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In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. [1]Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. [2]
An equivalent impedance is an equivalent circuit of an electrical network of impedance elements [note 2] which presents the same impedance between all pairs of terminals [note 10] as did the given network. This article describes mathematical transformations between some passive, linear impedance networks commonly found in electronic circuits.
The input impedance of an infinite line is equal to the characteristic impedance since the transmitted wave is never reflected back from the end. Equivalently: The characteristic impedance of a line is that impedance which, when terminating an arbitrary length of line at its output, produces an input impedance of equal value. This is so because ...
When there are dependent sources, the more general method must be used. The voltage at the terminals is calculated for an injection of a 1 ampere test current at the terminals. This voltage divided by the 1 A current is the Norton impedance R no (in ohms). This method must be used if the circuit contains dependent sources, but it can be used in ...
The properties of the parallel RLC circuit can be obtained from the duality relationship of electrical circuits and considering that the parallel RLC is the dual impedance of a series RLC. Considering this, it becomes clear that the differential equations describing this circuit are identical to the general form of those describing a series RLC.
In electrical engineering, the parallel operator can be used to calculate the total impedance of various serial and parallel electrical circuits. [nb 2] There is a duality between the usual (series) sum and the parallel sum. [7] [8]
The op-amp inverting amplifier is a typical circuit, with parallel negative feedback, based on the Miller theorem, where the op-amp differential input impedance is apparently decreased to zero. Zeroed impedance uses an inverting (usually op-amp) amplifier with enormously high gain .
Randles circuit schematic. In electrochemistry, a Randles circuit is an equivalent electrical circuit that consists of an active electrolyte resistance R S in series with the parallel combination of the double-layer capacitance C dl and an impedance (Z w) of a faradaic reaction.