Current Mode Winner-Take-All Circuits Shih-Chii Liu. Translinear Principle. Current-Mode Low-Pass Filter. Translinear Principle

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1 NE Lecture 6 Wier-Take-All 0/9/03 Curret Mode Wier-Take-All Circuits Shih-Chii Liu Outlie: Trasliear Priciple Curret-Mode Circuit Fuctios: Low-Pass Temporal Filter PseudoCoductaces Spatial Filteri Resistive Networks Curret Coveyor as Curret Mirror Normalizer Circuit 0/9/03 Wier-Take-All Circuits Trasliear Priciple Coied by Barrie Gilbert i 975, trasliear meas that the bipolar juctio trasistor s trascoductace is liear i its collector curret. a bipolar trasistor, the collector curret is expoetial i the baseemitter voltae. This expoetial depedece is also captured i the subthreshold domai of a MOSFET. Trasliear Priciple Curret-Mode Low-Pass Filter Kirchhoff's oltae Law aroud loop: CCW CW ( Substituti for i ( : UT lo UT lo CCW 0 CW 0 CCW CW (Frey, 98 Curret-Mode Low-Pass Filter PseudoCoductace Pseudo: bei apparetly rather tha actually as stated ( ( * * * s d * f s f d ( ( ( / UT s / UT d / UT 0 e ( e e s d (Frey, 98 PseudoCoductace 0/9/03 6 Neuromorphic Eieeri 03

2 NE Lecture 6 Wier-Take-All 0/9/03 Curret Divider i Basic Elemet of Pseudo-Resistive (Diffusor Network w e w ( / U T w ( e / UT c / UT 0 w e ( e / UT c / UT 0 Ratios of currets: 0/9/03 8 e R R =( - =(R -R =R( - i s T d i / UT s / UT d / UT 0 ( ( s/ UT ( d / UT 0 T e e e ( e e 0/9/03 9 Diffusor What if ates are at differet potetials? t l t t trasverse l lateral l l l e l l ( t l e t t e e l l ( t l Pseudocoductace! ( 0/9/03 t t j- R Diffusor Network j- outj- R outj j+ outj+ 0/9/03 j ij j j+ R Diffusor Network Curret Coveyor G j- G j- ij G j j j+ G y y z z z x x l y outj- outj outj+ R R R ( GR/ UT e ( out j out j out j out j i j d out x out x i x e ( /U G R T ( ( ( ; dx x x Used i Low-pass filters Multiplier circuits Wier-take-all circuits 0/9/03 3 0/9/03 4 Neuromorphic Eieeri 03

3 NE Lecture 6 Wier-Take-All 0/9/03 Curret Coveyor as a Multiplier y y z w x Usi trasliear priciple: z x y xw y 0 0 w x y w z z x y w Curret Coveyor as a Curret Mirror y Z Y X y y x y y y x w 0/9/03 5 0/9/03 6 Gilbert Normalizer WTA Networks d i out i d out di / UT ii 0e dic/ UT c/ U outi 0e iie T b outi i outi b ii i ii A WTA mechaism is a device that determies the idetity ad sometimes the amplitude, of its larest iput. This mechaism is ecessary to eforce competitio betwee differet possible outputs of a etwork. A variat, called softmax, assis each iput a weiht so that all weihts sum to ad the larest iput has the larest weiht. The WTA is the limiti case of the softmax. b b 0/9/03 7 0/9/03 9 Software Simulatios put Output 0/9/03 0 0/9/03 Neuromorphic Eieeri 03 3

4 NE Lecture 6 Wier-Take-All 0/9/03 Curret-Mode WTA Circuit A Buffered Curret Mirror A cotiuous-time aalo circuit that receives aalo iputs ad implemets the WTA fuctio. t was oriially desied by Lazzaro et al. i 989. out? Acts like curret sik M i? Source follower follows out 0/9/03 b out oes to where it eeds to be to make o to where it eeds to be to make M i sik 0/9/03 3 A Buffered Curret Mirror Acts like curret sik out? d M i? d b out out 0/9/03 4 0/9/03 5 out out ecodes max(, What happes whe <? b << follows the hiher of ad 0/9/03 6 ecodes max(, out =0, out = b 0/9/03 7 Neuromorphic Eieeri 03 4

5 NE Lecture 6 Wier-Take-All 0/9/03 f >, ecodes i d i i out out i d b b out out out 0/9/03 8 0/9/03 9 WTA Circuit A N-Cell WTA Assume iputs are iitially equal, that is,. i i i out out i Now let, i positive chae i voltae at ode (also eative chae i voltae at ode E d out 0 i e U / T d d d M 3 M 4 M M b d i out i out i3 out3 i4 out4 0/9/ /9/03 3 Hysteretic WTA WTA Circuits i Lab i out out i b b b diveri (997 0/9/03 3 Morris, Horiuchi, DeWeerth (998 WTA HWTA 0/9/03 33 Neuromorphic Eieeri 03 5

6 NE Lecture 6 Wier-Take-All 0/9/03 The Ed 0/9/03 34 Neuromorphic Eieeri 03 6

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