1EE105 - Fall 2006Microelectronic Devices and CircuitsProf. Jan M. Rabaey (jan@eecs)Lecture 24: Bipolar Junction TransistorSmall Signal Model(Chapter 7.5)2The Early EffectForward-activeSaturationVAVCEICVBE3VBE2VBE1Current in Forward-Active a Function impacted by VCEMain reason: Base-width modulationHence:/(1)BE thvVCS CEAiIe v V=+23Small-Signal ModelsAnalogy from MOSFET s.s. model:()BSDSGSDvvvfi ,,=()CEBECvvfi ,=4Transconductance gm The transconductance is analogous to diode conductance35Transconductance (cont) Forward-active large-signal current:/(1 )BE thvVCS CEAiIe v V=+• Differentiating and evaluating at Q = (VBE, VCE )/(1 )BEqV kTCSCE ABEQdiqIeVVdv kT=+CCmBEQdiqIgdvkT==6Comparison with MOSFET Typical bias point: drain/coll. current = 100 μA;Select (W/L) = 8/1, μnCox= 100 μA/V2 BJT: MOSFET:100μ4mS25mCmthIgV== =2DmGSTIgVV=−CCmthqIIgkTV==22 2 100μ 8 100μ 400μDmoxDGS TIWgCISVV Lμ== =×××=−47BJT Base CurrentsUnlike MOSFET, there is a DC current into thebase terminal of a bipolar transistor:()/(1 )BEqV kTBCF SF CEthIIIe VVββ== +To find the change in base current due to changein base-emitter voltage:1BBCmBE C BEQQQiiigvivβ∂∂∂==∂∂∂A8Small Signal Current GainCFBiiββΔ==Δ59Input Resistance rπ()11CmBBE BEQQigirvvπββ−∂∂== =∂∂In practice, the DC current gain βFand the small-signalcurrent gain βoare both highly variable (+/- 25%)Typical bias point: DC collector current = 100 μA10Output Resistance roWhy does current increase slightly with increasing vCE?Model: introduce the Early voltage)1(/ACEVvSCVveIithBE+=Base (p)Emitter (n+)Collector (n)BW611Graphical Interpretation of roslope~1/roslope12Current in Forward-Active a Function impacted by VCEMain reason: Base-width modulationHence:Forward-activeSaturationVAVCEICVBE3VBE2VBE1The Early Effect/(1 )BE thvVCS CEAiIe v V=+ACoVIr =−1713BJT Small-Signal Model14815BJT CapacitancesBase-charging capacitance Cb: due to minority carrier charge storage (mostly electrons in the base)FmbgC τ=Base-emitter depletion capacitance: CjE= 1.4 CjEoTotal B-E capacitance: Cπ= CjE+ Cb1691718101920112122Complete Small-Signal Modelπ1223IBM SiGe Heterojunction BJT24SiGe BJT/CMOS vs. RF CMOSFrom “IBM and Cadence collaborate to accelerate silicon-accurate design of advanced RF integrated circuits,”IBM Microelectronics Division, March 11, 2005.1325fTvs. ICFrom J. S. Dunn, et al,IBM J. Res. & Dev., 47, 101-138
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