Ch 4b 2006

Ch 4b 2006 - 4.2.3 Hybrid- Equivalent Circuit, Including...

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4.2.3 Hybrid- π Equivalent Circuit, Including the Early Effect So far in the small-signal equivalent circuit, we have assumed that the collector current is independent of the collector-emitter voltage. We discussed the Early effect in the last chapter in which the collector current does vary with collector-emitter voltage. Equation (3.16) in the previous chapter gives the relation EE 329 Introduction to Electronics 165
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Example 4.2 Objective: Determine the small-signal voltage gain, including the effect of the transistor output resistance r o . Reconsider the circuit shown in Figure 4.1, with the parameters given in Example 4.1. In addition, assume the Early voltage is 50V. EE 329 Introduction to Electronics 166
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The hybrid- π model derives its name from the hybrid nature of the parameter units. The four parameters of the equivalent circuits shown in Figures 4.13(a) and (b) are: 1. input resistance r π , (ohms), 2. β (dimensionless), 3. output resistance r 0 (ohms), and 4. transconductunce g m (mhos). Up to this point, we have considered only circuits with npn bipolar transistors. However, the same basic analysis and equivalent circuit also applies to the pop transistor. F'igure 4.14(a) shows a circuit containing a pnp transistor. EE 329 Introduction to Electronics 167
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Here again, we see the change of current directions and voltage polarities compared to the circuit containing the npn transistor. Figure 4.14(a) is the ac equivalent circuit, with the dc voltage sources replaced by an ac short circuit, and all current and voltages shown are only the sinusoidal components. The transistor in Figure 4.14(b) can now be replaced by either of the hybrid- π equivalent circuits shown in Figure 4.15. The hybrid- π equivalent circuit of the pnp transistor is the same as that of the npn device, except that all current directions and voltage polarities are reversed. EE 329 Introduction to Electronics 168
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Combining the hybrid- π of the pnp transistor Figure 4.15(a) with the ac equivalent circuit Figure 4. 14(b), we obtain the small-signal equivalent circuit shown in Figure 4.16. 4.2.4 Expanded Hybrid- π Equivalent Circuit Figure 4.17 shows an expanded hybrid- π equivalent circuit, which includes two additional resistances, r b , and r μ . r b is the series resistance of the semiconductor material between the external base terminal B and an idealized internal base region B'. A typical values is a few tens of ohms and is usually much smaller than r π , therefore it is normally negligible at low frequencies. However, at high frequencies it may not he negligible, since the input impedance becomes capacitive, as we will see in Chapter 7. The parameter r μ is the reverse-biased diffusion resistance of the base-collector junction. This resistance is typically on the order of megaohms and can normally be neglected (i.e. an open circuit). However, the resistance does provide some feedback between the output and input, meaning that the base current is a slight function of the EE 329 Introduction to Electronics 169
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collector- emitter voltage. Generally we will ignore these two components except in special cases.
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Ch 4b 2006 - 4.2.3 Hybrid- Equivalent Circuit, Including...

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