# Why h-Parameters are used?

What is the reason for using h-parameters when describing transistors? Why are they used instead of the physical description?

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This question needs some cleanup. Are you interested in comparing the hybrid-pi model with the h-parameter model? Or are you interested in comparing large-signal models (like $\alpha * I_E = I_C$ and $\beta * I_B = I_C$) with small-signal models like h-parameters? –  Kevin Vermeer Oct 4 '11 at 13:30
similar question: electronics.stackexchange.com/questions/14556/… –  Jon L Oct 4 '11 at 16:39
–  The Photon Sep 22 '12 at 5:05

You don't use h-parameters instead of a transistor. H-parameters are one system for characterizing bipolar transistors. The h-parameters of a transistor will give you a good idea what it can do, how to use it effectively in a circuit, and whether it is appropriate for a particular circuit.

In practise, only a few h-parameters are commonly used. The most common one if hfe, which stands for h-forward-emitter. That means it is the ratio of output to input in the common emitter configuration, which in turn means it is the ratio of collector current to base current, which is basically the gain of a bipolar transistor. Beta is another similar but not completely identical measure of gain, although in most cases the two can be used interchangably since a good circuit doesn't rely on exact values of gain anyway.

Sometimes you might see hre (h-reverse-emitter) which is a measure of how good a current source the transistor is at a particular fixed base current.

There are more h-parameters, but they get increasingly obscure and less commonly used.

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A small addition to Olin's good answer: a transistor (or many other kinds of analog circuits) can be considered as a two-port network, or quadripole. That means a block where the internal circuitry is not necessarily known, but are known the relationships between voltage and current at its ports.

So, you have a quadripole. You can draw it this way:

to describe the relationships between the four magnitudes, you need two equations of two variables, composing a square matrix. Depending on how the equations and the variables are arranged, the coefficients can be different magnitudes, and in this case:

• Adimensional: voltage over voltage, current over current

• Impedance: voltage over current

You can arrange the equations to have only impedances (z-parameters), only admittances (y-parameters) or a mix of them. This is the case of the hybrid parameters (h), where $\mathrm{V_1}$ and $\mathrm{I_2}$ are expressed as functions of $\mathrm{V_2}$ and $\mathrm{I_1}$. This leads to four h-parameters, specifically:

• $h_{11} = h_i = \left. \dfrac{v_1}{i_1} \right|_{v_2 = 0}$

• $h_{12} = h_r = \left. \dfrac{v_1}{v_2} \right|_{i_1 = 0}$

• $h_{11} = h_f = \left. \dfrac{i_2}{i_1} \right|_{v_2 = 0}$

• $h_{11} = h_0 = \left. \dfrac{i_2}{v_2} \right|_{i_1 = 0}$

Therefore $h_{fe}$ represents the h-parameter that describes the forward current gain in the common-emitter configuration, or commonly the current gain of the transistor.

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In my point of view h-parameters are used for small signal frequency analysis. It knows system performance by calculating the output gain. It has one disadvantage, it is not suitable for large signal amplification. In this model input voltage and output current are dependent.

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