Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

From another perspective the small signal model of

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changes the gate-source voltage of each transistor, thus changing the drain current considerably. From another perspective, the small-signal model of these two structures is identical to that of the diode-connected devices in Fig. 6.34, revealing a small-signal impedance of only (if ) rather than infinity. 7.2 Common-Source Stage 7.2.1 CS Core Shown in Fig. 7.5(a), the basic CS stage is similar to the common-emitter topology, with the input applied to the gate and the output sensed at the drain. For small signals, converts the input voltage variations to proportional drain current changes, and transforms the drain currents to the output voltage. If channel-length modulation is neglected, the small-signal model in Fig. 7.5(b) yields and . That is, (a) (b) R M 1 V DD D I D out V in V Input Applied to Gate Output Sensed at Drain g m v v 1 1 in v R out v D Figure 7.5 (a) Common-source stage, (b) small-signal mode. (7.34) a result similar to that obtained for the common emitter stage in Chapter 5.
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 329 (1) Sec. 7.2 Common-Source Stage 329 The voltage gain of the CS stage is also limited by the supply voltage. Since , we have (7.35) concluding that if or is increased, so is the voltage drop across ( ). For to remain in saturation, (7.36) that is, (7.37) Example 7.4 Calculate the small-signal voltage gain of the CS stage shown in Fig. 7.6 if mA, , V, and . Verify that operates in saturation. R M 1 W L = V DD D 0.18 1 k 10 in v out v = 1.8 V Figure 7.6 Example of CS stage. Solution We have (7.38) (7.39) Thus, (7.40) (7.41) To check the operation region, we first determine the gate-source voltage: (7.42) (7.43) It is possible to raise the gain to some extent by increasing , but “subthreshold conduction” eventually limits the transconductance. This concept is beyond the scope of this book.
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BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 330 (1) 330 Chap. 7 CMOS Amplifiers The drain voltage is equal to V. Since V, the device indeed operates in saturation and has a margin of 0.2 V with respect to the triode region. For example, if is doubled with the intention of doubling , then enters the triode region and its transconductance drops. Exercise What value of places at the edge of saturation? Since the gate terminal of MOSFETs draws a zero current (at very low frequencies), we say the CS amplifier provides a current gain of infinity. By contrast, the current gain of a common- emitter stage is equal to . Let us now compute the I/O impedances of the CS amplifier. Since the gate current is zero (at low frequencies), (7.44) a point of contrast to the CE stage (whose is equal to ). The high input impedance of the CS topology plays a critical role in many analog circuits. The similarity between the small-signal equivalents of CE and CS stages indicates that the output impedance of the CS amplifier is simply equal to (7.45) This is also seen from Fig. 7.7.
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