Basics of electronic ...

In the current topic, we will focus on using the properties of bipolar transistors as controlled elements to build a simple voltage amplifier.

The characteristics of bipolar transistors determined in the previous topic for the common-emitter system allow us to conclude that two families of characteristics are important for the description of the transistor: input \(U_{BE} = f(I_B, U_{CE})\) and output \(I_C = f(I_B, U_{CE})\). When we are interested in small changes of the independent variables \(I_B, U_{CE}\) and the dependent variables \(U_{BE}, I_C\), we should write the total differentials of both functions:

\( dU_{BE} = \frac{\partial U_{BE}}{\partial I_B} dI_B + \frac{\partial U_{BE}}{\partial U_{CE}} dU_{CE} \)

\( dI_{CE} = \frac{\partial I_C}{\partial I_B} dI_B + \frac{\partial I_C}{\partial U_{CE}} dU_{CE} \)

If you mark the corresponding derivatives as follows:

\( \frac{\partial U_{BE}}{\partial I_B} = h_{11} \) when \(U_{CE}=const.\)

\( \frac{\partial I_C}{\partial I_B} = h_{21} \) when \(U_{CE}=const.\)

\( \frac{\partial U_{BE}}{\partial U_{CE}} = h_{12} \) when \(I_B = const.\)

\( \frac{\partial I_C}{\partial U_{CE}} = h_{22} \) when \(I_B = const.\)

and the increments of the appropriate variables are marked with lowercase letters, always used for small signals: \(u_{be}\), \(i_c\), \(i_b\), \(u_{ce}\), then a bipolar transistor can be described by linear equations:

\( u_{be} = h_{11} i_b + h_{12} u_{ce} \)\( i_c = h_{21} i_b + h_{22} u_{ce} \)

which correspond to treating the transistor as a linear active quad (two port device) with the equivalent circuit shown in the figure below (fig. a). This diagram fully reflects the physical meaning of the introduced hybrid parameters.

Figure 1

\( h_{11} = \frac{u_{be}}{i_b} \) when \(u_{ce}=0\) is the input resistance of the transistor with the output shorted,

\( h_{12} = \frac{u_{be}}{u_{ce}} \) when \(i_b=0\) is the return transmittance of the transistor with the input open,

\( h_{21} = \frac{i_c}{i_b} \) when \(u_{ce}=0\) is the current gain of the transistor when the output is shorted,

\( h_{22} = \frac{i_c}{u_{ce}} \) when \(i_b=0\) is the output conductance of the transistor with the input open.

The conducted considerations concerning the bipolar transistor focus on the hybrid model of the transistor. There are more detailed models, e.g. hybrid-π, which take into account a number of other parameters of the transistor, such as base stray resistance, base-collector resistive coupling, emitter junction capacitance and collector junction capacitance. It is worth mentioning that for low-power transistors, the base stray resistance is an important component of the input resistance \(h_{11}\) in the hybrid model.

The individual hybrid parameters of the transistor depend on the position of the operating point. Therefore, in the abbreviated datasheets, the values of the h parameters are given for the indicated operating point, and in the more complete datasheets, the dependence of these parameters on the coordinates of the transistor operating point is also provided. It should be noted that the parameter values of a transistor operating in a common-base or common-collector system are different than in a common-emitter system, although they can be expressed by them. In addition, the description of the small-signal properties of the transistor using hybrid parameters is used in a limited range of signal frequencies, usually not exceeding several hundred kilohertz.