Lecture #27Small-Signal ModelSmall-Signal Model (cont.)Example: Small-Signal Model ParametersCutoff Frequency, fTSlide 6Base Widening at High IC: the Kirk EffectSummary: BJT Small Signal ModelBJT Switching - QualitativeTurn-on transientTurn-off transientReducing tB for Faster Turn-OffSchottky-Clamped BJTEE130 Lecture 27, Slide 1 Spring 2007Lecture #27OUTLINE •BJT small signal model•BJT cutoff frequency•BJT transient (switching) responseReading: Finish Chapter 12EE130 Lecture 27, Slide 2 Spring 2007Transconductance:vber gmvbeCE B EC +Small-Signal ModelCommon-emitter configuration,forward-active mode:kTqVFFCEBeII/0 qkTIeIdVdIdVdIgCkTqVFFEBCEBCmEB//0“hybrid-pi” BJT small signal model:EE130 Lecture 27, Slide 3 Spring 2007Small-Signal Model (cont.) , mFBECFBEDCFFgdVIdCIQBEFdVdQC BED,mdcdcmBECdcBEBgrgdVdIdVdIr 11BEDBEDBEJCCCC,,,BEdepsWAC,BEJ,where QF is the magnitude of minority-carrier charge stored in the base and emitter regions forward transit timeEE130 Lecture 27, Slide 4 Spring 2007A BJT is biased at IC = 1 mA and VCE = 3 V. dc=90, F=5 ps, and T = 300 K. Find (a) gm , (b) r , (c) C .Solution: (a) (b) r = dc / gm = 90/0.039 = 2.3 kc) Example: Small-Signal Model Parameterssiemens)(milliqkTIgCm mS 39VmA39mV 26mA 1)//( ad)(femto fargCmFfF 19F109.1039.01051412EE130 Lecture 27, Slide 5 Spring 2007The cutoff frequency is defined to be the frequency (f = /2) at which the short-circuit a.c. current gain equals 1:Cutoff Frequency, fT CBEJFTacqIkTCf/21at 1, CBEJFdcBEJmFdcmmmbcbemcbbbeqIkTCjCgjggCjrgiivgiCjriiv//11 //1)(/1admittanceinput ,,vber gmvbeCE B EC +EE130 Lecture 27, Slide 6 Spring 2007fT is commonly used as a metric for the speed of a BJT.SiGe HBT by IBMFor the full BJT equivalent circuit: ceBCJCBCJBEJFTrrCqIkTCCf,,,/21To maximize fT:–increase IC–minimize CJ,BE, CJ,BC –minimize re, rc–minimize FEE130 Lecture 27, Slide 7 Spring 2007•At very high current densities (>0.5mA/m2), base widening occurs, so QB increases. F increases, fT decreases. Top to bottom : VCE = 0.5V, 0.8V, 1.5V, 3V.Base Widening at High IC: the Kirk EffectConsider an npn BJT:At high current levels, the density of electrons (n IC/qAvsat) in the collector depletion region is significant, resulting in widening of the quasi-neutral base region.As W increases, the depletion width in the collector also increases, since the charge density decreases:At very high current densities, the excess hole concentration in the collector is so high that it effectively extends the p-type base.satCCCCdepAvIqNqnqN ,EE130 Lecture 27, Slide 8 Spring 2007Summary: BJT Small Signal Modelvber gmvbeCE B EC +Hybrid-pi model for the common-emitter configuration, forward-active mode:mdcgrmFBEJgCC, qkTIgCm/EE130 Lecture 27, Slide 9 Spring 2007BJT Switching - QualitativeEE130 Lecture 27, Slide 10 Spring 2007Turn-on transient•We know:•The general solution is:•Initial condition: QB(0)=0. since transistor is in cutoffBBBBBQIdtdQBtBBBBAeItQ/)()1()(/BtBBBBeItQrLCCrttBBBtBCttRVttAeItQtiB0)()(/where IBB=VS/RSBBBLCCBrIRVt/11lnEE130 Lecture 27, Slide 11 Spring 2007Turn-off transient•We know:•The general solution is:•Initial condition: QB(0)=IBBBBBBBBQIdtdQBtBBBBAeItQ/)( BtBBBBeItQ/1)( sdteBBBtBsdCCCttItQttIti Bt/1)(0)(BBBtCCBsdIIt1lnEE130 Lecture 27, Slide 12 Spring 2007Reducing B for Faster Turn-Off•The speed at which a BJT is turned off is dependent on the amount of excess minority-carrier charge stored in the base, and also the recombination lifetime B–By reducing B, the carrier removal rate is increasedExample: Add recombination centers (Au atoms) in the baseEE130 Lecture 27, Slide 13 Spring 2007Schottky-Clamped BJT•When the BJT enters the saturation mode, the Schottky diode begins to conduct and “clamps” the C-B junction voltage at a relatively low positive value. reduced stored charge in quasi-neutral
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