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Table of Contents
Admittance inverter
Definition
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.
For the ABCD matrix of an admittance 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 admittance inverter is a reciprocal network, it follows that AD-BC=1, and since A=D=0, we get: B.C=1.
Examples
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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