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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 smallsignal variables are indicated by a lowercase letter with lowercase subscripts, e.g. v s , i c . Total values are indicated by a lowercase letter with uppercase 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 collectorbase junction is reverse biased and the baseemitter junction is forward biased. For the npn device, the activemode collector and base currents are given by i C = I S exp p v BE V T P i B = i C β (1) where V T is the thermal voltage, I S is the saturation current, and β is the basetocollector 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) β = β p 1 + v CE V A P (4) where V A is the Early voltage and I S and β , respectively, are the zero bias values of I S and β . Because I S /β = I S /β , 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 emittertocollector current gain α is de¡ned as the ratio i C /i E . To solve for this, we can write i E = i B + i C = p 1 β + 1 P i C = 1 + β β i C (5) It follows that α = i C i E = β 1 + β β = i C i B = α 1α (6) Thus the currents are related by the equations i C = βi B = αi 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 basetoemitter voltage v BE with the collectortoemitter 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 basetoemitter 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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 Summer '08
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