We ordinarily think of capacitance as a property of a device consisting of two conductive plates with terminals or leads, separated by an electrolytic layer. There is also unintended or parasitic capacitance, where two conductive bodies take the form of a capacitor and exhibit similar properties. An example of this is the atmospheric situation preceding a lightning strike, when the electrolyte consists of air until an ionized path is formed through it.

Ordinary two-electrode capacitance may be quantified as the ratio of the electric charge on each plate to their voltage difference. In a device with greater capacitance, this ratio increases. The electric charge is greater for a given amount of voltage.

This discussion pertains to a two-plate or bipolar capacitance, but there are capacitive configurations that are not included in the conventional description. One of these is the counterintuitive phenomenon of self-capacitance. How can there be a difference in electrical potential when there is only a single electrode?

An isolated single conductor can actually be charged, and the self-capacitance is the amount of electric charge that must be applied to raise its electric potential by one volt. For this potential difference to be meaningful, of course, there must be a point of reference. This point of reference is a theoretical hollow conducting sphere of infinite radius, its center falling within the location of the single conductor.

This line of thinking presupposes that a difference in electrical potential can exist between a real conductive body and one that is at best hypothetical. This is possible provided that we can pump in (or remove) free electrons from a single isolated body. That can certainly take place if electrical energy is or can be applied.

In regard to the electrolytic layer, that is a realistic concept. Even the absolute vacuum of empty space has an electrolytic constant. Materials may be classified with respect to permittivity. Zero permittivity is a perfect dielectric. A material with a permittivity of less than one has a low conductivity or is a good dielectric. A material with a permittivity of one is a lossy conductor and also a lossy field propagation medium. Material with a permittivity over one is a good conductor or poor dielectric. If the permittivity is infinite, the material would be a perfect conductor and would not exhibit a dielectric property.

The permittivity of vacuum (free space), which defines the permittivity of other materials, is one. By way of perspective, the dielectric constant of glass is between five and ten, depending upon its chemical composition.

Our earth has self-capacitance in the amount of 710 µF. A sphere of a van de Graaf generator having a radius of a little less than eight inches, exhibits a self-capacitance of 22.24 pF.

Another non-standard capacitor configuration involves the possibility of multiple (more than two) plates. For example, suppose we were to build a capacitor with three plates separated by two electrolytic layers:

This is a test setup that will determine whether the charge applied to a capacitor is stored in the electrolyte (yes) or in the plates (no), in the latter case the electrolyte being merely an insulator and serving to preserve uniform spacing between the plates. For this test, a multimeter in capacitance mode is used.

Sometimes the term self-capacitance is used to refer to the inter-winding capacitance of a coil. This is a different phenomenon altogether, not related to the topic we are discussing.

When subjected to a high-frequency signal, a coil becomes in effect a transmission line that happens to have a helical configuration in three-dimensional space. As such, it consists of an array of series inductances and parallel capacitances. This being the case, the array becomes a parallel LC circuit exhibiting self-resonance. Often this circuit behavior is undesirable. It can be avoided by designing the coil so that its self-resonant frequency is higher than the circuit’s operating frequency.

A simplistic understanding of the capacitor is that it is a frequency-dependent resistor. And it is true that as the frequency rises, the capacitive reactance, which is the basic parameter that determines circuit impedance, declines as measured across the device. A capacitor can be deployed in either parallel or series configuration in a two-wire transmission line. Depending on which configuration is used, the amount of attenuation experienced by a signal that is being conveyed will have opposite relations to its frequency.

But in another sense also the model of a capacitor as a frequency-dependent resistor is not completely accurate. It breaks down in that power is not dissipated as heat when the capacitor limits current in a circuit. It is true that voltage drops across a capacitor. But rather than dissipating energy in the form of heat in the manner of a resistor, a capacitor temporarily stores the energy in the form of charged particles within the electrolytic layer.

Characteristic impedance is a property that is intrinsic to various types of transmission cable. Coaxial cable, for example, is manufactured in 50- and 75-Ω versions. The characteristic impedance does not depend upon the length. You could cut a 100-ft. piece of 75-Ω coaxial cable in half and end up with two 50-ft. pieces of coax each having a characteristic impedance of 75 Ω.

Characteristic impedance cannot be measured directly with an ohmmeter, with or without the far end of the cable conductors connected. Characteristic impedance is usually measured by means of a time-domain reflectometer or by an oscilloscope using a specialized procedure.

The characteristic impedance of coaxial cable depends upon a number of factors including thickness and dielectric constant of the dielectric layer and wire size of the center conductor and outer braid. These relate to characteristic impedance in accordance with a complex formula that is primarily of interest to the manufacturer.

To understand how characteristic impedance works, visualize an infinitely long transmission line composed of a two-conductor cable that has been cooled down to that strange Kelvin region where electrical resistance is not applicable. The two parallel conductors separated by an electrolytic layer can be modeled as an infinite number of parallel capacitors and series inductors. The conductor segments between each capacitor node have definite amounts of inductance.

When ac energy is fed into the input of the cable, it will experience a certain impedance that will be the same regardless of frequency. As this pulse travels through the cable, the impedance tends to drop as more capacitors are placed in parallel, and it tends to get higher as more inductors are placed in series. These two ongoing events balance one another and the bottom line is that the impedance does not vary.

When a voltage is applied to the input of the transmission line, the capacitors charge, each one in succession. This charging action drops the voltage. Concurrently, the series-connected inductors establish magnetic fields, whereupon they no longer oppose the flow of current.

However, downstream in this infinitely long cable, there are always more capacitors and more inductors. The operative capacitive and inductive reactance opposes the flow of current as impedance rather than as resistance. In an infinitely long cable, regardless of the frequency, the impedance is always the same, perhaps 50 or 75 Ω, depending upon the cable construction.

To maintain this uniform impedance, a necessary condition is that there are no data reflections from the output end of the cable. Such reflected waves would make interference that would disrupt the uniform transmission. What makes reflection-free operation possible is that the cable has no end. It is endless, infinite.

The problem that arises is that such an infinitely long cable does not exist in the real world. Are we back where we started? Not really. The solution is to terminate the transmission line in a load having an impedance equal to the characteristic impedance of the line. The result is that the source sees no end to the line, and in that sense, the line behaves as if it is infinite. This idea gives rise to the important concept of impedance matching.

Wave impedance of free space, vacuum impedance and intrinsic or characteristic impedance of a vacuum are alternative terms for a plane wave traveling through a dielectric medium. They are represented in equations by the Greek letter eta (η). Z_{0} or η_{0} is the quantity to be found.

Expressed in ohms, Z_{0} is equal to 119.9169832 times π, or 376.73031346177 . . . ohms. This, then, is the impedance of free space, if you can conceive of such a thing.

Stephen says

In the following paragraph, the use of “permittivity” is not technically accurate. It would be clearer to say “conductivity”. A perfect conductor has infinite conductivity, not infinite permittivity. ‘Good’ dielectrics can have a variety of permittivity values, but in general no less than epsilon_0, the permittivity of free space

“Materials may be classified with respect to permittivity. Zero permittivity is a perfect dielectric. A material with a permittivity of less than one has a low conductivity or is a good dielectric. A material with a permittivity of one is a lossy conductor and also a lossy field propagation medium. Material with a permittivity over one is a good conductor or poor dielectric. If the permittivity is infinite, the material would be a perfect conductor and would not exhibit a dielectric property.”

Nicolau Palm says

Interesting article, but the measuring of self capacitance is missing. How we make a setup to measure self capacitance of an object??