While there are situations in transmission lines that are special case. Charles Proteus Steinmetz team was brought in to tackle such a problem having a transformer pop in the early 1900's was a big deal. The drama was intense. Maxwell's equation needed to include boundary conditions and displacement current. And they must figure this out in quickly. They did and today the grid design handles surges except for an EMP event. This awareness is more passionate within some intellectual circles.

To answer the question about frequency. At this point the output remains the same frequency. It would not hurt to look for harmonics. We know that combining the waves may cause displacement where B is inversely proportional. Fortunately B is not zero but is indicating the build up of a dielectric field the circuit having final inductor removed.

What do I expect when connecting the 4 channel scope . The B center tap will be removed after showing the comparison to the control.
The TS configurations can be made by simply changing the input to the dual series capacitor. The charge dynamics change to simultaneous action top and bottom and the output phase top and bottom are the same.

 

One of my heroes: Charles Proteus Steinmetz, this is a classic.

https://www.google.com/books/editio...B38AAAAAMAAJ?hl=en&gbpv=1&printsec=frontcover
Theory Calculation Transient Electric Phenomena Oscillations

The component i, called the current, is defined as that factor of the electric power P which is proportional to the magnetic field , and the other component e, called the voltage, is defined as that factor of the electric power P which is proportional to the electrostatic field . Current i and voltage e , therefore, are mathematical fictions, factors of the power P , introduced to represent respectively the magnetic and the electrostatic or “ dielectric ” phenomena . The current i is measured by the magnetic action of a circuit, as in the ammeter ; the voltage e, by the electrostatic action of a circuit, as in the electrostatic voltmeter, or by producing a current i by the voltage e and measuring this current i by its magnetic action , in the usual voltmeter.

 

This is the configuration A the center plate is 180 degrees out of phase
The top and bottom trace are the same because the jumper.
Useful as a 180 degree shifter.

 

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.

The 4 configurations
View attachment 213522

The resistor value has the following effect on channel B the phase makes an abrupt flip when B amplitude dips to zero.
The resistance was lowered using a variable resistor the value was decreased from 240 to 60 Ohms.
1.) Lowering the resistance from 240 to 120 Ohm Channel B amplitude diminishes and the phase is 180 degrees.
2.) Lowering the resistance from 120 Ohm to 60 Ohm Channel B amplitude grows and the phase is 0 degrees.

*The impedance of this Audio transformer can be determined very precisely when channel B V/Div is set very low.
Being able to see the wave and approach Impedance visually is useful for simulators or could be constructed easily for DIY.
There are times when the an oscillator's output becomes distorted when inserting it into the next stage amplifier.
As a tool the dual series capacitor center node on scope is better than I expected.
Thank you Sir_kit

 

That is a great analysis. I never suspected these type of circuits would be useful in a conventional sense.

I am wondering if the magnetic field emitted by an actual coil might somehow affect the result, even if only slightly. Is there any theoretical basis for such an interaction?

 

there are situations in transmission lines that are special case

a good point out . . . but the specific dimensions and construction/geometry/design would make the cases A,B,C,D compliant with such or then not

... the model for such structure is likely as below (about wavelength https://en.wikipedia.org/wiki/Radio_frequency#Frequency_bands)

 

Last month the Royal Society of chemistry london admitted published a correction that the electrolytics can have negative capacitance.
Arrl said that long ago. But recently with ion thrusters and reconnection phenomena made science revisit Lorentz F page 18.
however before the flux density increases each flux line has it's counterpart orbitals. opinion or fact, time will tell.

https://www.slideshare.net/mrrifas/electric-charges-lorentz-force

The is sun flairs felt across the galaxy, Our magnetic shielding has been leaking.
It is never the less where our best efforts are needed. A new era of fusion development.
https://arxiver.moonhats.com/2019/0...ntz-force-variations-at-the-suns-surface-ssa/

 

https://arxiver.moonhats.com/2019/0...ntz-force-variations-at-the-suns-surface-ssa/

the scale , energies and "particle numbers" are far beyond of the ones that can be experimentally reached on the Earth -- there might be some macro phenomena that is not present at lower scale processes and are not ?fully? described by relatively simple models (a low "number of computations" / relatively simplistic "integration")

 

the scale , energies and "particle numbers" are far beyond of the ones that can be experimentally reached on the Earth -- there might be some macro phenomena that is not present at lower scale processes and are not ?fully? described by relatively simple models (a low "number of computations" / relatively simplistic "integration")

At the very high energies and particle densities seen in space we can have current density phase changes (superluminal polarization currents) that have >FTL group speeds. This creates EM energy wave-fronts (that can't actually exceed FTL) that are compressed much like a sonic shock-ware from a supersonic jet.
https://iopscience.iop.org/article/10.1088/0004-637X/770/1/18

We can duplicate this effect on earth using the right equipment.
https://aip.scitation.org/doi/10.1063/1.4928893
https://arxiv.org/abs/physics/0405062

 

5 step network analysis of CauerLP filter could serve as an example how to solve using a quantitative expression.
Dual series capacitor categorized as dual impedance. The sun flairs are more complex however comsol and the graphical method was addressed.
The context sun flair illustrates Math description. It uses a less common Lorentz force approach. The sun does not use a copper conductor. Also listed in the context of post #27 is the electrochemical Lorentz Force in solution. There are many examples that do not have copper conductor. Aether theory has the burden of vetting out the all the strange nonsense, too time consuming. There are various graphical methods and we can touch on that and examine the category that avoids the less common Lorentz cases. When the great masters used the term aether it had some merit. It is unnecessary controversy an inherent weakness. This case differs from the many cracks and strange fiascoes because it can demonstrated.

(age 13) faradistor. ( I wonder why this polar electrolytic capacitor has residual charge on it's aluminum casing.) Takes a very observant young man.

The Dual impedance model includes center tapped coil also. Derivation of equivalence model Z prime = 1/Z = Admittance Y prime.
*Note that wikapedia author did not list dual series non-polar capacitor. Tuff questions with ambiguous support.
The graphical method shows lump line analogs, how the equivalence models combine and can be detailed in different colors blue and red.
( An example Cauer LP 1942 ) these can be highlighted giving perspective facilitating solving method as component dual impedance network.
(A fundamental basis of EM wave analysis, the Lorentz force equations is more than a coincidence in the compact fusion reactor.
The unit's output is greater than it's input, it was built on a shoestring budget. The electrical principles have been published, just needs a 13 year old's inquisitive mindset. Removing elite interference. Allow academic pier review using conservative EE graduate programs.) I will move fusion to a new thread. Focusing on the TS question asked, I am guessing that past dual capacitor experiments somehow fell through a crack in the table.

Focusing on the question asked in post #24 also tuff question, possibly an approach called dimensional analysis like Joseph Fourier used.
https://en.wikipedia.org/wiki/Dual_impedance
The TS wants to know how the inductor (transformer's inductance) can play a role (as a dual impedance circuit) ?

 

D - Center tapped transformer.

this one should point it out best , me thinks -- ? you do realize that the very construction and connection.. (wires to/from -- how it's done) ..have a large influence on the behaviour of the entire grid/circuit ?

why i'm telling this is -- your circuit will do a lot of different.. (hard to track down to it's precise cause) ..funny things -- so you need a bit to predict and pre-determine what you want it to do ... and what (exactly) you can and going to measure . . . so you can build it for ?that? purpose , essentially

a poor model for option D (the party zone is 8 to 40 MHz - but the 1:100 PA likely can't reach that . . . and this is not correct model -- it's very ... very approximate)