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impedance_inverter [2025/05/04 07:55] – klimpedance_inverter [2025/12/27 16:06] (current) – [Definition] admin
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 \end{bmatrix}$$ \end{bmatrix}$$
  
-Since the impedance inverter is a reciprocal network, it follows that AD-BC=1, and since A=D=0, we get: B.C=1.+Since the impedance 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:+The general ABCD matrix of an impedance inverter is given by: 
 +$$ABCD=\begin{bmatrix} 
 +0 & -jK\\-\frac{j}{K} & 0 
 +\end{bmatrix}$$ 
 + 
 +====Example: inductive wireless power transfer coupling==== 
 + 
 +Different options exist to realize an impedance inverter, for example:
  
 {{ impedance_inverter_general_example.png?400 |}} {{ impedance_inverter_general_example.png?400 |}}
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 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). 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).
  
 +$$K=\omega L$$
  
 {{ immittance_inverter_t-l-network.png?300 |}} {{ immittance_inverter_t-l-network.png?300 |}}
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 Note that this is exactly the magnetic coupling for inductive wireless power transfer, where L is the mutual inductance!  Note that this is exactly the magnetic coupling for inductive wireless power transfer, where L is the mutual inductance! 
  
 +The ABCD matrix of this impedance inverter is given by:
 +$$ABCD=\begin{bmatrix}
 +0 & -j \omega L \\ -\frac{j}{\omega L} & 0
 +\end{bmatrix}$$
 +
 +The corresponding impedance and admittance matrix equals:
 +
 +$$Z=\begin{bmatrix}
 +0 & j \omega L \\ j \omega L & 0
 +\end{bmatrix}$$
 +
 +$$Y=\begin{bmatrix}
 +0 & -\frac{j}{\omega L} \\ -\frac{j}{\omega L} & 0
 +\end{bmatrix}$$
 +
 +
 +
 +====Another example====
 +
 +Many impedance inverters exist. Another example is the following circuit:
 +
 +{{ immittance_inverter_t-c-network.png?300 |}}
 +
 +Here, 
 +
 +$$K=-\frac{1}{\omega C}$$
 +
 +The ABCD matrix of the corresponding two-port network equals:
 +
 +$$\begin{bmatrix}
 +0 &  \frac{j}{\omega C} \\ j \omega C & 0
 +\end{bmatrix}$$
 +
 +The corresponding impedance and admittance matrix equals:
 +
 +$$Z=\begin{bmatrix}
 +0 & -\frac{j}{\omega C} \\ -\frac{j}{\omega C} & 0
 +\end{bmatrix}$$
 +
 +$$Y=\begin{bmatrix}
 +0 & j\omega C\\ j \omega C & 0
 +\end{bmatrix}$$
  
 +----
 +<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 admittance inverter? Looking for admittance inverter?
   * [[admittance inverter]]   * [[admittance inverter]]
  
  
impedance_inverter.1746345356.txt.gz · Last modified: by kl · Currently locked by: 216.73.216.38