Editing Network analysis (electrical circuits) (section)

===Two port network transfer function===
Transfer functions, in general, in control theory are given the symbol H(s). Most commonly in electronics, transfer function is defined as the ratio of output voltage to input voltage and given the symbol A(s), or more commonly (because analysis is invariably done in terms of sine wave response), ''A''(''jω''), so that;
<math display="block">A(j\omega)=\frac{V_o}{V_i}</math>

The ''A'' standing for attenuation, or amplification, depending on context. In general, this will be a complex function of ''jω'', which can be derived from an analysis of the impedances in the network and their individual transfer functions.  Sometimes the analyst is only interested in the magnitude of the gain and not the phase angle.  In this case the complex numbers can be eliminated from the transfer function and it might then be written as;
<math display="block">A(\omega)=\left|{\frac{V_o}{V_i}}\right|</math>

====Two port parameters====
{{main|Two-port network}}
The concept of a two-port network can be useful in network analysis as a [[black box]] approach to analysis. The behaviour of the two-port network in a larger network can be entirely characterised without necessarily stating anything about the internal structure.  However, to do this it is necessary to have more information than just the A(jω) described above. It can be shown that four such parameters are required to fully characterise the two-port network. These could be the forward transfer function, the input impedance, the reverse transfer function (i.e., the voltage appearing at the input when a voltage is applied to the output) and the output impedance. There are many others (see the main article for a full listing), one of these expresses all four parameters as impedances.  It is usual to express the four parameters as a matrix;
<math display="block">
\begin{bmatrix}
  V_1 \\
  V_0
\end{bmatrix}
=
\begin{bmatrix}
  z(j\omega)_{11} & z(j\omega)_{12} \\
  z(j\omega)_{21} & z(j\omega)_{22}
\end{bmatrix}
\begin{bmatrix}
  I_1 \\
  I_0
\end{bmatrix}
</math>

The matrix may be abbreviated to a representative element;

<math> \left [z(j\omega) \right] </math> or just <math> \left [z \right] </math>

These concepts are capable of being extended to networks of more than two ports. However, this is rarely done in reality because, in many practical cases, ports are considered either purely input or purely output. If reverse direction transfer functions are ignored, a multi-port network can always be decomposed into a number of two-port networks.

====Distributed components====
Where a network is composed of discrete components, analysis using two-port networks is a matter of choice, not essential. The network can always alternatively be analysed in terms of its individual component transfer functions. However, if a network contains [[distributed-element model|distributed components]], such as in the case of a [[transmission line]], then it is not possible to analyse in terms of individual components since they do not exist. The most common approach to this is to model the line as a two-port network and characterise it using two-port parameters (or something equivalent to them). Another example of this technique is modelling the carriers crossing the base region in a high frequency transistor. The base region has to be modelled as distributed resistance and capacitance rather than [[Lumped parameters|lumped components]].

====Image analysis====
{{Main|Image impedance}}
Transmission lines and certain types of filter design use the image method to determine their transfer parameters. In this method, the behaviour of an infinitely long cascade connected chain of identical networks is considered. The input and output impedances and the forward and reverse transmission functions are then calculated for this infinitely long chain. Although the theoretical values so obtained can never be exactly realised in practice, in many cases they serve as a very good approximation for the behaviour of a finite chain as long as it is not too short.