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Unformatted text preview: c c Copyright 2010. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering. The BJT Notation The notations used here for voltages and currents correspond to the following conventions: Dc bias values are indicated by an upper case letter with upper case subscripts, e.g. V DS , I C . Instantaneous values of small-signal variables are indicated by a lower-case letter with lower-case subscripts, e.g. v s , i c . Total values are indicated by a lower-case letter with upper-case subscripts, e.g. v BE , i D . Circuit symbols for independent sources are circular and symbols for controlled sources have a diamond shape. Voltage sources have a sign within the symbol and current sources have an arrow. Device Equations Figure 1 shows the circuit symbols for the npn and pnp BJTs. In the active mode, the collector-base junction is reverse biased and the base-emitter junction is forward biased. For the npn device, the active-mode collector and base currents are given by i C = I S exp p v BE V T P i B = i C (1) where V T is the thermal voltage, I S is the saturation current, and is the base-to-collector current gain. These are given by V T = kT q = 0 . 025 V for T = 290 K = 25 . 86mV for T = 300K (2) I S = I S p 1 + v CE V A P (3) = p 1 + v CE V A P (4) where V A is the Early voltage and I S and , respectively, are the zero bias values of I S and . Because I S / = I S / , it follows that i B is not a function of v CE . The equations apply to the pnp device if the subscripts BE and CE are reversed. The emitter-to-collector current gain is dened as the ratio i C /i E . To solve for this, we can write i E = i B + i C = p 1 + 1 P i C = 1 + i C (5) It follows that = i C i E = 1 + = i C i B = 1- (6) Thus the currents are related by the equations i C = i B = i E (7) 1 Figure 1: BJT circuit symbols. Transfer Characteristics The transfer characteristics are a plot of the collector current i C as a function of the base-to-emitter voltage v BE with the collector-to-emitter voltage v CE held constant. From Eqs. 1 and 3, we can write i C = I S p 1 + v CE V A P exp p v BE V T P (8) It follows that i C varies exponentially with v BE . A plot of this variation is given in Fig. 2. It can be seen from the plot that the collector current is essentially zero until the base-to-emitter voltage reaches a threshold value. Above this value, the collector current increases rapidly. The threshold value is typically in the range of . 5 to . 6 V. For high current transistors, it is usually smaller. The plot shows a single curve. If v CE is increased, the current for a given v BE is larger....
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