BIPOLAR JUNCTION TRANSISTOR MODELING

BJT TRANSISTOR MODELING

A model is the combination of circuit elements, properly chosen, that best approximates the actual behavior of a semiconductor device under specific operating conditions.

Once the ac equivalent circuit has been determined, the graphical symbol of the device can be replaced in the schematic by this circuit and the basic methods of ac circuit analysis (mesh analysis, nodal analysis, and Thévenin’s theorem) can be applied to determine the response of the circuit.

For many years the industrial and educational institutions relied heavily on the hybrid parameters (to be introduced shortly).

The hybrid-parameter equivalent circuit continues to be very popular, although it must now share the spotlight with an equivalent circuit derived directly from the operating conditions of the transistor—the re model. Manufacturers continue to specify the hybrid parameters for a particular operating region on their specification sheets. The parameters (or components) of the re model can be derived directly from the hybrid parameters in this region. However, the hybrid equivalent circuit suffers from being limited to a particular set of operating conditions if it is to be considered accurate.

The parameters of the other equivalent circuit can be determined for any region of operation within the active region and are not limited by the single set of parameters provided by the specification sheet. In turn, however, the re model fails to account for the output impedance level of the device and the feedback effect from output to input.

Since both models are used extensively today, they are both examined in detail in this text. In some analysis and examples the hybrid model will be employed, while in others the re model will be used exclusively. The text will make every effort, however, to show how closely related the two models are and how proficiency with one leads to a natural proficiency with the other.

In an effort to demonstrate the effect that the ac equivalent circuit will have on the analysis to follow, consider the circuit of Fig. 7.3. Let us assume for the moment that the small-signal ac equivalent circuit for the transistor has already been determined.

Since we are interested only in the ac response of the circuit, all the dc supplies can be replaced by a zero-potential equivalent (short circuit) since they determine only the dc (quiescent level) of the output voltage and not the magnitude of the swing of the ac output. This is clearly demonstrated by Fig. 7.4. The dc levels were simply important for determining the proper Q-point of operation. Once determined, the dc levels can be ignored in the ac analysis of the network. In addition, the coupling

capacitors C1 and C2 and bypass capacitor C3 were chosen to have a very small reactance at the frequency of application. Therefore, they too may for all

Figure 7.3 Transistor circuit under examination in this introductory discussion

Figure 7.4 the network of Fig. 7.3 following removal of the dc supply and insertion of the short-circuit equivalent for the capacitors.

Practical purposes are replaced by a low-resistance path or a short circuit. Note that this will result in the “s shorting out” of the dc biasing resistor RE. Recall that capacitors assume an “open-circuit” equivalent under dc steady-state conditions, permitting isolation between stages for the dc levels and quiescent conditions.

If we establish a common ground and rearrange the elements of Fig. 7.4, R1 and R2 will be in parallel and RC will appear from collector to emitter as shown in Fig.7.5. Since the components of the transistor equivalent circuit appearing in Fig. 7.5 employ familiar components such as resistors and independent controlled sources, analysis techniques such as superposition, Thévenin’s theorem, and so on, can be applied to determine the desired quantities.

THE re TRANSISTOR MODEL

The re model employs a diode and controlled current source to duplicate the behavior of a transistor in the region of interest. Recall that a current-controlled current source is one where the parameters of the current source are controlled by a current elsewhere in the network. In fact, in general:

BJT transistor amplifiers are referred to as current-controlled devices.

Common Base Configuration

In Fig. 7.16a, a common-base pnp transistor has been inserted within the two-port structure employed in our discussion of the last few sections. In Fig. 7.16b, the remodel for the transistor has been placed between the same four terminals. As noted in Section 7.3, the model (equivalent circuit) is chosen in such a way as to approximate the behavior of the device it is replacing in the operating region of interest. In other words, the results obtained with the model in place should be relatively close to those obtained with the actual transistor. The forward-biased junction will behave much like a diode (ignoring the effects of changing levels of VCE) as verified by the curves of Fig. 3.7. For the base-to-emitter junction of the transistor of Fig. 7.16a, the diode equivalence of Fig. 7.16b between the same two terminals seems to be quite appropriate. For the output side, recall that the horizontal curves of Fig. 3.8 revealed that Ic = Ie for the range of values of VCE. The current source of Fig. 7.16b establishes the fact that

Figure 7.16 (a) Common-base BJT transistor; (b) re model for the configuration of Fig. 7.16a.

Ic = Ie, with the controlling current Ie appearing in the input side of the equivalent circuit as dictated by Fig. 7.16a. We have therefore established equivalence at the input and output terminals with the current-controlled source, providing a link between the two—an initial review would suggest that the model of Fig. 7.16b is a valid model of the actual device.