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impedance_inverter [2025/05/04 08:21] – 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.
  
  
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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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 0 & -\frac{j}{\omega L} \\ -\frac{j}{\omega L} & 0 0 & -\frac{j}{\omega L} \\ -\frac{j}{\omega L} & 0
 \end{bmatrix}$$ \end{bmatrix}$$
 +
 +
  
 ====Another example==== ====Another example====
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 Many impedance inverters exist. Another example is the following circuit: Many impedance inverters exist. Another example is the following circuit:
  
-{{ immittance_inverter_pi-l-network.png?300 |}}+{{ immittance_inverter_t-c-network.png?300 |}}
  
 +Here, 
 +
 +$$K=-\frac{1}{\omega C}$$
  
 The ABCD matrix of the corresponding two-port network equals: The ABCD matrix of the corresponding two-port network equals:
  
-$$ABCD=\begin{bmatrix} +$$\begin{bmatrix} 
-0 & j \omega L \\ \frac{j}{\omega L} & 0+0 &  \frac{j}{\omega C} \\ j \omega C & 0
 \end{bmatrix}$$ \end{bmatrix}$$
  
 The corresponding impedance and admittance matrix equals: The corresponding impedance and admittance matrix equals:
- 
  
 $$Z=\begin{bmatrix} $$Z=\begin{bmatrix}
-0 & -j \omega L \\ -j \omega L & 0+0 & -\frac{j}{\omega C} \\ -\frac{j}{\omega C} & 0
 \end{bmatrix}$$ \end{bmatrix}$$
  
 $$Y=\begin{bmatrix} $$Y=\begin{bmatrix}
-0 & \frac{j}{\omega L} \\ \frac{j}{\omega L} & 0+0 & j\omega C\\ j \omega C & 0
 \end{bmatrix}$$ \end{bmatrix}$$
- 
  
 ---- ----
impedance_inverter.1746346909.txt.gz · Last modified: by kl · Currently locked by: 216.73.216.38