6 002 CIRCUITS AND ELECTRONICS Amplifiers Small Signal Model Cite 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 6 002 Fall 2000 Lecture 10 Review MOSFET amp VS RL vO vI iDS Saturation discipline operate MOSFET only in saturation region Large signal analysis 1 Find vO vs vI under saturation discipline 2 Valid vI vO ranges under saturation discipline Reading Small signal model Chapter 8 Cite 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 6 002 Fall 2000 Lecture 10 Large Signal Review 1 vO vs vI K vI 1 2 RL 2 valid for vI VT and vO vI VT K 2 same as iDS vO 2 vO VS Cite 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 6 002 Fall 2000 Lecture 10 Large Signal Review 2 Valid operating ranges VS vO 5V corresponding interesting region for vO vO vI VT vO vI VT vO vI VT 1V vI VT 1V 2V interesting region for vI Saturation discipline satisfied Cite 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 6 002 Fall 2000 Lecture 10 But 5V VS vO vO vI VT vO 1V vI VT 1V Demo vI 2V Amplifies alright but distorts vI vO t Amp is nonlinear Cite 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 6 002 Fall 2000 Lecture 10 Small Signal Model vO 5V VS Focus on this line segment VI VO 1V vI VT 1V 2V 2 K vI VT vO VS RL 2 Amp all right but nonlinear Hmmm So what about our linear amplifier Insight But observe vI vs vO about some point VI VO looks quite linear Cite 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 6 002 Fall 2000 Lecture 10 Trick vO vo VO vi VI VO looks linear VI vI Operate amp at VI VO DC bias good choice midpoint of input operating range Superimpose small signal on top of VI Response to small signal seems to be approximately linear Cite 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 6 002 Fall 2000 Lecture 10 Trick vO vo VO vi VI VO looks linear VI vI Operate amp at VI VO DC bias good choice midpoint of input operating range Superimpose small signal on top of VI Response to small signal seems to be approximately linear Let s look at this in more detail I graphically II mathematically III from a circuit viewpoint next week Cite 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 6 002 Fall 2000 Lecture 10 I Graphically We use a DC bias VI to boost interesting input signal above VT and in fact well above VT VS RL interesting input signal vI VI vO Offset voltage or bias Cite 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 6 002 Fall 2000 Lecture 10 Graphically VS RL interesting input signal vO vI VI VS vO operating point VO 0 VI VO vO vI VT vI VT Good choice for operating point midpoint of input operating range VI Cite 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 6 002 Fall 2000 Lecture 10 Small Signal Model aka incremental model aka linearized model Notation Input vI VI vi total DC small variable bias signal like vI bias voltage aka operating point voltage Output vO VO vo Graphically vI vO vi vo VI VO 0 t 0 t Cite 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 6 002 Fall 2000 Lecture 10 II Mathematically watch my fingers RL K 2 vO VS vI VT VO VS RL K VI VT 2 2 2 substituting vI VI vi vi VI RL K vO VS 2 VI vi vT 2 RL K 2 VI VT vi 2 VS RL K VI VT 2 2 VI vT vi vi 2 VS 2 RL K VO vo VS VI VT 2 RL K VI VT vi 2 From vo RL K VI VT vi gm related to VI Cite 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 6 002 Fall 2000 Lecture 10 Mathematically vo RL K VI VT vi gm related to VI vo g m RL vi For a given DC operating point voltage VI VI VT is constant So vo A vi constant w r t vi In other words our circuit behaves like a linear amplifier for small signals Cite 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 6 002 Fall 2000 Lecture 10 Another way RL K vO VS vI VT 2 2 R K 2 L v V VS I T 2 d vo dv I vi v V I I slope at VI vo RL K VI VT vi g m K VI VT A g m RL amp gain Also see Figure 8 9 in the course notes for a graphical interpretation of this result Cite 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 6 002 Fall 2000 Lecture 10 More next lecture Demo iDS load line input signal response operating point VI VO vO How to choose the bias point 1 Gain component g m VI 2 vi gets big distortion So bias carefully 3 Input valid operating range Bias at midpoint of input operating range for maximum swing Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT …
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