Significance and Derivation

Author: Leonard Krugman

The open-circuit parameters, r₁₁, r₁₂, r₂₁, and r₂₂ are used exclusively throughout this book primarily because they are the most familiar four-pole equivalents. Some engineers prefer the short-circuit conductance parameters g₁₁, g₁₂, g₂₁, and g₂₂. The conductance parameters serve well for the junction transistor, but do not work out too well for the point-contact type, which inherently exhibit short circuit instability.

The disadvantages in both the r and g forms suggest a combination or hybrid type of representation which will be applicable to all transistor types without requiring elaborate measuring techniques. The so-called 'h' or hybrid parameters are becoming more and more popular. Since many of the manufacturer rating sheets now specify the h parameters, it is important to be able to convert the hybrid values into the more familiar r form for use in the design and performance equations. On a four-terminal basis, the hybrid parameters are equated as:

The basic circuits for measuring the h parameters are illustrated in Fig. 7-10, which define the values of the parameters in terms of the input and output currents and voltages as follows:

when e₂ = 0 (output short-circuited)

when i₁ = 0 (input open-circuited)

when e₂ = 0 (output short-circuited)

when i₁ = 0 (input open-circuited)

Fig. 7-10. Basic circuits for measuring four-terminal h parameters.

Notice that two of the measurements are made with the output short-circuited, and the remaining two are made with the input open-circuited. Furthermore, none of the parameters are exact equivalents, since r₁₁ is a resistance (ohms), h₂₂ is a conductance (mhos), h₁₂ is a numeric (voltage ratio), and h₂₁ is also a numeric (current ratio).