# Voltage Monitor for an LC circuit

#### Paul Colby

Gold Member
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.

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#### 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:

#### Paul Colby

Gold Member
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

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

#### Paul Colby

Gold Member
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

the voltage gain is proportional to one over the root of the capacitance.
Sorry, the voltage gain across a reactive component 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 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

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#### Paul Colby

Gold Member
It may take some effort to break this down.

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#### Tom.G

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

#### Paul Colby

Gold Member
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

Gold Member
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 thats 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

Gold Member
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

Gold Member
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

Gold Member
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

Gold Member
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?

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#### Paul Colby

Gold Member
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

Gold Member
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

Gold Member
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

Gold Member
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

Mentor
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

Gold Member
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

Gold Member
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

Gold Member
Tapped inductors are pretty common for antenna matching.
These are used as transformers, right?

#### sophiecentaur

Gold Member
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

Gold Member
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.

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