By Paul R. Gray
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Additional resources for Analysis and Design of Analog Integrated Circuits
As shown in Fig. 19, there are significant resistances rb and r, in series with the base and collector contacts, respectively. There is also a resistance re, of several ohms in series with the emitter lead that can become important at high bias currents. 15 This occurs at high collector currents where the dc base current produces a lateral voltage drop in the base that tends to forward bias the base-emitter junction preferentially around the edges of the emitter. Thus the transistor action tends to occur along the emitter periphery rather than under the emitter itself, and the distance from the base contact to the active base region is reduced.
57) in ( 1 . 1 l 1 ) gives AVCE - V A - ro AI, I, where V Ais the Early voltage and r, is the small-signal output resistance of the transistor. Since typical values of V A are 50 to 100 V, corresponding values of r, are 50 to 100 ki2 for Ic = 1mA. Note that r, is inversely proportional to I,, and thus r, can be related to g,, as are many of the other small-signal parameters. 6 characteristics of Fig. 10. X 1oP4at 25OC. 5 Basic Small-Signal Model of the Bipolar Transistor Combination of the above small-signal circuit elements yields the small-signal model of the bipolar transistor shown in Fig.
The charge d Q is where W is the width of the device perpendicular to the plane of Fig. 28 and Qr is the induced electron charge per unit area of the channel. At a distance y along the channel, the voltage with respect to the source is V ( y )and the gate-to-channel voltage at that point is 1 \ ~e~letion rein Y Y + ~ Y Y p-type substrate 4 - - v? 28 NMOS device with bias voltages applied. We assume this voltage exceeds the threshold voltage Vt. Thus the induced electron charge per unit area in the channel is Also, where vd is the electron drift velocity at a distance y from the source.
Analysis and Design of Analog Integrated Circuits by Paul R. Gray