Lecture 7 Large And Small Signal Modelling Of PN Junction .
Lecture 7Large and Small Signal Modelling of PN Junction DiodesIn this lecture you will learn: Circuit models of PN junction diodes Small signal modeling of nonlinear circuit elements Small signal models of PN junction diodes Junction resistance and capacitancesECE 315 – Spring 2006 – Farhan Rana – Cornell UniversityArea “A”Current Flow in a PN Junction DiodeI D W qVDDp Wp JT qni2 n coth coth n e KT 1 NaLn Ln Nd Lp Lp ID qVD ID AJT Io e KT 1 D W Dp Wp coth n Io qni2 A n coth Lp NaLnLNL n d p Reverse biasJunction breakdownVONVDForward biasECE 315 – Spring 2006 – Farhan Rana – Cornell University1
Simplest Circuit Model for a PN Junction Diode VD-RFor most diodes:0.4 VON 0.8Load Line:VIDIDV I D R VD IDSlope VRV VD RVONSolution for current:If V VON:VVDIf V VON:VD VVD VONV VONID RID 0ECE 315 – Spring 2006 – Farhan Rana – Cornell UniversityBetter Circuit Model a PN Junction DiodeIDVDSlopeIDdI D gddVDVONVDECE 315 – Spring 2006 – Farhan Rana – Cornell University2
Circuit Example for a PN Junction Diode VD-RVIDLoad Line:IDV I D R VD ID SlopedI D gddVDVRV VDRVONSolution for current:If V VON:VIf V VON:VDgd RV VON1 gd R1 gd Rgd V VON 1 gd RVD VD VID 0IDECE 315 – Spring 2006 – Farhan Rana – Cornell UniversityLinear Circuit ElementsOhm’s Law:II Slope GV IVV GVROhm’s law implies a LINEARrelationship between currentand voltage-R 1GThe current-voltage relationship of resistors is linearECE 315 – Spring 2006 – Farhan Rana – Cornell University3
Nonlinear Circuit ElementsI V INonlinear Element:VCurrent is a function of thevoltage (but the current-voltagerelationship is not linear)For example:I V A V BeCV V-IThe current-voltage relationship of most devices is not linear!ECE 315 – Spring 2006 – Farhan Rana – Cornell UniversitySmall Signal Modeling of Nonlinear Circuit ElementsII V IBIASII V iac t IBIASBias pointVBIAS Vv ac t VVVBIAS-V -I IBIAS iac t I IBIAS- VBIAS- v ac t - VBIASECE 315 – Spring 2006 – Farhan Rana – Cornell University4
Small Signal Modeling of Nonlinear Circuit ElementsISlope gI V iac t Taylor expand the current-voltage relationaround the bias voltage:IBIASv ac t IBIAS i ac t I VBIAS v ac t I VBIAS IBIASdIdVdI i ac t I VBIAS dVVVBIASAssume smallV VBIASV VBIASv ac t 21d I2 dV 22 t .v acV VBIASDifferential resistance ordifferential conductancev ac t 1dI g rdV V VBIAS I VBIAS gv ac t i ac t gv ac t Incremental resistance orincremental conductanceECE 315 – Spring 2006 – Farhan Rana – Cornell UniversitySmall Signal Modeling of Nonlinear Circuit Elements-Slope giac t IBIASIBIAS iac t Iiac t gv ac t Complete circuit is:v ac t - v ac t VBIASVVBIASSmall signal equivalentcircuit is:iac t r -v ac t 1giac t gv ac t In small signal models,nonlinear circuit elements arereplaced by their linearizedmodels that are valid over alimited range of excursionaround the bias pointECE 315 – Spring 2006 – Farhan Rana – Cornell University5
Small Signal Modeling of Nonlinear Circuit ElementsA difficult problem:VBIAS LR- v ac t IBIASBias pointIBIAS iac t Slope g- I V -VBIASVDCDC Load Line:VDC IBIASR VBIAS IBIASA simpler problem:V VBIAS DCRgLRiac t 1dI g rdV V VBIAS- v ac t ECE 315 – Spring 2006 – Farhan Rana – Cornell UniversitySmall Signal Model of a PN Junction Diode: Junction Conductance- - - - - - - - - -P-dopedNaID id VD- N-dopedNdvd- qVD I D Io e KT 1 q VD v d I I D id Io e KT 1 I D D v d . I D gd v d VD i d gd v dgd qI I1 D oerd VD KTqVDKT Slope gq I D Io qI D KTKTIn strong forwardbiasDifferential resistanceDifferential conductanceECE 315 – Spring 2006 – Farhan Rana – Cornell University6
Small Signal Model of a PN Junction Diode: Junction Conductance- - - - - - - - - -P-dopedNa VDID id- N-dopedNdvd-I D i d I D gd v d id gd v d1gdrd gd qIDKTvdidSmall signal circuit model of a PN diodeECE 315 – Spring 2006 – Farhan Rana – Cornell UniversitySmall Signal Model of a PN Junction Diode: Junction DepletionCapacitancexn xp0- - - - - - - - - -P-dopedNa ID id VD- N-dopedNdvd-At high frequencies, part of the current id flows through the junction but part of italso charges up the junction capacitanceid gd v d C jdv ddtCj sA x p x n rdCjidvdECE 315 – Spring 2006 – Farhan Rana – Cornell University7
Small Signal Model of a PN Junction Diode: Diffusion Capacitance- - - - - - - - - -P-dopedNa -VDID id N-dopedNdvd-There is also charge stored in the quasi-neutral regions that changes as the junctionvoltage is varied (negative and positive charge stored at the same location!!)Minoritycarriersp' x n' x n' x p' x xp Wp x p0Wn x nxnxMajoritycarriersCharge stored:Wn x n xpxn Wp x p p' x dx qAQd qA p' x dxECE 315 – Spring 2006 – Farhan Rana – Cornell UniversitySmall Signal Model of a PN Junction Diode: Diffusion Capacitance- - - - - - - - - -P-dopedNa ID idCd qKT- xpxn Wp x p p' x dx qADiffusion Capacitance: Cd qVDA KTeVDWn x nCharge stored: Qd qA2 Qd VDN-dopedNdvd- p' x dx W Wp cosh n 1 1cosh 2 L 2n ni p Ln i Lp N LnWN W pd asinh sinh n L Ln p Increases exponentially with bias!ECE 315 – Spring 2006 – Farhan Rana – Cornell University8
Small Signal Model of a PN Junction Diode: Total Capacitance- - - - - - - - - -P-dopedNa ID id VD- N-dopedNdvd-At high frequencies, part of the current id flows through the junction but part of italso charges up the junction capacitance and the diffusion capacitanceid gd v d C j Cd dv ddtCdrdCjvdidECE 315 – Spring 2006 – Farhan Rana – Cornell UniversityCapacitances of a PN Junction DiodeTotal Capacitance:C C j CdCdrdCjidvdDECE 315 – Spring 2006 – Farhan Rana – Cornell University9
Small Signal Model of a PN Junction Diode in Revere Biasgd 1 q I D Io 0rdKTCd 0CjidvdDECE 315 – Spring 2006 – Farhan Rana – Cornell UniversityBreadboard Wiring: Good WiringECE 315 – Spring 2006 – Farhan Rana – Cornell University10
Breadboard Wiring: Bad WiringECE 315 – Spring 2006 – Farhan Rana – Cornell UniversityECE 315 – Spring 2006 – Farhan Rana – Cornell University11
Large and Small Signal Modelling of PN Junction Diodes In this lecture you will learn: Circuit models of PN junction diodes Small signal modeling of nonlinear circuit elements Small signal models of PN junction diodes Junction resistance and capacitances ECE 315
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