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Table of Contents
Impedance inverter
Definition
An impedance inverter changes an output impedance $Z_{out}$ to its inversely proportional value $Z_{in}$, multiplied by a value K²:
$$Z_{in}=\frac{K^2}{Z_{out}}$$
K is a reactance (in ohm), and is called the characteristic impedance of the inverter.
For the ABCD matrix of an impedance inverter, it holds that A=0 and D=0, with the ABCD matrix of a two-port network defined as: $$\begin{bmatrix} V_1 \\ I_1 \end{bmatrix} =\begin{bmatrix} A & B\\ C & D \end{bmatrix} \begin{bmatrix} V_2 \\ -I_2 \end{bmatrix}$$
Since the impedance inverter is a reciprocal network, it follows that AD-BC=1, and since A=D=0, we get: B.C=1.
The general ABCD matrix of an impedance inverter is given by: $$ABCD=\begin{bmatrix} 0 & -jK\\-\frac{j}{K} & 0 \end{bmatrix}$$
Examples
Different options exist to realize an admittance inverter, for example:
For example, when we choose an inductor, K equals $\omega L$ and we get the following circuit. (Note: a negative inductor corresponds to an capacitance, i.e., a capacitor instead of a coil).
Note that this is exactly the magnetic coupling for inductive wireless power transfer, where L is the mutual inductance!
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