This article explains the basic key parameter of capacitors – capacitance – and its relations: dielectric material constant / permittivity, capacitance calculations, series and parallel connection, E tolerance fields and how it is formed by dipoles / dielectric absorption.
The Capacitance is determined by, among other things, the characteristics of the dielectric material. International standards speak of the Dielectric Constant or permittivity, designated by the symbol ε.
Description
A capacitor serves as a reservoir for electric charges. The size of the ”reservoir” is called capacitance and is expressed in the quantity F(arad) or As/V. The principle Figure 1. shows how the capacitance is directly proportional to the active area A and to the dielectric constant and inversely proportional to the distance between the electrodes. The formula in the figure is applicable to vacuum and air.
A = area (m2),
d = distance between electrodes (m),
ε0 = dielectric constant for vacuum (≈air) = 1×10-9/36π.
If the electric charge quantity of the capacitor is designated with Q (As), then the general formula 1 is valid.
……………………………… [1]
If we now insert an insulator material between the electrodes as shown in Figure 2., the formula in the figures 1. and 2. get the following general expression:
………………………………. [2]
εr is a relative number – the relative dielectric constant – which tells us how many times the capacitance is magnified when we exchange the air gap between the electrodes with different dielectric materials. That’s the relative dielectric constant εr which is given in technical tables and catalogues.
Table below shows dielectric constant of the most common materials.
Some more organic dielectric material constants can be found in article here.
Capacitive Reactance
If we change polarity in Figure 2. by applying an AC voltage over the capacitor, it will cause a certain resistance in the circuit, a so called capacitive reactance, XC, expressed in ohms.
The reactance is inversely proportional to frequency according to the formula
…………………….. [3]
- ω = 2 x π x f,
- f = frequency in Hz,
- C = capacitance in F.
Measure of miniaturization
The desired miniaturization of different capacitor types can be expressed in different ways. The smallest rated voltage for electrostatic capacitors often is more than enough for the application. Hence we usually disregard the voltage and compare the various types by means of their maximum possible C/V rate which means capacitance C per unit volume V (d * A in the Figure 1). According to the Formula [2] we get C/V = ε0 * εr * A/(d * A * d) = ε0 * εr /d2. The rate C/V will be at maximum for dmin, i.e., for VRmin.
In electrolytic capacitors the rated voltage plays a greater role because it can be adopted also to very low working voltages. Here the capacitors are grouped according to their charge quantity, that is to CR*VR. We refer to the CV product.
