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bjt_ac_analysis

# bjt_ac_analysis - BJT AC Analysis by Kenneth A Kuhn Oct 20...

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BJT AC Analysis 1 by Kenneth A. Kuhn Oct. 20, 2001, rev Aug. 31, 2008 Introduction This note will discuss AC analysis using the beta, re transistor model shown in Figure 1 for the three types of amplifiers: common-emitter, common-base, and common-collector. For each type of amplifier the goal is to determine the input resistance, r IN , output resistance, r O , and voltage gain. The voltage gain may be either the unloaded stage gain, the loaded stage gain, or the net voltage gain depending on what is needed. The analysis is simplified by first developing general equations for the AC terminal resistances of the transistor and then using this result to compute the input and output resistances of each of the three amplifier types. Before proceeding with AC analysis, we must have values for beta and r e . We nominally use a beta of 100 unless we want to know the specific characteristics over a specific range of beta. The dynamic resistance of the forward biased base-emitter junction is given by r e = V T / I E Eq. 1 where V T is the thermal voltage. We nominally use a V T of 0.026 Volts but if specific AC characteristics for a particular temperature are needed, then the V T for that temperature is used instead. AC terminal resistances The first step in AC analysis is to develop equations that give us the AC resistance looking into each transistor terminal. The result of these calculations will enable us to easily calculate the input and output resistances of transistor amplifiers including the bias circuit. The beta, r e model for the transistor and the standard circuit is shown in Figure 2. We define one set of AC resistances looking out of the transistor terminals and another set of AC resistances looking into the transistor terminals. Each of these is easy to calculate. Any combination of resistances can be reduced to a single resistor. In order that we do not have to be concerned about the specific resistors in the external circuit for our analysis, the external circuit is reduced to three resistances, R B ’, R E , and R C ’. These are the external AC resistances seen looking out of the particular terminal of the transistor.

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BJT AC Analysis 2 Figure 1: Simple transistor model and equivalent circuit
BJT AC Analysis 3 Figure 2: Transistor impedances

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