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=====Admittance inverter=====

An admittance inverter changes an output admittance $Y_{out}$ to its inversely proportional value $Y_{in}$, multiplied by a value B²:

$$Y_{in}=\frac{B^2}{Y_{out}}$$

B is a susceptance, and is called the characteristic admittance of the inverter.

Different options exist to realize an admittance inverter, for example:

The susceptance B can be an inductance or a capacitance. For example, when we choose an inductor, B equals $\omega L$ and we get the following circuit. (Note: a negative inductance corresponds to a capacitance, i.e., a capacitor instead of a coil).

For example, when we choose a capacitor, B equals $\omega C$ and we get the following circuit. (Note: a negative capacitance corresponds to an inductance, i.e., a coil instead of a capacitor).

Note that this is exactly the magnetic coupling for inductive wireless power transfer, where L is the mutual inductance!

The impedance matrix of the corresponding two-port network equals:

$$\begin{bmatrix}
0 & j\omega L\\j \omega L & 0
\end{bmatrix}$$

When considering relay resonators, the ABCD matrix of the admittance inverter is relevant, given by:
$$\begin{bmatrix}
0 & j\omega L\\j \omega L & 0
\end{bmatrix}$$

For example, when we choose a capacitor, B equals $\omega C$ and we get the following circuit. (Note: a negative capacitance corresponds to an inductance, i.e., a coil instead of a capacitor).

Note that this is identical to the electric coupling for capacitive wireless power transfer.

$$\begin{bmatrix}
0 & \frac{-j}{\omega C}\\-j \omega C & 0
\end{bmatrix}$$

Reference: Tosic, D. V., & Potrebic, M. (2006). Symbolic analysis of immittance inverters, 14th Telecommunication Forum. Belgrade (Serbia), 21-23.

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