Hybrid parameters, also known as h-parameters, are a set of four parameters used to analyze linear electrical circuits with input and output terminals.
Understanding Hybrid Parameters
As stated in the reference, every linear circuit having input and output terminals can be analyzed by four parameters (one measured in ohm, one in mho and two dimensionless) called hybrid or h Parameters. The term "hybrid" means "mixed." These parameters are called hybrid parameters specifically since these parameters have mixed dimensions. This mixture of units (Ohms, Mhos, and dimensionless values) differentiates them from other parameter sets like Z-parameters (all Ohms) or Y-parameters (all Mhos).
These parameters are particularly useful for modeling bipolar junction transistors (BJTs) at low frequencies, though they can be applied to any two-port network. They define the relationship between the input voltage ($V_1$), input current ($I_1$), output voltage ($V_2$), and output current ($I_2$) of a two-port network.
The Four Hybrid Parameters
The four hybrid parameters relate the variables through the following equations:
$V1 = h{11}I1 + h{12}V_2$
$I2 = h{21}I1 + h{22}V_2$
Where:
- $h_{11}$ is the input impedance with the output short-circuited ($V_2 = 0$). Dimension: Ohms.
- $h_{12}$ is the voltage feedback ratio with the input open-circuited ($I_1 = 0$). Dimension: Dimensionless.
- $h_{21}$ is the current gain with the output short-circuited ($V_2 = 0$). Dimension: Dimensionless.
- $h_{22}$ is the output admittance with the input open-circuited ($I_1 = 0$). Dimension: Mhos (or Siemens).
This aligns perfectly with the reference stating the four parameters have dimensions of Ohm, Mho, and two dimensionless values.
Parameter Dimensions Summary
| Parameter | Description | Condition | Dimension |
|---|---|---|---|
| $h_{11}$ | Input Impedance | Output Shorted ($V_2=0$) | Ohms ($\Omega$) |
| $h_{12}$ | Reverse Voltage Transfer Ratio | Input Open ($I_1=0$) | Dimensionless |
| $h_{21}$ | Forward Current Transfer Ratio | Output Shorted ($V_2=0$) | Dimensionless |
| $h_{22}$ | Output Admittance | Input Open ($I_1=0$) | Mhos (S) |
Practical Applications
Hybrid parameters are widely used in transistor circuit analysis.
- Modeling Transistors: They provide a simplified model for transistors, especially in the common-emitter configuration, allowing engineers to calculate gain, input impedance, and output impedance.
- Circuit Analysis: They facilitate the analysis of complex circuits by representing sub-circuits as two-port networks described by their h-parameters.
- Design: Understanding h-parameters helps in designing circuits with specific characteristics, such as amplifiers with desired gain or impedance levels.
In essence, hybrid parameters offer a convenient way to characterize linear two-port networks by mixing voltage/current ratios and impedance/admittance values, reflecting their "hybrid" nature.
