Editing Electrical element (section)

==Two-port elements==
All the above are two-terminal, or [[one-port]], elements except the dependent sources. Two lossless, passive, linear [[two-port network|two-port]] elements are typically introduced into network analysis. Their constitutive relations in matrix notation are;

;Transformer:

: <math> \begin{bmatrix}  V_1  \\ I_2  \end{bmatrix} = \begin{bmatrix} 0 & n \\ -n & 0 \end{bmatrix}\begin{bmatrix} I_1  \\ V_2 \end{bmatrix}</math>

;Gyrator:

: <math> \begin{bmatrix}  V_1  \\ V_2  \end{bmatrix} = \begin{bmatrix} 0 & -r \\ r & 0 \end{bmatrix}\begin{bmatrix} I_1  \\ I_2 \end{bmatrix}</math>

The transformer maps a voltage at one port to a voltage at the other in a ratio of ''n''. The current between the same two ports is mapped by 1/''n''. On the other hand, the [[gyrator]] maps a voltage at one port to a current at the other. Likewise, currents are mapped to voltages. The quantity ''r'' in the matrix is in units of resistance. The gyrator is a necessary element in analysis because it is not [[Reciprocity (electrical networks)|reciprocal]]. Networks built from just the basic linear elements are necessarily reciprocal, so they cannot be used by themselves to represent a non-reciprocal system. It is not essential, however, to have both the transformer and gyrator. Two gyrators in cascade are equivalent to a transformer, but the transformer is usually retained for convenience. The introduction of the gyrator also makes either capacitance or inductance non-essential since a gyrator terminated with one of these at port 2 will be equivalent to the other at port 1. However, transformer, capacitance, and inductance are normally retained in analysis because they are the ideal properties of the basic physical components [[transformer]], [[inductor]], and [[capacitor]], whereas a [[Gyrator#Implementation: a simulated inductor|practical gyrator]] must be constructed as an active circuit.<ref>Wadhwa, C.L., ''Network analysis and synthesis'', pp.17–22, New Age International, {{ISBN|81-224-1753-1}}.</ref><ref>Herbert J. Carlin, Pier Paolo Civalleri, ''Wideband circuit design'', pp.171–172, CRC Press, 1998 {{ISBN|0-8493-7897-4}}.</ref><ref>Vjekoslav Damić, John Montgomery, ''Mechatronics by bond graphs: an object-oriented approach to modelling and simulation'', pp.32–33, Springer, 2003 {{ISBN|3-540-42375-3}}.</ref>