Fundamentals-of-Microelectronics-Behzad-Razavi.pdf

Unlike the early effect in bipolar devices chapter 4

Info icon This preview shows pages 325–328. Sign up to view the full content.

View Full Document Right Arrow Icon
implications of channel-length modulation. Unlike the Early effect in bipolar devices (Chapter 4), the amount of channel-length modula- tion is under the circuit designer’s control. This is because is inversely proportional to : for a longer channel, the relative change in (and hence in ) for a given change in is smaller (Fig. 6.26). (By contrast, the base width of bipolar devices cannot be adjusted by the circuit designer, yielding a constant Early voltage for all transistors in a given technology.) V DS I D V DS I D 1 L L 2 Figure 6.26 Channel-length modulation. Example 6.9 A MOSFET carries a drain current of 1 mA with V in saturation. Determine the change in if rises to 1 V and . What is the device output impedance? Since different MOSFETs in a circuit may be sized for different ’s, we do not define a quantity similar to the Early voltage here.
Image of page 325

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 301 (1) Sec. 6.2 Operation of MOSFET 301 Solution We write (6.35) (6.36) and hence (6.37) With mA, V, V, and , (6.38) The change in is therefore equal to 48 A, yielding an output impedance of (6.39) (6.40) Exercise Does affect the above results? The above example reveals that channel-length modulation limits the output impedance of MOS current sources. The same effect was observed for bipolar current sources in Chapters 4 and 5. Example 6.10 Assuming , calculate and in Example 6.9 if both and are doubled. Solution In Eqs. (6.35) and (6.36), remains unchanged but drops to 0.05 . Thus, (6.41) (6.42) That is, A and (6.43)
Image of page 326
BR Wiley/Razavi/ Fundamentals of Microelectronics [Razavi.cls v. 2006] June 30, 2007 at 13:42 302 (1) 302 Chap. 6 Physics of MOS Transistors Exercise What output impedance is achieved if and are quadrupled and is halved. 6.2.4 MOS Transconductance As a voltage-controlled current source, a MOS transistor can be characterized by its transcon- ductance: (6.44) This quantity serves as a measure of the “strength” of the device: a higher value corresponds to a greater change in the drain current for a given change in . Using Eq. (6.17) for the saturation region, we have (6.45) concluding that (1) is linearly proportional to for a given , and (2) is linearly proportional to for a given . Also, substituting for from (6.17), we obtain (6.46) That is, (1) is proportional to for a given , and (2) is proportional to for a given . Moreover, dividing (6.45) by (6.17) gives (6.47) revealing that (1) is linearly proportional to for a given , and (2) is inversely proportional to for a given . Summarized in Table 6.1, these dependencies prove critical in understanding performance trends of MOS devices and have no counterpart in bipolar transistors. . Among these three expressions for , (6.46) is more frequently used because may be predetermined by power dissipation requirements. Example 6.11 For a MOSFET operating in saturation, how do and change if both and are doubled? Solution Equation (6.46) indicates that is also doubled. Moreover, Eq. (6.17) suggests that the over- drive remains constant. These results can be understood intuitively if we view the doubling of and as shown in Fig. 6.27. Indeed, if remains constant and the width of the device
Image of page 327

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 328
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern