Tài liệu Circuits & Electronics P7 pdf

6.002 Fall 2000 Lecture 1 7 6.002 CIRCUITS AND ELECTRONICS Incremental Analysis 6.002 Fall 2000 Lecture 2 7 Nonlinear Analysis X Analytical method X Graphical method Today X Incremental analysis Reading: Section 4.5 Review 6.002 Fall 2000 Lecture 3 7 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 4 7 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 5 7 Insight: D v D i D I D V DC offset or DC bias Trick: dDD iIi += I V D v + - )( tv i + – LED + – I v dDD vVv += I V i v small region looks linear (about V D , I D ) 6.002 Fall 2000 Lecture 6 7 Result v d very small D i D v d i D I D V 6.002 Fall 2000 Lecture 7 7 Result t D v D V ID vv = t D I D i ~linear! Demo d v d i D i 6.002 Fall 2000 Lecture 8 7 total variable DC offset small superimposed signal The incremental method: (or small signal method) 1. Operate at some DC offset or bias point V D , I D . 2. Superimpose small signal v d (music) on top of V D . 3. Response i d to small signal v d is approximately linear. Notation: dDD iIi += 6.002 Fall 2000 Lecture 9 7 ( ) DD vfi = What does this mean mathematically? Or, why is the small signal response linear? We replaced DDD vVv ∆+= using Taylor’s Expansion to expand f(v D ) near v D =V D : () D Vv D D DD v dv vdf Vfi DD ∆⋅+= = )( "+∆⋅+ = 2 2 2 )( !2 1 D Vv D D v dv vfd DD large DC increment about V D nonlinear d v neglect higher order terms because is small D v∆ 6.002 Fall 2000 Lecture 10 7 () D Vv D D DD v vd vfd Vfi DD ∆⋅+≈ = )( equating DC and time-varying parts, D Vv D D D v vd vfd i DD ∆⋅=∆ = )( constant w.r.t. ∆ v D constant w.r.t. ∆ v D slope at V D , I D ( ) DD VfI = operating point constant w.r.t. ∆ v D X : We can write () D Vv D D DDD v vd vfd VfiI DD ∆⋅+≈∆+ = )( so, DD vi ∆∝∆ By notation, dD ii =∆ dD vv =∆ . 6.002 Fall 2000 Lecture 1 7 6.002 CIRCUITS AND ELECTRONICS Incremental Analysis 6.002 Fall 2000 Lecture 2 7 Nonlinear. to expand f(v D ) near v D =V D : () D Vv D D DD v dv vdf Vfi DD ∆⋅+= = )( "+∆⋅+ = 2 2 2 )( !2 1 D Vv D D v dv vfd DD large DC increment about V D