Hybrid Equivalent Circuits are a way to represent linear electrical networks with multiple types of elements, such as resistors capacitors, inductors, and sources, using a combination of two different models: the Z-parameter model and the Y-parameter model.
Z-Parameter Model (Impedance Parameters):
- Z-Parameters represent a network in terms of impedances.
- They describe the relationship between the input and output voltages and currents in terms of impedances.
- For a two-port network, Z-parameters are represented as a matrix:
Z_{11} Z_{12}
Matrix (Z) =
Z_{21} Z_{22}
Where:
- ( Z_{11} ) represents the input impedance looking into port 1 with port 2 open-circuited.
- ( Z_{12} ) represents the impedance when a voltage source is applied at port 1 while port 2 is short-circuited.
- ( Z_{21} ) represents the impedance when a voltage source is applied at port 2 while port 1 is short-circuited.
- ( Z_{22} ) represents the output impedance looking into port 2 with port 1 open-circuited.
Y-Parameter Model (Admittance Parameters):
- Y-Parameters represent a network in terms of admittances.
- They describe the relationship between the input and output currents and voltages in terms of admittances.
- For a two-port network, Y-parameters are represented as a matrix:
Y_{11} & Y_{12}
Matrix (Y) =
Y_{21} & Y_{22}
Where:
- ( Y_{11} ) represents the input admittance looking into port 1 with port 2 open-circuited.
- ( Y_{12} ) represents the admittance when a current source is applied at port 1 while port 2 is short-circuited.
- ( Y_{21} ) represents the admittance when a current source is applied at port 2 while port 1 is short-circuited.
- ( Y_{22} ) represents the output admittance looking into port 2 with port 1 open-circuited.
Hybrid Parameters (h-Parameters):
- Hybrid parameters are derived from both Z-parameters and Y-parameters to create a hybrid equivalent circuit model.
- These parameters describe the relationship between the voltages and currents of a two-port network.
- The hybrid parameters for a two-port network are:
- ( h_{11} ): Voltage at port 1 with current injected into port 2, while port 1 is open-circuited.
- ( h_{12} ): Voltage at port 1 with port 2 short-circuited.
- ( h_{21} ): Voltage at port 2 with port 1 short-circuited.
- ( h_{22} ): Voltage at port 2 with current injected into port 1, while port 2 is open-circuited.
These hybrid equivalent circuit models are helpful in analyzing and designing complex electrical networks, especially in RF (radio frequency) and microwave engineering, where the characteristics of multi-port networks need to be understood for efficient signal transmission and reception.
0 Comments