Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

The above phenomenon is quite similar to charging and

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for the collector current to drop to zero. The above phenomenon is quite similar to charging and discharging a capacitor: to change the collector current, we must change the base charge profile by injecting or removing some electrons or holes. Modeled by a second capacitor between the base and emitter, , this effect is typically more significant than the depletion region capacitance. Since and appear in parallel, they are lumped into one and denoted by [Fig. 11.20(c)]. As mentioned in Chapter 4, both forward-biased and reversed-biased junctions contain a depletion region and hence a capacitance associated with it.
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 553 (1) Sec. 11.2 High-Frequency Models of Transistors 553 In integrated circuits, the bipolar transistor is fabricated atop a grounded substrate [Fig. 11.21(a)]. The collector-substrate junction remains reverse-biased (why?), exhibiting a junction capacitance denoted by . The complete model is depicted in Fig. 11.21(b). We hereafter employ this model in our analysis. In modern integrated-circuit bipolar transistors, , , and are on the order of a few femtofarads for the smallest allowable devices. C B E Substrate C n p n + g m E π v π v π r r O C μ C (b) C π CS CS (a) C μ C π C CS E B C (c) B C Figure 11.21 (a) Structure of an integrated bipolar transistor, (b) small-signal model including collector- substrate capacitance, (c) device symbol with capacitances shown explicitly. In the analysis of frequency response, it is often helpful to first draw the transistor capacitances on the circuit diagram, simplify the result, and then construct the small-signal equivalent circuit. We may therefore represent the transistor as shown in Fig. 11.21(c). Example 11.12 Identify all of the capacitances in the circuit shown in Fig. 11.22(a). V Q Q b1 V CC 1 2 in V out V R C Q V CC 1 in V out V R C C μ 1 C CS1 C π 1 Q C μ C C π V b 2 2 2 CS2 (a) (b) Figure 11.22 Solution From Fig. 11.21(b), we add the three capacitances of each transistor as depicted in Fig. 11.22(b). Interestingly, and appear in parallel, and so do and . Exercise Construct the small-signal equivalent circuit of the above cascode.
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 554 (1) 554 Chap. 11 Frequency Response 11.2.2 High-Frequency Model of MOSFET Our study of the MOSFET structure in Chapter 6 revealed several capacitive components. We now study these capacitances in the device in greater detail. Illustrated in Fig. 11.23(a), the MOSFET displays three prominent capacitances: one between the gate and the channel (called the “gate oxide capacitance” and given by ), and two associated with the reverse-biased source-bulk and drain-bulk junctions. The first component presents a modeling difficulty because the transistor model does not contain a “channel.” We must therefore decompose this capacitance into one between the gate and the source and another between the gate and the drain [Fig. 11.23(b)]. The exact partitioning of this capacitance is be- yond the scope of this book, but, in the saturation region, is about of the gate-channel capacitance whereas .
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