EE105 Fall 2006 Microelectronic Devices and Circuits Prof Jan M Rabaey jan eecs Lecture 23 Bipolar Junction Transistor Models Chapter 7 Administrative Midterm results Lab 7 this week no lab next week Homework 10 due homework 11 posted tomorrow One more homework after that Schedule for the rest of the semester Week 12 Bipolar Transistor Large and Small signal Model Week 13 Thanksgiving week CE CB and CC amplifiers Week 14 Emitter degeneration frequency response Week 15 Some more advanced topics and recap 2 1 Midterm2 Total 20 Mean 16 25 Standard Deviation 6 35 Median 17 88 Max 25 00 12 10 8 6 4 2 0 5 4 7 6 5 5 5 5 5 2 24 5 3 2 22 5 1 2 20 5 9 1 18 5 7 1 16 5 5 1 14 5 3 1 12 5 1 1 10 5 3 2 9 8 1 0 3 The semester so far Midterm 1 2 Total 20 Mean 11 92 Standard Deviation 4 37 Median 12 52 Max 19 07 12 B 12 10 8 6 4 2 0 18 16 14 12 10 8 6 4 2 0 4 2 Ideal BJT Structure IC Collector N Base P Emitter N IB VCE VBE IE Emitter P VEB Base N IB Collector P IE VEC IC NPN or PNP sandwich Two back to back diodes How does current flow Base is very thin A good BJT satisfies the following IC I E I C I B IC I S e qVBE kT 5 Operations Modes 6 3 Collector Characteristics IB Saturation Region Low Output Resistance Breakdown Linear Increase Reverse Active Bad Transistor Forward Active Region Very High Output Resistance 7 Base Emitter Voltage Control Saturation Region Low Output Resistance 0 3V Breakdown Exponential Increase Reverse Active Bad Transistor Forward Active Region High Output Resistance 8 4 Forward Active Operation Carrier Concentration E nb 0 Depletion Regions B C pc0 nb0 pe0 x 0 W WB 9 10 5 Diffusion Currents Minority carriers in base form a uniform diffusion current Since emitter doping is higher this current swamps out the current portion due to the minority carriers injected from base 11 Origin of F Base emitter junction some reverse injection of holes into the emitter base current isn t zero Some electrons lost due to recombination E Typical F 99 B C F 100 12 6 Current Components B E C 1 IE 2 IC 3 x electrons IB holes 13 BJT Currents Collector current is nearly identical to the magnitude of the emitter current define F 999 I C F I E KCL I E IC I B DC Current Gain I C F I E F I B I C IC F IB F IB 1 F F F 999 999 1 F 001 14 7 Collector Current Diffusion of electrons across base results in J diff n qDn n pB 0 qVkTBE qDn e dx WB dn p qDn n pB 0 AE IS WB IC I S e qVBE kT 15 Base Current Diffusion of holes across emitter results in J diff p dpnE qD p pnE 0 qVkTBE qD p e 1 dx WE qD p pnE 0 AE qVkTBE IB 1 e WE 16 8 Current Gain qDn n pBo AE WB IC Dn n pB 0 WE F I B qD p pnEo AE D p pnE 0 WB WE Minimize base width ni2 N A B N D E n pB 0 2 ni N A B pnE 0 N D E Maximize doping in emitter 17 Large Signal Model Forward Active E E Reverse Active Carrier Concentration Depletion Regions Carrier Concentration B nb 0 B pc0 pc0 nb0 pe0 C nb W C nb0 pe0 nb 0 x x 0 0 W W WB WB Saturated Carrier Concentration nb 0 E Cutoff Carrier Concentration B C E B C nb W QA pc0 QS pe0 0 nb0 nb W pc0 x x W WB nb 0 pe0 nb0 0 W WB 18 9 Ebers Moll Equivalent Circuit Write emitter and collector currents in terms of internal currents at two junctions Building blocks diodes and I controlled I sources 19 Ebers Moll Equations Derivation Write emitter and collector currents in terms of internal currents at two junctions I E I ES eVBE Vth 1 R I CS eVBC Vth 1 I C F I ES eVBE Vth 1 I CS eVBC Vth 1 F I ES R I CS 20 10 Forward Active Region B C junction is not forward biased IR is very small Typical Values VBE 0 7 VCE 0 2 21 Simplified Ebers Moll Forward Active Case IB B IC C IC F I B VBE 0 7 E Saturation both diodes are forward biases batteries IB B VBE 0 7 IC C VCE 0 1 E 22 11 The Early Effect IC Forwardactive VBE3 Saturation VBE2 VBE1 VA VCE Current in Forward Active a Function impacted by VCE Main reason Base width modulation Hence iC I S evBE Vth 1 vCE VA 23 Small Signal Models Analogy from MOSFET s s model iD f v GS v DS v BS iC f v BE v CE 24 12 Transconductance gm The transconductance is analogous to diode conductance 25 Transconductance cont Forward active large signal current iC I S evBE Vth 1 vCE VA Differentiating and evaluating at Q VBE VCE diC dvBE Q q I S eqVBE kT 1 VCE VA kT gm diC dvBE Q qI C kT 26 13 Comparison with MOSFET Typical bias point drain coll current 100 A Select W L 8 1 nCox 100 A V2 qI C I C BJT gm kT I 100 gm C 4mS Vth 25m gm MOSFET gm Vth 2I D VGS VT 2I D W 2 Cox I D 2 100 8 100 400 S VGS VT L 27 BJT Base Currents Unlike MOSFET there is a DC current into the base terminal of a bipolar transistor I B I C F I S F e qVBE kT 1 VCE Vth To find the change in base current due to change in base emitter voltage iB vBE Q iB iC iC Q vBE Q 1 gm 28 14 Small Signal Current Gain iC F iB 29 Input Resistance r r 1 iB vBE Q 1 iC vBE Q gm In practice the DC current gain F and the small signal current gain o are both highly variable 25 Typical bias point DC collector current 100 A 30 15 Output Resistance ro Why does current increase slightly with increasing vCE Collector n WB Base p Emitter n Model introduce the Early voltage iC I S e vBE Vth 1 vCE V A 31 Graphical Interpretation of ro slope 1 ro slope 32 16 BJT Small Signal Model 33 17
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