6.002 Fall 2000 Lecture 1 6 6.002 CIRCUITS AND ELECTRONICS Nonlinear Analysis 6.002 Fall 2000 Lecture 2 6  Discretize matter t LCA m1 X KVL, KCL, i-v m2 X Composition rules m3 X Node method m4 X Superposition m5 X Thévenin, Norton any circuit linear circuits Review 6.002 Fall 2000 Lecture 3 6  Discretize value t Digital abstraction X Subcircuits for given “switch” setting are linear! So, all 5 methods (m1 – m5) can be applied 1 1 = = B A A B S V L R C S V L R C ON R ON R SR MOSFET Model Review 6.002 Fall 2000 Lecture 4 6 Today  Nonlinear Analysis X Analytical method based on m1, m2, m3 X Graphical method X Introduction to incremental analysis 6.002 Fall 2000 Lecture 5 6 How do we analyze nonlinear circuits, for example: D v + - D D i D v D i 0,0 D bv D aei = a D v + - V + – Hypothetical nonlinear device D D i (Expo Dweeb ☺) (Curiously, the device supplies power when v D is negative) 6.002 Fall 2000 Lecture 6 6 Method 1: Analytical Method Using the node method, (remember the node method applies for linear or nonlinear circuits) D bv D aei = 2 0=+ − D D i R Vv 1 2 unknowns 2 equations Solve the equation by  trial and error  numerical methods 6.002 Fall 2000 Lecture 7 6 Method 2: Graphical Method Notice: the solution satisfies equations and 21 D v D i a D bv D aei = 2 D v D i 1 R v R V i D D −= R V V R slope 1 −= 6.002 Fall 2000 Lecture 8 6 Combine the two constraints 1 4 1 1 1 = = = = b a R V e.g. Ai Vv D D 4.0 5.0 = = D v D i 5.0~ 4.0~ R V V 1 1 a ¼ called “loadline” for reasons you will see later 6.002 Fall 2000 Lecture 9 6 Method 3: Incremental Analysis Motivation: music over a light beam Can we pull this off? LED: Light Emitting expoDweep ☺ D v + - )( tv I + – D i LED R i AMP light intensity I R in photoreceiver RR Ii ∝ light intensity DD iI ∝ I v t music signal )( tv I light sound )( ti R )( ti D nonlinear linear problem! will result in distortion 6.002 Fall 2000 Lecture 10 6 Problem: The LED is nonlinear distortion ID vv = D v D i v D t t D i v D D i t . 6.002 Fall 2000 Lecture 1 6 6.002 CIRCUITS AND ELECTRONICS Nonlinear Analysis 6.002 Fall 2000 Lecture 2 6  Discretize. Thévenin, Norton any circuit linear circuits Review 6.002 Fall 2000 Lecture 3 6  Discretize value t Digital abstraction X Subcircuits for given “switch” setting