Input impedance

The input impedance of an electrical network is the impedance from the source into the network being connected. In other words, the input impedance is the impedance, if placed across the input terminals, that would produce the same voltage across and current through the input terminals as the electrical network being connected. Therefore, the input impedance of the network being connected and the output impedance of the source determines the transfer function from the source to the input terminals of the circuit.

The Thévenin's equivalent circuit of the electrical network uses the concept of input impedance to determine the impedance of the equivalent circuit.

The circuit to the left of the open circles models the source circuit, while the circuit to the right models the connected circuit. ZS is the output impedance seen by the load, and ZL is the input impedance seen by the source).

Input impedance

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. To calculate the input impedance, short the input terminals together and reduce the circuit by determining the equivalent circuit with only one component.

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 interdependently. 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,

$Z_{in} \gg Z_{out}$
The input impedance of the driven stage (load) is much larger than the output impedance of the source.

Power factor

In AC circuits carrying power, the losses 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 of) 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 modeled with an ideal source, an output impedance, and an input impedance; the circuits input reactance can be sized to be the negative of the output reactance of the load. In this scenario the reactive component of the input impedance cancels the reactive component of the output impedance of the load. From the ideal sources perspective the circuit between the output and input impedance is purely resistive in nature, and there are no losses due to phase imbalance in the source or the load.

\begin{align} Z_{in} & = X - \operatorname{Im}(Z_{out}) \times j \\ \end{align}

Power transfer

The 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. Also note that this equation does not work in reverse, the optimal output impedance of the source is 0 regardless of the input impedance of the load.

\begin{align} Z_{in} & = Z_{out}^* \\ & = \left\vert Z_{out} \right\vert e^{j - \Theta_{out}} \\ & = \operatorname{Re}(Z_{out}) - \operatorname{Im}(Z_{out}) \times j \\ \end{align}
When there is no reactive component this equation simplifies to $Z_{in} = Z_{out}$

Impedance matching

To minimize reflections the characteristic impedance of the transmission line, and the load impedance have to be equal (or "matched"). Failure to match impedance will create standing waves on the transmission line due to reflections. This is known as a matched connection, and the process of correcting an impedance mismatch is called impedance matching.

$Z_{in} = Z_{line}$

Applications

Audio systems

Generally in audio and hi-fi systems, amplifiers have an input impedance several orders of magnitude higher than the output impedance of the source device connected to that input. This concept is also called voltage bridging or impedance bridging.

In general, this configuration will be more resistant to noise (particularly mains hum). Also the loading effects on the driving amplifier stage are reduced. In certain circuits a voltage follower stage is used to match the source and load impedance, which results in maximum power transfer.

Video and high frequency (RF) systems

In RF systems, typical values for line and termination impedance are 50 Ω and 75 Ω. In analog video circuits, impedance mismatch can cause "ghosting", where the time-delayed echo of the principal image appears as a weak and displaced image (typically to the right of the principal image). In high-speed digital systems, such as HD video, reflections result in interference and potentially corrupt signal.