some sort of compromise on the added source resistance could still give you high volts if, as I suspect, the main source of damping is the generator - despite the reduced source volts.
It looks as though you are getting places at the moment. That can't be bad.

 

[sophiecentaur]

r, series resonance may work better on the primary.

OH yes - I just found that in your earlier post. The Q could be better in the input resonance.

 

[Tom.G]

The circuit that @Baluncore suggested but using the Quartz crystal in place of the 1nF (and with correction for the inductor value) would be a good next step. Resonance will be around 3MHz, with a Q≅50 when driven with the 50Ω generator. This will give a theoretical voltage step-up of 400. Take that into account before you put a 'scope probe on the secondary... 'scope repairs are Expensive.

Try this tapped coupling. Trigger on Channel 1, adjust frequency for zero phase between scope channels.

 

[sophiecentaur]

I've been thinking that a power mosfet might make a good class C or D drive for the primary.

A different RF Power source could always help; 50Ω would not necessarily be the idea source impedance. But do you want to get involved with RF Power Amp spec and design? You need to find a local radio ham who could get involved and bring all his test gear with him (as well as his knowledge).
Can you just confirm that it's high E field across the quartz crystal that you're after and that other circuit parameters can be chosen to produce it? (The gap is presumably determined by the length of the crystal).
PS I think the actual coil design is probably the most important factor in this and that's a pain. Winding large coils is hard work and a good inductance calculator could save time and trouble. I found this one which is all singing all dancing but a bit overwhelming with the information it produces.
Edit: I added the link URL

 

[Paul Colby]

But do you want to get involved with RF Power Amp spec and design?

Money can solve nearly every problem. The real approach to this is spend the time and write a just the facts paper on the intended experiment with some reasonably complete S/N calculation showing the level of difficulty. I kind of view this activity as learning enough to do this with some confidence. To get a paper to the level needed for publication in a real journal is significant work in itself. Frankly, I would likely meet my goals just by getting a paper on arXiv.org but I don't know if it would even get past the spam filters.

Anyway, it's o-dark-thirty and time to go to the airport (I hate flying). I'll be away from the "lab" for a week or so. Thanks

 

[Paul Colby]

Okay, I keep forgetting that voltage dividers don't have to be resistors. Clearly a series combination of capacitors does what I need

Configured this way, the voltage drop across the 350 pF cap is 1/100 that appearing across the 3.5 pF. Also as an added benefit, the net capacitance of the pair is only slightly more than 3.5 pF.

 

[Baluncore]

The problem there is that the signal generator's 50 ohm impedance is in series with the LC circuit and so will spoil the Q.
You need something like post #37 where the inductor is also a fixed ratio autotransformer and the crystal takes the place of the capacitor.

 

[Paul Colby]

The problem there is that the signal generator's 50 ohm impedance is in series with the LC circuit and so will spoil the Q.
You need something like post #37 where the inductor is also a fixed ratio autotransformer and the crystal takes the place of the capacitor.

Yes, the previous post, #43, just shows my favored solution to the initial problem posed, how to monitor the voltage waveform across the 3.5pF cap without cap loading the circuit or blowing up my scope. I've spent my time away MacSpiceing several alternative drive circuits. Modeling the taped coil was fun and informative. I'll post some sims and data after I recover from traveling tomorrow.

 

[Baluncore]

Remove the .txt extensions to make Ltspice .asc and .plt files.
R1 = 10k drops a voltage in phase with the drive current.
R2 = 10Meg is the oscilloscope Chan-2 input set to x10.
R3 = 50 ohm matches the signal generator and may be the oscilloscope Chan-1 input, 50 ohm if available.
Ch2 will give the peak signal, pp / 11.
Tune for zero phase between Ch1 and Ch2. Notice the deep dip at resonance.

 

[Paul Colby]

R3 = 50 ohm matches the signal generator and may be the oscilloscope Chan-1 input, 50 ohm if available.

Thanks for the sims. I'll translate to MacSpice and give it a go. One question though, shouldn't R3 be in series with V1 to simulate the internal impedance? The way it is draw infinite current will flow if the generator (V1 + R3) is shorted?

 

[Paul Colby]

Okay, yesterday was spent playing with the circuit shown in #43. The capacitive voltage divider worked as advertised which is gratifying. However, as noted by several just the preponderance of stray capacitances will make this circuit problematic. Indeed, waving a hand about changes the resonance (a lot) which still shows up 1MHz low by my estimate. So, random capacitances to ground are a serious issue. Perhaps some careful layout and fabrication could minimize this but I think I've determined (hence the point of this exercise) that this approach has dragons. On the up side, this effort suggests changes in approach that I will explore so more later in another thread with a new set of issues.

 

[Baluncore]

One question though, shouldn't R3 be in series with V1 to simulate the internal impedance? The way it is draw infinite current will flow if the generator (V1 + R3) is shorted?

You are correct, the generator will probably have a 50 ohm output impedance. I should have set it's parameter Rser=50 ohm. R3 is either an external termination or the CH1 input to the scope which provides the generator output with a matched 50 ohm load impedance. I did not model that bit accurately, because I had less than 10 minutes to get it together and was more concerned with getting a realistic estimate of the Q. The modeled mismatch does not change the simulated Q.

How could ( V1 + R3 ) be shorted? The model is numerical, the real generator will have an output current limit.

To reduce the stray capacitance, construction would place the crystal capacitor inside the inductor, with the inductor inside a copper box. I would ground the centre of the coil and feed it one turn from the centre.

 

[Paul Colby]

How could ( V1 + R3 ) be shorted?

What could possibly go wrong ? That's just an internal mental consistency check I run. Making equivalent circuit models is an art unto itself.

To reduce the stray capacitance, construction would place the crystal capacitor inside the inductor, with the inductor inside a copper box. I would ground the centre of the coil and feed it one turn from the centre.

Really good thought, however nothing removes the stray coil to ground. A copper box will solidify the problem (make static) but not remove it.