Editing Input impedance (section)

== Calculation ==
If one were to create a circuit with equivalent properties across the input terminals by placing the input impedance across the load of the circuit and the output impedance in series with the signal source, [[Ohm's law]] could be used to calculate the transfer function. 

===Electrical efficiency===
The values of the input and output impedance are often used to evaluate the electrical efficiency of networks by breaking them up into multiple stages and evaluating the efficiency of the interaction between each stage independently. To minimize electrical losses, the output impedance of the signal should be insignificant in comparison to the input impedance of the network being connected, as the gain is equivalent to the ratio of the input impedance to the total impedance (input impedance + output impedance). In this case, 
:<math> Z_{in} \gg Z_{out} </math> (or <math> Z_{L} \gg Z_{S} </math>)
:''The input impedance of the driven stage (load) is much larger than the output impedance of the drive stage (source).''

====Power factor====
In AC [[electrical network|circuits]] carrying [[power (physics)|power]], the losses of energy in conductors due to the reactive component of the impedance can be significant. These losses manifest themselves in a phenomenon called phase imbalance, where the current is out of phase (lagging behind or ahead) with the voltage. Therefore, the product of the current and the voltage is less than what it would be if the current and voltage were in phase. With DC sources, reactive circuits have no impact, therefore power factor correction is not necessary. 

For a circuit to be modelled with an ideal source, output impedance, and input impedance; the circuit's input reactance can be sized to be the negative of the output reactance at the source.  In this scenario, the reactive component of the input impedance cancels the reactive component of the output impedance at the source. The resulting equivalent circuit is purely resistive in nature, and there are no losses due to phase imbalance in the source or the load.
:<math>\begin{align}
Z_{in} & = X - j\operatorname{Im}(Z_{out}) \\
\end{align}</math>

===Power transfer===
The condition of [[maximum power theorem|maximum power]] transfer states that for a given source maximum power will be transferred when the resistance of the source is equal to the resistance of the load and the power factor is corrected by canceling out the reactance. When this occurs the circuit is said to be ''[[complex conjugate]] matched'' to the signals impedance. Note this only maximizes the power transfer, not the efficiency of the circuit. When the power transfer is optimized the circuit only runs at 50% efficiency. 

The formula for complex conjugate matched is 
:<math>\begin{align}
Z_{in} & = Z_{out}^* \\
& = \left\vert Z_{out} \right\vert e^{- j \Theta_{out}} \\
& = \operatorname{Re}(Z_{out}) - j \operatorname{Im}(Z_{out}). \\
\end{align}</math>
When there is no reactive component this equation simplifies to <math>Z_{in} = Z_{out}</math> as the imaginary part of <math>Z_{out}</math> is zero.

===Impedance matching===
When the characteristic impedance of a [[transmission line]], <math>Z_{line}</math>, does not match the impedance of the load network, <math>Z_{in}</math>, the load network will reflect back some of the source signal. This can create [[standing waves]] on the transmission line. To minimize reflections, the characteristic impedance of the [[transmission line]] and the impedance of the load circuit have to be equal (or "matched"). If the impedance matches, the connection is known as a ''matched connection'', and the process of correcting an impedance mismatch is called ''[[impedance matching]]''. Since the characteristic impedance for a homogeneous transmission line is based on geometry alone and is therefore constant, and the load impedance can be measured independently, the matching condition holds regardless of the placement of the load (before or after the transmission line).
:<math>Z_{in} = Z_{line}</math>