# Capacitance measurement

## Capacitance measurement

The measurement of the ratio of the charge induced on a conductor to the change in potential with respect to a neighboring conductor which induces the charge. In a multiconductor system there are capacitances between each pair of conductors. In general, these capacitances are functions of the total geometry, that is, the location of all of the conducting and dielectric bodies. When, as is usually true, only the capacitance between two conductors is of interest, the presence of other conductors is an undesirable complication. It is then customary to distinguish between two-terminal and three-terminal capacitors and capacitance measurements. In a two-terminal capacitor, either one of the conductors of primary interest surrounds the other (in which case the capacitance between them is independent of the location of other bodies except in the vicinity of the terminals); or the somewhat indefinite contributions of the other conductors to the capacitance of interest are accepted.

A three-terminal capacitor consists of two active electrodes surrounded by a third, or shield, conductor. The direct capacitance between the two active electrodes is the capacitance of interest, and, when shielded leads are used, it is independent of the location of all other conductors except the shield.

Every physically realizable capacitor has associated loss in the dielectric and in the metal electrodes. At a single frequency these are indistinguishable, and the capacitor may be represented by either a parallel or series combination of pure capacitance and pure resistance. The measurement of capacitance, then, in general involves the simultaneous measurement of, or allowance for, an associated resistive element. *See* Permittivity

Most capacitance measurements involve simply a comparison of the capacitor to be measured with a capacitor of known value. Methods which permit comparison of essentially equal capacitors by simple substitution of one for the other at the same point in a circuit are frequently possible and almost always preferable.

#### Bridge comparison methods

When capacitors must be compared with high accuracy, bridge methods must be adopted. *See* Bridge circuit, Wheatstone bridge

Resistance-ratio bridges are Wheatstone-bridge configurations in which the potential division of the capacitor being measured and either a parallel combination of a standard loss-free capacitor *C*_{s} and a conductance *G*_{s} or a series combination of *C*_{s} and a resistor *R*_{s} is equated, when the detector is nulled, to the ratio of potentials across resistors *R*_{1} and *R*_{2}. More commonly now, the reference potential division is that of a variable-ratio autotransformer known as an inductive voltage divider (IVD). *See* Inductive voltage divider

The Schering bridge yields a measurement of the equivalent series-circuit representation of a capacitor.

The resistance-ratio and Schering bridges are useful for two-terminal capacitance measurements. Their use may be extended to three-terminal measurements and extended in accuracy and range by the introduction of shielding and the addition of the Wagner branch.

#### Time-constant methods

If a direct voltage is suddenly applied to the series combination of a resistor and an initially discharged capacitor, the charge and the voltage on the capacitor increase exponentially toward their full magnitudes with a time constant equal in seconds to the product of the resistance in ohms and the capacitance in farads. Similarly, when a charged capacitor is discharged through a resistor, the charge and the voltage decay with the same time constant. Various methods are available for the measurement of capacitance by measurement of the time constant of charge or discharge through a known resistor. *See* Time constant

In one such method the time required for the output voltage of an operational amplifier having a capacitor as a feedback component to increase to a value equal to the step-function input voltage applied through a resistor to its input is determined by an electronic voltage-comparison circuit and timer. With the assumption of ideal characteristics for the amplifier, such as infinite gain without feedback, infinite input impedance, and zero output impedance, the measured time interval is equal to the product of the values of the known resistance and the capacitance being measured.