# Capacitors with Three Plates - Plates Only. Two Plates with Coil Between

#### Sir Kit

Joined Feb 29, 2012
54
I am investigating the interaction between capacitors and coils arranged in a stack. The configurations I intend to try are illustrated in the diagram below. There is an assumption that the input is bipolar, as if from the push-pull amplifier. The signal is any audio sine wave. I visualise the effects in the following way.

A - First half cycle: Inner plate goes high. Second half: outer plates go low. Net potential constant. (No coil)
B - Same as above, but coil is loaded with a resistor to emit an EM field. My question here is how the R value affects the potential between coil and plates, or other behavior of the circuit.
C - Same as above, but the coil is fed direct from the signal source in series with the transformer primary. This eliminates the prior load resistor, but the coil's voltage remains at line level. Potential is in effect halved.
D - Center tapped transformer. First half cycle: Coil goes high while plates go low (simultaneous). Second half: this reverses. Potential is halved.

Any correction or advice on my reasoning so far would be greatly appreciated.

I would also like to understand the effect of each configuration upon the signal source with regard to loading or reflection issues, etc. Or perhaps some ideas on different ones to try.

#### Delta prime

Joined Nov 15, 2019
361
Any correction or advice on my reasoning so far would be greatly appreciated
I believe you're missing a dielectric and I know where it went it seeped through a

#### Sir Kit

Joined Feb 29, 2012
54
I believe you're missing a dielectric and I know where it went it seeped through a
The dielectric is not missing. It is just white. For the sake of clarity I suppose.

#### ci139

Joined Jul 11, 2016
1,528
A reduces to a single cap at low frequencies
(at high frequencies the inductance and geometry of the particular wiring/connectors will start having it's infuence)

B ? . . . the magnetic circuit of the trasnsformer and the capacitor also emit the EMF ?
( redefine the ® target problem (what you thought such connection would ?illustrate?) here )

C -- the capacitor geometry / frequency / circuit geometry are molding your results here

D -- the currents in capacitor are defined by the light speed and potential fields = device geometry

at low (audio) frequencies all your 3 plates reduce to 2 plate cap.

#### Sir Kit

Joined Feb 29, 2012
54
B ? . . . the magnetic circuit of the trasnsformer and the capacitor also emit the EMF ?
( redefine the ® target problem (what you thought such connection would ?illustrate?) here )

D -- the currents in capacitor are defined by the light speed and potential fields = device geometry
Can you please explain how, "at low (audio) frequencies all your 3 plates reduce to 2 plate cap." Is there any way to prevent this?

B - This circuit is intended to replace the center plate with a flat coil. The object is to interact an inserted magnetic field with the displacement current. Without the resistor, the coil would sit at the same potential as the plates. We can disregard the transformer's own EM field for the moment. On this basis, can you comment further?

D - Can you please be more specific? How does the geometry and split winding affect the capacitor "currents"?

Which of the three circuits with coils do you believe would provide the greatest electrodynamic interaction between the respective fields of the coil and cap. For example, the charge on the plates affecting the force vectors of the coil.

Let's assume the frequency is high enough for this type of effect.

#### ci139

Joined Jul 11, 2016
1,528
http://deepfriedneon.com/tesla_f_platecap.html (at the end of the article)
the difference in between 2 and 3 plate capacitor is mostly how you calculate their capacity

... at the high frequencies the preferred current paths/-distributions and the dynamic charge densities (along with the parasitic elements of each component) may define additional dependencies for the current flows and potentials in the circuit

i don't got any specialized software , so i would have to write a huge 3D- electrical simulation engine ... to illustrate such numerically and near correct

UPS! -- i missed the fact that the B , C , D have a coil in the center - the flat coil has a "reversed" magnetic field ... something like the Fig. below
. . . if it's tightly wound (there's inter-turn capacities + a high impedance) // if it's loosely wound it won't be much for the effective plate of the "outer" capacitor

= you have a lot of factors that affect your test results in "un-predictable" or non-wanted ways ... you need to precision retail your experiment for the effects you want to study
(i speak in general/non-specific -- but you haven't specified in detail your aim)

#### Sir Kit

Joined Feb 29, 2012
54
= you have a lot of factors that affect your test results in "un-predictable" or non-wanted ways ... you need to precision retail your experiment for the effects you want to study
(i speak in general/non-specific -- but you haven't specified in detail your aim)
Thank you for clarifying those points. What I would like to better understand now is the difference in electrodynmaics between the four configurations as illustrated. I believe this will allow me to better interpret subsequent experimental results.

#### sparky 1

Joined Nov 3, 2018
246
Possibly the same idea but a little structure for a test involving AC.
When a parallel tank circuit becomes resonant the capacitive reactance equals the inductive reactance, the Q is highest.
This peak can be measured 2 diodes arranged as a rectifier (sometimes called Avremenko plug) A relative Q measurement

Both magnetic and electric fields on both hollow core inductor and 2 plate capacitor can be found and the Q can be measured.
Replacing the 2 plate capacitor with an equal capacitance 3 plate should result in another resonant tank.
Both E and M fields for the three plate capacitor could also be found and the Q can be measured.
Using an alternating current, Will there be a natural charge distribution and a natural field ? How does that effect the Q.
If the hollow core inductor is now changed to a spyder coil of comparable inductance does that change the tanks Q.
The Q and the plate distances and the surface area of the plates effect the capacitance and voltage but the frequency is kept the same.

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#### Sir Kit

Joined Feb 29, 2012
54
Helpful pointers for bench work. First I would like to better understand what happens in each configuration. This is no doubt more obvious to some here than myself. If so, a brief explanation of the field interactions in each instance from A through D would be appreciated.

#### sparky 1

Joined Nov 3, 2018
246
yes, electronics workbench. ltspice
The schematic conveys the essential information. The output is a sine wave. The space between C1 and C2 appears to be negligible.
A Brief explanation of capacitor field : C1 top attraction then C3 bottom repulsion. C1 and C3 are simultaneous
Inductor L1 attraction repulsion is simultaneous but in the opposite direction. The tank becomes resonant after tuning.
It is a 16kHz Hertzian wave having sinusoidal form. James C. Maxwell describes this.

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#### Sir Kit

Joined Feb 29, 2012
54
Very enlightening. But your schematic is not the same as my diagram D to which I assume it refers. You have also only put 4Vpp across the cap and coil. The PA transformer would apply about 100V. I am thinking that is a lot more displacement current.

Discounting the gap itself, I am wondering if having the coil physically between the cap plates would change the expected outcome. e.,g. resonant frequency.

I would still like to share a thought analysis of the three configurations that do not use the split secondary.

#### ci139

Joined Jul 11, 2016
1,528
? Is there anything "you can remind us about" the 3 plate capacitor -- the only difference i can imagine is the bulk E field around it being "unipolar" at any particular instant of time while the 2-plate producing better spreading EMF . . . is there anything else ?

e.g. where your 3 plate idea comes from

#### Sir Kit

Joined Feb 29, 2012
54
? Is there anything "you can remind us about" the 3 plate capacitor -- the only difference i can imagine is the bulk E field around it being "unipolar" at any particular instant of time while the 2-plate producing better spreading EMF . . . is there anything else ?

e.g. where your 3 plate idea comes from
Using example D again, the assembly is really two capacitors face-to-face with E fields opposing. The state of opposition is reliant upon the potential of the coil. In this ense it is bipolar. The coil acts as a modulator. That is the idea. The diagrams in my OP are simply different proposals for implementing this.

The plates in B, C and D could just as well sit at DC. But the transformer provides a ready means of step-up.

#### sparky 1

Joined Nov 3, 2018
246
Electrodynamics was explored for natural capacitor field and the brief explanation given.
Correcting the wordy playfulness the Q used here means quality factor.
Because the tank was tuned the field was summerized to Hertzian standards.
It is not the self resonant frequency even if it is close words and the lack of schematic is insufficient for real science.

The SRF requires more than a Hertzian wave. The compression and rarefaction is not the same.
We cannot change the science and mislead people in order to accommodate. James C Maxwell describes but
in this specific case it is first necessary to remove the snakes. The transformer chosen has ratio 1:1 shown
The V(p-p) = 5.65

#### nsaspook

Joined Aug 27, 2009
7,329
When you hear the term displacement current in a discussion of these types of circuits you know it's broken pot time.

http://farside.ph.utexas.edu/teaching/em/lectures/node46.html

Of course, the displacement current is not a current at all. It is, in fact, associated with the generation of magnetic fields by time-varying electric fields. Maxwell came up with this rather curious name because many of his ideas regarding electric and magnetic fields were completely wrong. For instance, Maxwell believed in the æther, and he thought that electric and magnetic fields were some sort of stresses in this medium. He also thought that the displacement current was associated with displacements of the æther (hence, the name). The reason that these misconceptions did not invalidate his equations is quite simple. Maxwell based his equations on the results of experiments, and he added in his extra term so as to make these equations mathematically self-consistent. Both of these steps are valid irrespective of the existence or non-existence of the æther.

But, hang on a minute,'' you might say, you can't go around adding terms to laws of physics just because you feel like it! The field equations (400)-(403) are derived directly from the results of famous nineteenth century experiments. If there is a new term involving the time derivative of the electric field which needs to be added into these equations, how come there is no corresponding nineteenth century experiment which demonstrates this? We have Faraday's law which shows that changing magnetic fields generate electric fields. Why is there no Joe Blogg's'' law that says that changing electric fields generate magnetic fields?'' This is a perfectly reasonable question. The answer is that the new term describes an effect which is far too small to have been observed in nineteenth century experiments. Let us demonstrate this.
...
So,'' you might say, why did you bother mentioning this displacement current thing in the first place if it is undetectable?'' Again, a perfectly fair question. The answer is that the displacement current is detectable in some experiments. Suppose that we take an FM radio signal, amplify it so that its peak voltage is one hundred volts, and then apply it to the parallel plate capacitor in the previous hypothetical experiment. What size of magnetic field would this generate? Well, a typical FM signal oscillates at
Hz, so
in the previous example changes from
seconds to
seconds. Thus, the induced magnetic field is about
gauss. This is certainly detectable by modern technology. So, it would seem that if the electric field is oscillating fast then electric induction of magnetic fields is an observable effect. In fact, there is a virtually infallible rule for deciding whether or not the displacement current can be neglected in Eq. (413). If electromagnetic radiation is important then the displacement current must be included. On the other hand, if electromagnetic radiation is unimportant then the displacement current can be safely neglected. Clearly, Maxwell's inclusion of the displacement current in Eq. (413) was a vital step in his later realization that his equations allowed propagating wave-like solutions. These solutions are, of course, electromagnetic waves. But, more of this later.

#### sparky 1

Joined Nov 3, 2018
246
The circuit ground and the 4 channel scope's ground needs double check. It is to early to say, being tired I am concerned about mistakes.
doing it your way the transformer ratio 1:1.5 gives 100Vpp. Ammeter monitoring is needed. results using a load is needed.
3 channels are: top, middle, bottom are channel A,B,C not to be confused with example ABCD
Example A. Channels A and C are the same. Channel B is 180 out but equal. The resistor, inserting values 30 to 2k made no difference.
I will double check give a better report at a later date. At this point I tend to think ABCD examples are all the same.

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#### Sir Kit

Joined Feb 29, 2012
54
The circuit ground and the 4 channel scope's ground needs double check. It is to early to say, being tired I am concerned about mistakes.
doing it your way the transformer ratio 1:1.5 gives 100Vpp. Ammeter monitoring is needed. results using a load is needed.
3 channels are: top, middle, bottom are channel A,B,C not to be confused with example ABCD
Example A. Channels A and C are the same. Channel B is 180 out but equal. The resistor, inserting values 30 to 2k made no difference.
I will double check give a better report at a later date. At this point I tend to think ABCD examples are all the same.
Tantalising. But I have a few questions.

"A and C are the same". So we are assuming the lesser voltage to the coil in C has no effect?

Can you please explain what you mean by B being "180 degrees out". Why does the included resistance value make no difference?

#### ci139

Joined Jul 11, 2016
1,528
the B vector for outer (crust) plates of the cap cancels out (if the wires to "up"/"down" plates are attached at the same (x,z) at (x,y±∆y,z) )

. . . anyway you have a weird ... (up to) a messy structure to deal with

EDIT :: Legend : The blue lines are B vectors for the balancing current of the plate capacitor. The segment of such current - the RP(ink)G(ray) - with it's current density fading towards the plate edges (as and the B vector density) . . . if the coil is apx. at the half-way in between the plates - the B cancels out so ... the *coil current likely won't couple with the "capacitor current" . . . but it* may induce something on the capacitor plates and couple with itself . . . (the wave theory might state something different tough ...)

PS! : why it's mentioned is because usually you set up a parallel mathematical/theoretical model for your experiment to compare/predict the results with/for
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#### sparky 1

Joined Nov 3, 2018
246
The unmodified 2 series capacitor the transformer is almost equal so the center plate has very small Vpp
As I increase the number of turns of the top half of the secondary winding of the transformer the center plate begins to
increase such that Vpp of A=B+C In this picture the phase difference between A and B is 180 degrees. THD remains 0% ABCD
There is no inductor. When the transformer is set to 10:11:10 these are turns, this gives A. 6.02Vpp B is 118mVpp C. 5.84Vpp
Changing the transformer was done In order to illustrate that the sum of (B+C) = A For anyone following this. The control is 10:10:10 If B=0 then A=C this is for reference in comparing the 4 configurations ABCD where A and C are in phase.

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