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admittance_inverter [2025/05/04 07:55] – kladmittance_inverter [2025/05/04 08:27] (current) – kl
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 Since the admittance inverter is a reciprocal network, it follows that AD-BC=1, and since A=D=0, we get: B.C=1. 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====+The general ABCD matrix of an admittance inverter is given by: 
 +$$ABCD=\begin{bmatrix} 
 +0 & -\frac{j}{J}\\-jJ & 0 
 +\end{bmatrix}$$ 
 + 
 + 
 +====Example: capacitive wireless power transfer coupling====
  
 Different options exist to realize an admittance inverter, for example: Different options exist to realize an admittance inverter, for example:
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 {{ admittance_inverter_general_example.png?400 |}} {{ admittance_inverter_general_example.png?400 |}}
  
-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).+For example, when we choose a capacitor, J 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). 
 + 
 +$$J=\omega C$$
  
 {{ immittance_inverter_pi-c-network.png?300 |}} {{ immittance_inverter_pi-c-network.png?300 |}}
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 Note that this is exactly the electric coupling for capacitive wireless power transfer, where C is the mutual capacitance!  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: +The ABCD matrix of this admittance inverter is given by:
- +
-$$Y=\begin{bmatrix} +
-0 & -j\omega C\\-j \omega C & 0 +
-\end{bmatrix}$$ +
- +
-When considering repeater resonators, the ABCD matrix of the admittance inverter is relevant, given by:+
 $$ABCD=\begin{bmatrix} $$ABCD=\begin{bmatrix}
 0 & \frac{-j}{\omega C}\\-j \omega C & 0 0 & \frac{-j}{\omega C}\\-j \omega C & 0
 \end{bmatrix}$$ \end{bmatrix}$$
  
 +The corresponding impedance and admittance matrix equals:
  
-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).+$$Z=\begin{bmatrix} 
 +0 & \frac{j}{\omega C} \\ \frac{j}{\omega C} & 0 
 +\end{bmatrix}$$
  
 +$$Y=\begin{bmatrix}
 +0 & -j\omega C\\-j \omega C & 0
 +\end{bmatrix}$$
  
 +====Another example====
  
- +Many admittance inverters exist. Another example is the following circuit:
-Note that this is identical to the electric coupling for capacitive wireless power transfer. +
- +
  
 {{ immittance_inverter_pi-l-network.png?300 |}} {{ immittance_inverter_pi-l-network.png?300 |}}
  
 +Here, 
  
-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).+$$J=-\frac{1}{\omega L}$$
  
-{{ immittance_inverter_t-c-network.png?300 |}}+The ABCD matrix of the corresponding two-port network equals:
  
 +$$ABCD=\begin{bmatrix}
 +0 & j \omega L \\ \frac{j}{\omega L} & 0
 +\end{bmatrix}$$
  
-The impedance matrix of the corresponding two-port network equals:+The corresponding impedance and admittance matrix equals:
  
-$$\begin{bmatrix} + 
-0 & j\omega L\\j \omega L & 0+$$Z=\begin{bmatrix} 
 +0 & -j \omega L \\ -j \omega L & 0
 \end{bmatrix}$$ \end{bmatrix}$$
  
-$$\begin{bmatrix} +$$Y=\begin{bmatrix} 
-0 & j\omega L\\j \omega L & 0+0 & \frac{j}{\omega L} \\ \frac{j}{\omega L} & 0
 \end{bmatrix}$$ \end{bmatrix}$$
  
-Reference: Tosic, D. V., & Potrebic, M. (2006). Symbolic analysis of immittance inverters, 14th Telecommunication Forum. Belgrade (Serbia), 21-23. 
  
 +----
 +<color #808080>**References**</color>
 +  * <color #808080>Tosic, D. V., & Potrebic, M. (2006). Symbolic analysis of immittance inverters, 14th Telecommunication Forum. Belgrade (Serbia), 21-23.</color>
 +  * <color #808080>J.S.G. Hong and  M.J. Lancaster, ``M.J. Microstrip filters for RF/microwave applications,'' John Wiley and Sons.: Hoboken, NJ, USA, 2004.</color>
 +
 +----
 Looking for impedance inverter? Looking for impedance inverter?
   * [[Impedance inverter]]   * [[Impedance inverter]]
admittance_inverter.1746345335.txt.gz · Last modified: by kl