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An admittance inverter changes an output admittance $Y_{out}$ to its inversely proportional value $Y_{in}$, multiplied by a value J²:

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

J is a susceptance (in siemens), and is called the characteristic admittance of the inverter.

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

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 electric coupling for capacitive wireless power transfer, where C is the mutual capacitance!

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

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

When considering repeater resonators, the ABCD matrix of the admittance inverter is relevant, given by: $$ABCD=\begin{bmatrix} 0 & \frac{-j}{\omega C}\\-j \omega C & 0 \end{bmatrix}$$

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.

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).

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

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

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

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

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