# Transformer based on electric field instead of magnetic field

#### electroman85

Joined Aug 15, 2011
12
Transformed is designed based on magnetic field changes. Simmilarly can a transformer be made by electric field changing. Like how inductor and capacitor are opposite to each other in their functioning, a transformer made using capacitor type principle ?

#### thatoneguy

Joined Feb 19, 2009
6,359
Like in a Charge pump or DC-DC converter?

#### crutschow

Joined Mar 14, 2008
27,703
There is no known easy way to make an electric field coupled transformer that will increase or decrease AC voltages, as you can easily do with a magnetic field. Also, by their nature, magnetic fields can provide isolation between input and output, electric fields cannot.

#### davebee

Joined Oct 22, 2008
540
If you charge a capacitor, isolate it, then change its plate separation, the voltage between the plates should change.

So I would think that you could conceiveably make a mechanical voltage transformer based on this principle.

#### THE_RB

Joined Feb 11, 2008
5,438
There is no known easy way to make an electric field coupled transformer that will increase or decrease AC voltages, as you can easily do with a magnetic field. Also, by their nature, magnetic fields can provide isolation between input and output, electric fields cannot.
I'm going to argue that a little.

If you have three 1uF capacitors in series and connect to 120v AC, the middle cap will have a reduced voltage (that is something like a "voltage transformer" effect). Also the middle cap is DC isolated so it could be connected to a reference DC voltage, and the cap's "output" AC voltage would then be referenced to that DC voltage.

It's not as good (or as isolated!) as a magnetic transformer but it is roughly comparable in those two ways.

#### electroman85

Joined Aug 15, 2011
12
How about adding an extra pair of secondary plates, with reduced surface area, so voltage across these secondary plates is less so therefore stepped down.

#### nsaspook

Joined Aug 27, 2009
8,657
How about adding an extra pair of secondary plates, with reduced surface area, so voltage across these secondary plates is less so therefore stepped down.
A 'capacitive divider' is sometimes used for very high voltage AC/pulse circuits (200kV+) but its normally just for a monitoring circuit, no power is drawn from it.

BUT I have seen very cheap electronics from China (not sold in the USA) that used one instead of a transformer to make a DC supply for a simple toy, 120AC to 12DC at a few mA.

#### crutschow

Joined Mar 14, 2008
27,703
I'm going to argue that a little.

If you have three 1uF capacitors in series and connect to 120v AC, the middle cap will have a reduced voltage (that is something like a "voltage transformer" effect). Also the middle cap is DC isolated so it could be connected to a reference DC voltage, and the cap's "output" AC voltage would then be referenced to that DC voltage.

It's not as good (or as isolated!) as a magnetic transformer but it is roughly comparable in those two ways.
That circuit does give you a lower voltage, but it's poorly regulated for any significant current draw.

It's DC isolated but not AC isolated from the mains and thus still dangerous.

#### crutschow

Joined Mar 14, 2008
27,703
How about adding an extra pair of secondary plates, with reduced surface area, so voltage across these secondary plates is less so therefore stepped down.
How would you physically build such a device?

Show a diagram of how you think this would work in an actual circuit.

Joined Dec 26, 2010
2,148
If you charge a capacitor, isolate it, then change its plate separation, the voltage between the plates should change.

So I would think that you could conceiveably make a mechanical voltage transformer based on this principle.
That is actually part of the principle behind some kinds of electrostatic generators, such as Wimshurst machines. These are not transformers, more like electrostatic equivalents of dynamos. The point is that mechanical effort is requited to separate the plates of a charged capacitor.

It is simple to see that the required mechanical energy turns up as increased electrical energy in the charged capacitor.

Suppose the capacitance is reduced from C to C/2, with no loss of the initial charge of Q coulombs.

Since Q = CV, if the capacitor is initially charged to V volts, the capacitor voltage has to increase to a new voltage (V2, say).

Q = CV = 0.5*C*V2 so V2 = 2*V: The energy stored initally is 0.5*C*V$$^{2}$$, so as C is halved but V is doubled, overall the energy is doubled

#### electroman85

Joined Aug 15, 2011
12
bottom is primary plates,
top is secondary plates

lower voltage across secondary due to smaller size

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#### thatoneguy

Joined Feb 19, 2009
6,359
What is shown would be picofarads in capacitance.

What makes larger capacitors have capacitance is multiple layers in a dielectric material (solid)

Though I'll admit I'm not sure if you had two sets of plates in a good dielectirc, each a different size and insulated from the other plate.

#### gojirasan

Joined Dec 17, 2011
22
I think you guys are somewhat missing the point of his question. You are trying to figure out ways to convert between two different electromotive forces based on systems that just use electric charge. While that might be more useful that doesn't seem like the parallel he is referring to.

An electrical transformer uses changing electrical currents in coils of wire to generate a magnetomotive force (MMF) in a high magnetic permeability material like silicon iron or supermalloy loop which transfers the power via magnetic flux to another coil which converts the magnetic flux back to electric current again, usually with a different EMF (and current) determined by the turns ratio.

But what would a magnetic transformer be like? A system which takes a magnetic flux, converts it to electric current and then back to a higher or lower magnetic flux or MMF again. Of course we can quite easily create a constantly changing electric current with a generator. How would you create a constantly changing magnetic flux? I guess you could just use an alternating current electromagnet to produce a constantly changing flux, but that is really cheating for this example since you are actually starting with electricity as the primary source. Although the electric current in the generator windings is actually created with a moving magnetic field.

Actually... Isn't a generator a kind of magnetic transformer if it's connected to an electromagnet or inductor or transformer? Well not exactly. It starts with a moving magnetic field which may not be exactly the same as a magnetic field that is changing in intensity and direction.

I think the most literal analogy would be if you could create an alternating magnetic flux in a supermalloy wire that is coiled around a copper core. Let's use a toroidal core for simplicity. The primary supermalloy coil has a constantly changing flux density between 0 and 1 Tesla and you want to create a constantly changing flux density in the secondary supermalloy coil of between 0 and .5 Tesla. Let's say you had 100 turns of magnetic wire in the primary and 50 turns of magnetic wire in the secondary. Would that system work as a step down magnetic transformer? Would the alternating magnetic flux change to an alternating electric current in the copper toroid and then be converted back to half the magnetic flux density,but with twice the MMF? I don't know. I find the idea of wrapping a magnetic conductor around an electrical conductor kind of confusing (but interesting). Damn. Now I really want to find out what would happen.

But there is really no need for such a literal analogy. You just need to be able to use electric current as an intermediary between two different levels of magnetic flux or MMF. Let's say you had two bar electromagnets separated by enough distance to make any magnetic interactions negligible. You have 20 turns of copper wire on the primary electromagnet and and 10 turns of copper wire on the secondary electromagnet/inductor. the wire forms a single closed loop between the two bars of high permeability material like supermalloy.

Maybe you use another electrical loop on the primary bar to create the changing magnetic field or maybe you use some kind of mechanical system that moves a NIB permanent magnet closer to and further away from the primary bar many times per second. However you do it you directly induce a changing magnetic field in the bar.

The first inductor would really be a sort of generator and the second just a plain old AC electromagnet. But can you make a generator just by changing the magnetic field of a magnet with coils of wire wrapped around it? Maybe you have to actually move the magnet across the direction of the coils so that the magnetic field lines physically move across the wires. It seems like you can create electricity by just altering the magnitude and direction of magnetic flux because that is exactly how power is transferred on the secondary side of a transformer core.

Since the primary inductor has twice the number of turns as the secondary inductor in my example I think the primary electromagnet/inductor would have half the flux density and twice the MMF of the secondary electromagnet/inductor with a copper loop creating the magnetic flux in the secondary electromagnet. So maybe that system could be described as a magnetic transformer. Basically two different valued inductors in a closed series circuit with one inductor exposed to (or creating) a rapidly changing magnetic field.

#### crutschow

Joined Mar 14, 2008
27,703
I think you guys are somewhat missing the point of his question.
...........
No, I don't believe we are. He was asking about a transformer using only electric fields, not magnetic fields and that's what we have been discussing.

#### steveb

Joined Jul 3, 2008
2,436
Transformed is designed based on magnetic field changes. Simmilarly can a transformer be made by electric field changing. Like how inductor and capacitor are opposite to each other in their functioning, a transformer made using capacitor type principle ?
How about adding an extra pair of secondary plates, with reduced surface area, so voltage across these secondary plates is less so therefore stepped down.
It sounds like you are asking if there is a dual principle to use with capacitors, as compared with coils, and I think the answer is yes, and it is along the lines you are suggesting with additional capacitor plates.

Let's start with the fact that Faraday's Law is the relevant law for transformer operation. Faraday's law says that the integrated electric field around a closed loop (i.e. the electro motive force, emf) equals the negative time rate of change of magnetic flux penetrating a surface bounded by the loop. In equation form this is as follows, where E is electric field and B is magnetic field density.

$$emf=\oint {\rm \vec E}\cdot {\rm d\vec l}=-{{d}\over{dt}}\int {\rm \vec B}\cdot {\rm d\vec s}$$

Maxwell's Law of displacement current is the dual relation that describes a similar idea for electric flux. In the field region between capacitor plates, the displacement current I penetrating a closed loop equals the rate of change of electric flux as follows, where epsilon is the permittivity and mu is the permeability of the medium.

$$I=\oint {{{\rm \vec B}\over{\mu}}\cdot {\rm d\vec l}={{d}\over{dt}}\int {\rm \epsilon \vec E}\cdot {\rm d\vec s}$$

With Faraday's law, it's clear that the time varying magnetic field generated from one coil can overlap with the closed loop of the another coil and allow voltage to be induced in a separate circuit.

With Maxwell's law, it's clear that a time varying electric field generated from one capacitor can overlap with the dielectric region of another capacitor and allow displacement current to be induced in the other capacitor circuit.

So, just as two coils that have mutually interacting magnetic fields can make a transformer via mutual inductance, one can say that mutually interacting electric fields can make a "dual device" (i can't think of the right name for it) via mutual capacitance.

The best discussion I've seen on the general theory of capacitance (which includes mutual capacitance effects) is found in section 2.8 of "The Principles of Electrodynamics" by Melvin Schwartz, 1972, available in a paperback Dover edition which is well worth the 10 dollars.

http://www.amazon.com/Principles-Electrodynamics-Dover-Books-Physics/dp/0486654931

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#### THE_RB

Joined Feb 11, 2008
5,438
It sounds like you are asking if there is a dual principle to use with capacitors, as compared with coils, and I think the answer is yes, and it is along the lines you are suggesting with additional capacitor plates.
...
"Additional capacitor plates" is very similar to the "capacitors in series" suggestion which I posted earlier (especially if you use different value capacitors).

The specific effect of the multi-plate model should be easy enough to emulate with a model built from typcial 2pin capacitors in the correct series/parallel combination, provided you know the effective capacitance between the plates (from plate interaction).

#### steveb

Joined Jul 3, 2008
2,436
That's like saying that a transformer is similar to a series and/or parallel combinations of coils. In some sense they are similar, but they are not the same thing, neither for mutually coupled coils (transformers) nor for mutually coupled capacitors. The key difference between isolated circuit components and mutually interacting components is that the latter share a common region of space where field interactions can occur, while the former have isolated field effects (at least ideally).

In my response above, I'm making an assumption, or an interpretation of what question the OP is actually asking. I may or may not have properly identified his question. But, if I understand him correctly, we need to include the more general situation of mutual interaction of fields. The interesting thing is that, in linear media, the principe of superposition can be used to help derive a general capacitance theory, as elegantly derived by Schwartz, which makes use of a capacitance matrix that includes the various interactions between multiple conductors. Parallel and series combinations of capacitors would only describe a subset of the possible situations that can be handled by the general capacitance matrix. For example, two isolated capacitors that are not connected at all, will have no interactions, just as two isolated coils have no interaction. However, if the fields of each device, are allowed to overlap in space, the mutual coupling implies that the separate isolated circuits can still interact. Hence, we have transformers, and whatever the hell people call these mutual capacitance devices.

#### THE_RB

Joined Feb 11, 2008
5,438
So are you saying you would not be capable of modeling the "multiplate" design from Electroman's post #11 using discrete caps?

#### steveb

Joined Jul 3, 2008
2,436
So are you saying you would not be capable of modeling the "multiplate" design from Electroman's post #11 using discrete caps?
As it is drawn, I think not. Although, there should be special cases of interconnecting the plates where you could model it that way. Under the assumptions of my interpretation of what the OP is asking, I don't see that as the correct way to model it. The general case of four conductors with isolated conductors requires a 4 by 4 matrix to specify all configurations allowed in a general field problem. This could of course be simplified in a particular circuit arrangement, but the model should at least include a coupled or mutual capacitance term, similar to what we do when we model mutual inductance.

Even the case of a 2 plate capacitor is not fully and properly modeled by a single capacitance value, but technically requires a 2 by 2 matrix. The simplification is allowed in circuit theory because in circuit applications the charges on each plate are equal in magnitude and opposite in sign. Or, in other words the device does not have a net charge as a whole.

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