Electrical elastance is the reciprocal of capacitance. The SI unit of elastance is the inverse farad (F−1). The concept is not widely used by electrical and electronic engineers. The value of capacitors is invariably specified in units of capacitance rather than inverse capacitance. However, it is used in theoretical work in network analysis and has some niche applications at microwave frequencies.
The term elastance was coined by Oliver Heaviside through the analogy of a capacitor as a spring. The term is also used for analogous quantities in some other energy domains. It maps to stiffness in the mechanical domain, and is the inverse of compliance in the fluid flow domain, especially in physiology. It is also the name of the generalised quantity in bond-graph analysis and other schemes analysing systems across multiple domains.
Usage
The definition of capacitance (C) is the charge (Q) stored per unit voltage (V).
Elastance (S) is the reciprocal of capacitance, thus,
Expressing the values of capacitors as elastance is not done much by practical electrical engineers, although it is sometimes convenient for capacitors in series. The total elastance is simply the sum of the individual elastances in that case. However, it is used by network theorists in their analysis. One advantage is that an increase in elastance increases impedance. This is in the same direction as the other two basic passive elements, resistance and inductance. An example of the use of elastance can be found in the 1926 doctoral thesis of Wilhelm Cauer. On his path to founding network synthesis, he formed the loop matrix A,
where L, R, S and Z are the network loop matrices of inductance, resistance, elastance and impedance respectively and s is complex frequency. This expression would be significantly more complicated if Cauer had tried to use a matrix of capacitances instead of elastances. The use of elastance here is merely for mathematical convenience, in much the same way as mathematicians use radians rather than the more common units for angles.
Elastance is also used in microwave engineering. In this field varactor diodes are used as a voltage variable capacitor in frequency multipliers, parametric amplifiers and variable filters. These diodes store a charge in their junction when reverse biased which is the source of the capacitor effect. The slope of the voltage-stored charge curve is called differential elastance in this field.
Units
The SI unit of elastance is the reciprocal farad (F−1). The term daraf is sometimes used for this unit, but it is not approved by SI and its use is discouraged. The term is formed by writing farad backwards, in much the same way as the unit mho (unit of conductance, also not approved by SI) is formed by writing ohm backwards.
The term daraf was coined by Arthur E. Kennelly. He used it from at least 1920.
History
The terms elastance and elastivity were coined by Oliver Heaviside in 1886. Heaviside coined a great many of the terms used in circuit analysis today, such as impedance, inductance, admittance, and conductance. Heaviside's terminology followed the model of resistance and resistivity with the -ance ending used for extensive properties and the -ivity ending used for intensive properties. The extensive properties are used in circuit analysis (they are the "values" of components) and the intensive properties are used in field analysis. Heaviside's nomenclature was designed to highlight the connection between corresponding quantities in field and circuit. Elastivity is the intensive property of a material corresponding to the bulk property of a component, elastance. It is the reciprocal of permittivity. As Heaviside put it,