6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.002CIRCUITS ANDELECTRONICSAmplifiers --Small Signal Model6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. MOSFET amp Saturation discipline — operateMOSFET only in saturation regionLarge signal analysis1. Find vOvs vIunder saturation discipline.2. Valid vI, vOranges under saturation discipline.Reading: Small signal model -- Chapter 8SVLRIvOvDSiReview6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Large Signal Reviewvalid for vI≥ VTandvO≥ vI–VT(same as )22ODSvKi ≤()LISORvKVv212−−=1IOvvsv6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Large Signal Review“interesting” region for vI. Saturation discipline satisfied.correspondinginterestingregion for vOIvSVOvTVTIOVvv−=TIOVvv−>TIOVvv−<V5V1V1V22Valid operating ranges6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].But…Amp is nonlinear … /IvSVOvTVTIOVvv−=DemoAmplifies alright,but distortsV5V1V1V2OvIvOvIvt6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Small Signal Model()LTISORVvKVv22−−=Amp all right, but nonlinear!Hmmm … So what about our linear amplifier ???IvSVOvTVV1V2~V1~V5~Insight:But, observe vIvs vOabout somepoint (VI , VO) … looks quite linear !()OIV,VFocus on this line segment6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Trick Operate amp at VI , VOÆ DC “bias” (good choice: midpointof input operating range) Superimpose small signal on top of VI Response to small signal seems to beapproximately linearIvΔovivIVOV()OIVV,OvΔlookslinear6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Trick Operate amp at VI , VOÆ DC “bias” (good choice: midpointof input operating range) Superimpose small signal on top of VI Response to small signal seems to beapproximately linearIvΔovivIVOV()OIVV,OvΔlookslinearLet’s look at this in more detail —I graphicallyII mathematicallyIII from a circuit viewpointnextweek6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].We use a DC bias VIto “boost” interesting input signal above VT, and in fact, well above VT .interestinginput signalSVLRIVOv+–+–I GraphicallyOffset voltage or biasIvΔ6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Good choice for operating point:midpoint of input operating rangeinterestinginput signalSVLRIVOv+–+–IvSVOvOVoperatingpointOIVV,IVTVTIOVvv−=0GraphicallyIvΔ6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Small Signal Modelaka incremental modelaka linearized modelovOVIVivNotation —totalvariableDCbiassmallsignal (like ΔvI)Input: vI= VI+ viOutput: vO= VO+ vobias voltage aka operating point voltageGraphically,OvttIv006.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].II Mathematically(… watch my fingers)()22TILSOVvKRVv −−=()iTILovVVKRv−−=gmiIIvVv+=substitutingIiVv<<[]()22TiILSOvvVKRVv −+−=[]()22iTILSvVVKRV +−−=[][]()2222iiTITILSvvvVVVKRV +−+−−=() ()iTIL2TILSoOvVVKRVV2KRVvV−−−−=+From ,()2TILSOVV2KRVV −−=related to VI6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Mathematically()iTILovVVKRv−−=gmiLmovRgv −=For a given DC operating point voltage VI, VI– VTis constant. So,constant w.r.t. viiovAv −=related to VIIn other words, our circuit behaves like a linear amplifierfor small signals6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Also, see Figure 8.9 in the course notesfor a graphical interpretation of this resultAnother way()22TILSOVvKRVv −−=()iovIVIv2TVIv2KLRSVIdvdv ⋅=⎥⎥⎦⎤⎢⎢⎣⎡−−=()iTILovVVKRv⋅−−=()TImVVKg−=LmRgA−=amp gainslope at VI6.002 Fall 2000 Lecture 10Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare
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