EECS 105 Fall 2003 Lecture 15 Lecture 15 Small Signal Modeling Prof Niknejad Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Lecture Outline Department of EECS Review Diffusion Revisited BJT Small Signal Model Circuits Small Signal Modeling Example Simple MOS Amplifier University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Notation Review iC f vBE vCE Large signal I C DiC f VBE DvBE VCE DvCE Quiescent Point bias Q VBE VCE I C ic f VBE vbe VCE vce f ic vBE transconductance f vbe vCE Q vce small signal DC bias small signal less messy Q Output conductance Since we re introducing a new confusing subject let s adopt some consistent notation Please point out any mistakes that I will surely make Once you get a feel for small signal analysis we can drop the notation and things will be clear by context yeah right good excuse Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Diffusion Revisited Why is minority current profile a linear function Recall that the path through the Si crystal is a zig zag series of acceleration and deceleration due to collisions Note that diffusion current density is controlled by width of region base width for BJT Half go left half go right Density here fixed by potential injection of carriers Physical interpretation How many electrons holes have enough energy to cross barrier Boltzmann distribution give this number Density fixed by metal contact Wp Decreasing width increases current Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Diffusion Capacitance The total minority carrier charge for a one sided junction is area of triangle qV D 1 1 Qn qA bh2 qA W xdep p n p 0e kT n p 0 2 2 For a one sided junction the current is dominated by these minority carriers qVD qADn ID n p 0 e kT n p 0 W p xdep p Dn ID 2 Qn W x p dep p Department of EECS Constant University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Diffusion Capacitance cont The proportionality constant has units of time Qn W p xdep p tT ID Dn Temperature q W p xdep p tT kT mn 2 2 Distance across P type base Diffusion Coefficient Mobility The physical interpretation is that this is the transit time for the minority carriers to cross the p type region Since the capacitance is related to charge Qn t T I D Department of EECS Qn I Cd t T g dt T V V University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad BJT Transconductance gm The transconductance is analogous to diode conductance Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Transconductance cont Forward active large signal current iC I S evBE Vth 1 vCE VA Differentiating and evaluating at Q VBE VCE iC vBE Q q I S e qVBE kT 1 VCE VA kT iC gm vBE Department of EECS Q qI C kT University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad BJT Base Currents Unlike MOSFET there is a DC current into the base terminal of a bipolar transistor I B I C bF I S bF e qVBE kT 1 VCE VA To find the change in base current due to change in base emitter voltage ib iB vBE vbe Q iB vBE Q iB iC iC Q vBE Q 1 gm bF gm ib vbe bF Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Small Signal Current Gain b0 DiC bF DiB DiC b0 DiB ic b0ib Since currents are linearly related the derivative is a constant small signal large signal Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Input Resistance r rp 1 iB vBE Q iC 1 bF vBE Q gm bF bF rp 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 rp 100 25 mV 25 kW 1mA Ri W Department of EECS MOSFET University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Output Resistance ro Why does current increase slightly with increasing vCE Collector n WB Base p Emitter n Answer Base width modulation similar to CLM for MOS Model Math is a mess so introduce the Early voltage iC I S e vBE Vth 1 vCE V A Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Graphical Interpretation of ro slope 1 ro slope Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad BJT Small Signal Model ib rp vbe 1 ic g m vbe vce ro Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad BJT Capacitors Emitter base is a forward biased junction depletion capacitance C j BE 1 4C j BE 0 Collector base is a reverse biased junction depletion capacitance Due to minority charge injection into base we have to account for the diffusion capacitance as well Cb t F g m Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad BJT Cross Section Core Transistor External Parasitic Core transistor is the vertical region under the emitter contact Everything else is parasitic or unwanted Lateral BJT structure is also possible Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Core BJT Model Reverse biased junction Base Collector g m vp Reverse biased junction Diffusion Capacitance Fictional Resistance no noise Emitter Given an ideal BJT structure we can model most of the action with the above circuit For low frequencies we can forget the capacitors Capacitors are non linear MOS gate overlap caps are linear Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Complete Small Signal Model core BJT Reverse biased junctions Real Resistance has noise External Parasitics Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Circuits When the inventors of the bipolar transistor first got a working device the first thing they did was to build an audio amplifier to prove that the transistor was actually working Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A Niknejad Modern ICs Source Intel Corporation Used without permission Source Texas Instruments Used without permission First IC TI Jack Kilby 1958 A couple of transistors Modern IC Intel Pentium 4 55 million transistors 3 GHz Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 15 Prof A
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