mutual capacitance?

I have a capacitive transformer--sort of-- not far away from where I am sitting now in what truly is an electronic junk pile. A vendor sent it to me to try out. I believe it has found some use in battery operated fluorescent lamp lanterns. I am not sure where else.

It consists of a piezoelectric ceramic bar. It polarized across the bar for about half its length and along the bar for the rest of its length. If you apply a voltage across the cross-polarized half at the bar's mechanical resonance, a high voltage appears at the other end. This acts as the starting and running source for the lamp. Because of its high leakage reactance, it is the lamps ballast.

Getting back to your spherical capacitors, the voltage you measure is because of MUTUAL capacitance. Unless the spheres are extremely far apart, the mutual capacitance between them is much greater than their self capacitances. Again. I refer you to Smythe. It is a comprehensive but difficult book.

--

Sam

Conservatives are against Darwinism but for natural selection.
Liberals are for Darwinism but totally against any selection.

I remember playing with one of those.. They break apart quite easily. As far as I know they actually convert E-field into mechanical vibrations and then back to E-field. This of course is different from a magnetic transformer where the energy transfer is completely by the EM field alone.

It does, however, not 'succeed to replacing the functions of the lamp ballast: 1) High ignition voltage by resonance 2) Limiting the current during operation. 3) Filter out harmonics to prevent EMI. 4) Provide an inductive load to the switch-mode converter (for loss-less switching).

At least points 3 and 4 are not very well fulfilled! So not much savings in component count..

Not at all! If they are 1 diameter apart, then the mutual C is already about 3 times _lower_ then the self-C. Which means that with an AC voltage on one sphere, the voltage division would give about 1/4th of the voltage on a floating neighbor sphere.

Yes, Smythe is cool!

--
Jos

Items 1 and 2 are met very well indeed.

My trial gizmo worked very well as a transformer. IIRC i ran at about

30kHz.

Point 3 is not met well by inductive ballasts. My shortwave receiver just cannot operate near CFLs because of EMI. If inderstand your point

4, it is irrelevant. You just design your electronics for a capacitive load, and not an inductive load.

--

Sam

Conservatives are against Darwinism but for natural selection.
Liberals are for Darwinism but totally against any selection.

The historic development of electricity included years of experimenting with 'capacitors' that were, in fact, metal shells (suspended on insulating strings). The capacitance of two balls and the ability to induce a charge (ground ball2, move it near ball1, remove the ground, then pull ball2 far from ball1) made it possible to get a repeatable quantity of charge many times (because the induced charge on ball2 doesn't at all discharge ball1).

So, 'an isolated sphere' means a spherical conductor far from (many radii from) the nearest other conductors. The formula for the capacitance of an isolated sphere is quite valid. Also, useful.

Every dry winter day when you shock yourself on a light switch, your self capacitance IS an important feature.

That means it is sensitive. It does not disprove that the ballast coil reduces the harmonics. It actually is essential to meet the FCC requirements. With your gizmo you will fail, unless you add a coil after all!

Well, let's say you understood it as well as you understood Smythe about the two-sphere capacitances. :-)

And also you "just" design it to generate a pure sine wave, so no harmonics need be suppressed! We'll "just" let you do all the design for us and I'm sure we can remove all components in all our circuits!

--
Jos

e:

Thanks for the voice of reason whit3rd.

I wanted to add that anyone who has tried to get short response times from a high input impedance circuit knows all about self capacitance.

Short thin traces and no ground plane!

George H.

The equivalent formula for the Electric field is: div E =3D p where E is the electric field and p is thr electric charge density. When the charge density is zero (p=3D0), div E =3D 0 Under the condition of zero electric charge density, the electric field lines are closed.

Interesting question! Capacitance between two conducting bodies depends ONLY on geometry. Now we started with concentric spheres and allowed the outer sphere to get larger and larger (we won't use the mathematical term "infinite"). And what we found was that at some very large diameter the capacitance no longer depends on the diameter of the outer sphere. But what if we repeat the experiment with the outer conductor being a hemisphere? Or as you suggest a bunch of segmented plates around the universe. Or what if we substitute a flat plate for the inner sphere? I suggest that for a sphere as the outer conductor gets far away, the shape of the inner terminal again is the only thing determining capacitance. I presume that every geometrical shape for the inner terminal has some kind of "equivalent sphere" that one can use to calculate self-capacitance. But it is not clear to me that if the outer terminal is say a hemisphere instead of a full sphere that the capacitance will be the same no matter how far away it is. Same would go for a "universe" made up of various plates distributed around in some manner.

depends ONLY on geometry. Now we started with concentric spheres and allowed the outer sphere to get larger and larger (we won't use the mathematical term "infinite"). And what we found was that at some very large diameter the capacitance no longer depends on the diameter of the outer sphere. But what if we repeat the experiment with the outer conductor being a hemisphere? Or as you suggest a bunch of segmented plates around the universe.

"Infinite" is here doubled. It is obvious that in "infinity" (distance) is the "infinity" number of charges.

the inner sphere? I suggest that for a sphere as the outer conductor gets far away, the shape of the inner terminal again is the only thing determining capacitance.

For "doubled" infinity.

the inner terminal has some kind of "equivalent sphere" that one can use to calculate self-capacitance.

Maxwell calculated the self capacitance for a long cylinder and for a disc.

the outer terminal is say a hemisphere instead of a full sphere that the capacitance will be the same no matter how far away it is. Same would go for a "universe" made up of various plates distributed around in some manner.

If in infinity is infinity number of electrons no matter.

But to calculate the self capaticance you must take the both works. To push electrons from infinity to the sphere and to compress the electrons on the sphere. The both are the stored energy.

Of course in "hydraulic analogy" the second work do not exists. But to calculate the self capacitance you must use the gas analogy.

S*

Huh? The only thing that shows is as much electric flux enters a closed surface as leaves it. How does that show that an electric flux line forms a closed loop?

--

Sam

Conservatives are against Darwinism but for natural selection.
Liberals are for Darwinism but totally against any selection.

ctric

The electric charge density within the closed surface is not zero in the diagrams that you are thinking of. The electric fields are being generated by an electric charge. If there is a point charge inside the closed surface, the charge density at the point is infinite. Electric fields can be generated by changing magnetic fields without any electric charge around. This is called electromotive inductance. Electric fields generated this way are in a closed loop. The total charge of a circuit elements is usually zero. So as a course approximation, the average charge density in a circuit is zero. Nonzero electric charge accumulates in some parts of the circuit with capacitance. However, a capacitance is basically a bipolar element. Some poster in this thread used the word bipolar. Although I have never heard the word used by an engineer or scientist, it is apparent what he meant. He was talking about objects where there are equal and opposite charges separated on the objects. Such an object is bipolar. A point charge by itself would be monopolar. In this sense, circuit elements are mostly nonpolar (resistors) or bipolar (capacitors, batteries). There are no monopolar circuit elements. Each half of the capacitor has an equal and opposite charge. If you divided a capacitor in two, each plate has a nonzero electric charge. There is an electric field in the capacitor that isn't closed. However, this electric field is generated by what you may call a bipolar charge. A circuit can have a total nonzero charge, of course. However, this nonzero charge doesn't affect the flow of current. The total nonzero charge may be characterized by the ground potential. A lot of interesting things are covered by ground potentials. However, this is not relevant to the question of mutual capacitance. There are no active monopoles in a circuit. All the electric moments in a circuit are dipole or higher. Sources of electromotive power a bipolar. Capacitors can be considered bipolar. However, there are better ways to analyze the effect of a capacitance in the circuit. One of the best ways to figure out what is going on reducing the entire circuit to a collection of circuit elements with complex impedance, and currents to Fourier transforms in time. Then the issue of "charge separation" doesn't come up. You may consider "complex impedance" a mathematical fiction. Maybe so. However, it is easier to design electronics with "mathematical fictions" than to sort out the "charge separation" for each and every element.

here is a nice statement from an old textbook:

if little loss of a resonant circuit is in the capacitator, hte Q of a res. circ. is practically the Q of the coil unless resistance is added. It's often convenient to speak of the Q of an RF coil rather than its resistance, because the Q of a RF coil is likely to be more nearly constant over the useful freq. range of the coil, than in the effective resistance (sik?) (The comparitive constancy of Q is due to the effect of distributed capacitance in the coil, skin effect in the wires, and related phenomena.)

There is dispute about the capacitance between the earth and the moon. Some people claim about 3 uF, some claim about 160 uF. I think the first is the "mutual" or 3-terminal capacitance, and the second is the

2-terminal capacitance.

3 uF

earth--------||---------moon | | | | ___ ___ ___ 710 uF ___ 193 uF | | | | | | +----------------------+----- universe

John

(snip)

The series capacitor rule doesn't apply if the connection between the two is grounded (for example).

Given the circuit above, (assume it is smaller scale) one can measure the 3uF capacitance with the other two in place.

Apply an AC voltage across the 710uF, measure the AC current across the 193uF. (That is, shunt current through a low resistance ammeter.)

-- glen

Cool! It's only the 3 uF that counts for coupling electrostatic signals between the two.

George H.

Right. That one will taper off with distance. The 2-terminal capacitance wouldn't change much if the moon moved out past Jupiter. You'd just need longer test leads.

John

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The 710uF is calculated for the hydraulic analogy. For this value the Earth's potential would be 10^9V. In reality no such voltage.

In space are ions and electrons. Each body is negatively charged. It is the plasma physics.

S*

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I like it. How old is the book?

The plate capacitor and coil are both capacitors. The both have the large surfaces to collect the electrons. The important difference is the rate of the electron flow. From the plates the electrons can flow quickly, from the coils very slowly. S*