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MIT 6 002 - Small Signal Circuits

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6.002 Fall 2000 Lecture 11Cite 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 ANDELECTRONICSSmall Signal Circuits6.002 Fall 2000 Lecture 11Cite 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 notationvA= VA+ vatotaloperatingpointsmallsignal()iVvIIoutIOUTvvfdvdvvfvII⋅===)(SVLRoOOvVv +=IV+–+–iIIvVv +=ivReview:6.002 Fall 2000 Lecture 11Cite 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].I Graphical view (using transfer function)behaves linearfor smallperturbationsIvOvReview:6.002 Fall 2000 Lecture 11Cite 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 Mathematical view()LTISORVvKVv22−−=()iVvLTISIovRVvKVdvdvII⋅⎥⎦⎤⎢⎣⎡−−==22related to VI constant for fixedDC bias()iLTIovRVVKv⋅−−=gmReview:6.002 Fall 2000 Lecture 11Cite 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].DemoDChoosing a bias point:SiOvLSLTIKRVKRVv211 ++−+=TIVv =2ODSv2Ki <load lineLOLSDSRvRVi −=How to choose the bias point,using yet another graphical view based on the load lineOVIVinput signalresponseILmVRg∝1. Gain2. Input valid operating range for amp.3. Bias to select gain and input swing.6.002 Fall 2000 Lecture 11Cite 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].III The Small Signal Circuit ViewWe can derive small circuit equivalentmodels for our devices, and thereby conductsmall signal analysis directly on circuits()2TIDVv2Ki −=+–ROUTvVS+–Iv1e.g. large signalcircuit modelfor ampWe can replace large signal models withsmall signal circuit models.Foundations: Section 8.2.1 and also in the last slide in this lecture.6.002 Fall 2000 Lecture 11Cite 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 Circuit Analysis1Find operating point using DC bias inputs using large signal model.Develop small signal (linearized) models for elements.Replace original elements with smallsignal models.23Analyze resulting linearized circuit…Key: Can use superposition and otherlinear circuit tools with linearizedcircuit!6.002 Fall 2000 Lecture 11Cite 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 ModelsMOSFETAlargesignal()22TGSDSVvKi −=DSGSvSmall signal?6.002 Fall 2000 Lecture 11Cite 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 ModelsMOSFETAlargesignal()22TGSDSVvKi −=DSGSvSmall signal:smallsignalDSgsv()gsTGSdsvVVKi −=gsmdsvgi=()22TGSDSVvKi −=()gsVvTGSGSdsvVvKviGSGS⋅⎥⎦⎤⎢⎣⎡−∂∂==22()gsTGSdsvVVKi⋅−=gmidsis linear in vgs!6.002 Fall 2000 Lecture 11Cite 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].DC Supply VSBlargesignalSSVv=sIiSSsiiVvSS⋅∂∂==0vs=+–SSVv=Si+–svsiDC source behavesas short to smallsignals.Small signal6.002 Fall 2000 Lecture 11Cite 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].Similarly, RClargesignalsmallsignalR+–RvRiR+–rvriRRiRv=()rIiRRriiRivRR⋅∂∂==rriRv ⋅=6.002 Fall 2000 Lecture 11Cite 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()22TIDSVvKi −=()LTISORVvKVv22−−=LROv+–Iv+–SVDSiLRov+–ivdsi()iTIdsvVVKi ⋅−=0=+oLdsvRiLdsoRiv−=()iLTIovRVVKv⋅−−=iLmvRg⋅−=Small signalNotice, first we need to find operatingpoint voltages/currents.Get these from a large signal analysis.Amplifier example:6.002 Fall 2000 Lecture 11Cite 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].To find the relationship between the small signal parameters of a circuit, we can replace large signal device models with corresponding small signal device models, and then analyze the resulting small signal circuit.Foundations: (Also see section 8.2.1 of A&L)KVL, KCL applied to some circuit C yields:III The Small Signal Circuit ViewbBoutOUTaAvVvVvV+++++++"""Replace total variables with operating point variables plus small signal variablesOperating point variables themselves satisfy thesame KVL, KCL equationsBOUTAVVV++++"""so, we can cancel them outBOUTAvvv++++++""""1boutavvv++++"""Leaving2Since small signal models are linear, our linear tools will nowapply…But is the same equation as with small signal variables replacing total variables, so must reflect same topology as in C, except that small signal models are used.


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MIT 6 002 - Small Signal Circuits

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