Capacitance Topics

• stray capacitance
• elastic sphere
• metal electrodes
• displacement field
• nonlinear function
• time dependence
• quantum theory
• elastic properties
• parallel plate
• modern approach
• vortices
• limiting factor
• polarization
• dielectric
• free space
• capacitor
• deformation
• high frequency
• virtue
• maxwell

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Capacitance, Capacitance

For some materials represented by complicated behavior of D , the capacitance can be a function of voltage and may exhibit time dependence related to the ability of the medium to respond to the signal (see subsections below).

Consequently, a capacitance still is present. For example, a system of metal electrodes in free space may possess a capacitance.

Then the effect upon C of inserting a dielectric between the plates was determined. See The theory of molecular Vortices applied to Statical Electricity , p. 21 Today, capacitance is viewed primarily in terms of the capacity for storage of charge, whereas Maxwell's paper stressed the current that flowed through a capacitor. He calculated this current focusing upon the specific calculation of polarization for an "elastic sphere" distorting under an applied field and resisting deformation by virtue of its elastic properties, and the current that flowed when this state of polarization altered. The modern approach attempts to treat the polarization of materials by modeling the microscopic events contributing to the displacement field using quantum theory: for example, see below.

This field polarizes the dielectric, which polarization, in the case of a ferroelectric, is a nonlinear S -shaped function of field, which, in the case of a large area parallel plate device, translates into a capacitance that is a nonlinear function of the voltage causing the field.

This (unwanted) effect is termed "stray capacitance". Stray capacitance can allow signals to leak between otherwise isolated circuits (an effect called crosstalk), and it can be a limiting factor for proper functioning of circuits at high frequency.

It is often convenient for analytical purposes to replace this capacitance with a combination of one input-to-ground capacitance and one output-to-ground capacitance. (The original configuration — including the input-to-output capacitance — is often referred to as a pi-configuration.) Miller's theorem can be used to effect this replacement. Miller's theorem states that, if the gain ratio of two nodes is 1:K, then an impedance of Z connecting the two nodes can be replaced with a Z/(1-k) impedance between the first node and ground and a KZ/(K-1) impedance between the second node and ground. (Since impedance varies inversely with capacitance, the internode capacitance, C, will be seen to have been replaced by a capacitance of KC from input to ground and a capacitance of (K-1)C/K from output to ground.) When the input-to-output gain is very large, the equivalent input-to-ground impedance is very small while the output-to-ground impedance is essentially equal to the original (input-to-output) impedance.

Source: Wikipedia > Capacitance