Ideal Transistor h-Parameters Explained

Understanding the characteristics of an ideal transistor is crucial in electronics. An ideal transistor is a theoretical model that simplifies the behavior of a real transistor, making it easier to analyze circuits. When we talk about h-parameters (hybrid parameters), we are describing the small-signal behavior of a transistor, which relates its input and output voltages and currents.

The h-parameters are defined by a set of equations that relate input voltage ($\text{V}_{\text{1}}$) and output current ($\text{I}_{\text{2}}$) to input current ($\text{I}_{\text{1}}$) and output voltage ($\text{V}_{\text{2}}$):

• $\text{V}_{\text{1}} = \text{h}_{\text{i}}\text{I}_{\text{1}} + \text{h}_{\text{r}}\text{V}_{\text{2}}$
• $\text{I}_{\text{2}} = \text{h}_{\text{f}}\text{I}_{\text{1}} + \text{h}_{\text{o}}\text{V}_{\text{2}}$

For an ideal transistor, specific assumptions are made to simplify its model. These assumptions directly impact the values of its h-parameters, especially the reverse parameters.

Reverse Voltage Ratio ($\text{h}_{\text{r}}$) for Ideal Transistors

The parameter $\text{h}_{\text{r}}$ is known as the reverse voltage ratio or reverse transfer voltage ratio. It is defined as the ratio of input voltage to output voltage when the input current is zero (open-circuited input):

$\text{h}_{\text{r}} = \frac{\text{V}_{\text{1}}}{\text{V}_{\text{2}}} \text{ |}_{\text{I}_{\text{1}}=0}$

For an ideal transistor, there is no feedback from the output to the input. This means that any change in the output voltage ($\text{V}_{\text{2}}$) does not affect the input voltage ($\text{V}_{\text{1}}$) when the input current is kept constant (or zero, as in this definition). In other words, the output and input sections are perfectly isolated from each other in the reverse direction. Therefore, for an ideal transistor, the reverse voltage ratio $\text{h}_{\text{r}}$ is considered to be zero.

Output Admittance ($\text{h}_{\text{o}}$) for Ideal Transistors

The parameter $\text{h}_{\text{o}}$ is known as the output admittance. It is defined as the ratio of output current to output voltage when the input voltage is zero (short-circuited input):

$\text{h}_{\text{o}} = \frac{\text{I}_{\text{2}}}{\text{V}_{\text{2}}} \text{ |}_{\text{V}_{\text{1}}=0}$

The output admittance is the reciprocal of the output impedance ($\text{Z}_{\text{out}} = 1/\text{h}_{\text{o}}$). For an ideal transistor, it is assumed to have infinite output impedance. An infinite output impedance means that the transistor acts as a perfect current source, providing a constant current irrespective of the load voltage (within its operating limits). If the output impedance is infinite, then its reciprocal, the output admittance $\text{h}_{\text{o}}$, must be zero.

Summary of Ideal Transistor Reverse Parameters

In summary, for an ideal transistor:

• The reverse transfer voltage ratio ($\text{h}_{\text{r}}$) is zero because there is no feedback from the output to the input.
• The output admittance ($\text{h}_{\text{o}}$) is zero because the output impedance is considered infinite, making it a perfect current source.

Therefore, both reverse parameters, $\text{h}_{\text{o}}$ and $\text{h}_{\text{r}}$, are zero for an ideal transistor.