Lecture 11ANNOUNCEMENTS•Prob. 5 of Pre‐Lab #5 has been clarified. (Download new version.)Prob. 5 of PreLab #5 has been clarified. (Download new version.)• HW#6 has been posted.• Review session: 3‐5PM Friday (10/5) in 306 Soda (HP Auditorium)• Midterm #1 (Thursday 10/11):• Material of Lectures 1‐10 (HW# 2‐6; Chapters 2, 4, 5)•2 pgs of notes (double‐sided, 8.5”×11”), calculator allowedOUTLINEf lf2 pgs of notes (doublesided, 8.5×11 ), calculator allowed• Review of BJT Amplifiers• Cascode StageEE105 Fall 2007 Lecture 11, Slide 1Prof. Liu, UC BerkeleyReading: Chapter 9.1Review: BJT Amplifier Design• A BJT amplifier circuit should be designed to1. ensure that the BJT operates in the active mode, p ,2. allow the desired level of DC current to flow, and3. couple to a small‐signal input source and to an output “load”.Æ Proper “DC biasing” is required!(DC analysis using large‐signal BJT model)• Key amplifier parameters: (AC analysis using small‐signal BJT model)Voltage gainA≡v/v–Voltage gain Av ≡vout/vin– Input resistance Rin≡ resistance seen between the input node and ground (with output terminal floating)Ot t itRit bt th ttEE105 Fall 2007 Lecture 11, Slide 2Prof. Liu, UC Berkeley–Output resistance Rout≡resistance seen between the output node and ground (with input terminal grounded)Large‐Signal vs. Small‐Signal Models• The large‐signal model is used to determine the DC operating point (VBE, VCE, IB, IC) of the BJT.pgp (BE,CE,B,C)• The small‐signal model is used to determine how the output responds to an input signal.EE105 Fall 2007 Lecture 11, Slide 3Prof. Liu, UC BerkeleySmall‐Signal Models for Independent Sources• The volt age across an independent voltage source does not vary with time. (Its small‐signal voltage is always zero.)y(g g y )It is reg arded as a short circuit for small‐signal analysis.Large-SignalSmall-SignalLarge-SignalModelSmall-SignalModel• The current through an independent current source does not vary with time. (Its small‐signal current is always zero.)Iti dd iitf llil liEE105 Fall 2007 Lecture 11, Slide 4Prof. Liu, UC BerkeleyIt is regarded as an open circuit for small‐signal analysis.Comparison of Amplifier TopologiesCommon EmitterLA0Common BaseLA0Emitter Follower0A1•Large Av< 0‐ Degraded by RE‐ Degraded by RB/(β+1)•Large Av> 0‐Degraded by RE and RS‐ Degraded by RB/(β+1)•0 < Av≤ 1‐ Degraded by RB/(β+1)•LargeRi• Moderate Rin‐ Increased by RB‐ Increased by RE(β+1)• Small Rin‐ Increased by RB/(β+1)‐ Decreased by RELarge Rin(due to RE(β+1))• Small Rout yE(β)• Rout ≅ RC•rodegradesA,RotyE• Rout ≅ RC•rodegradesA,Rot‐ Effect of source impedance is reduced by β+1DdbRrodegrades Av, Routbut impedance seenlooking into the collector can be “boosted” by rodegrades Av, Routbut impedance seenlooking into the collector can be “boosted” by ‐Decreased by RE• rodecreases Av, Rin, andRoutEE105 Fall 2007 Lecture 11, Slide 5Prof. Liu, UC Berkeleyyemitter degenerationyemitter degenerationand RoutCommon Emitter StageRv∞=AV∞<AVBECinoutRRgRvv+++−≈11βEBinmRRRrRRg+++=+)1(1ββπ[]())||(1||RRR+EE105 Fall 2007 Lecture 11, Slide 6Prof. Liu, UC BerkeleyCoutRR=[]())||(1||πrRgrRREmOCout+≈Common Base Stage∞=AVESEBESCinoutRRRRRRRvv+⋅++≈1ESmg+1βBR⎞⎜⎛1VEBminRRgR⎟⎠⎞⎜⎜⎝⎛++≈11βRR[]())||(1||RRR+∞<AVEE105 Fall 2007 Lecture 11, Slide 7Prof. Liu, UC BerkeleyCoutRR=[]())||(1||πrRgrRREmOCout+≈Emitter Follower∞=AV∞<AV1=EoutRRvOEoutRrRv1||=11+++βSmEinRgRvRR)1(β()()SmOEinRRRgrRv||111||+++ββEinRrR)1(βπ++=sRRR||1⎞⎜⎜⎛+=()()sOEinrRRRrRrR||||1||1⎞⎜⎜⎛+=++=βπEE105 Fall 2007 Lecture 11, Slide 8Prof. Liu, UC BerkeleyEmoutRgR||1⎠⎜⎜⎝++=βOEmoutrRgR||||1⎠⎜⎜⎝++=βIdeal Current SourceEquivalent CircuitCircuit Symbol I-V Characteristic•An ideal current source has infinite output impedance•An ideal current source has infinite output impedance.How can we increase the output impedance of a BJT that d ?EE105 Fall 2007 Lecture 11, Slide 9Prof. Liu, UC Berkeleyis used as a current source?Boosting the Output Impedance• Recall that emitter degeneration boosts the impedance seen looking into the collector.g– This improves the gain of the CE or CB amplifier. However, headroom is reduced.()[]rRrrRgR||||1++=EE105 Fall 2007 Lecture 11, Slide 10 Prof. Liu, UC Berkeley()[]ππrRrrRgREOEmout||||1++=Cascode Stage• In order to relax the trade‐off between output impedance and voltage headroom we can use aimpedance and voltage headroom, we can use a transistor instead of a degeneration resistor:||)]||(1[rrrrrgR++=()121112112||||)]||(1[πππrrrgRrrrrrgROOmoutOOOmout≈++=•VforQcan be as low as ~0 4V (“soft saturation”)1 if 1212>>≅=βCECIIIEE105 Fall 2007 Lecture 11, Slide 11 Prof. Liu, UC Berkeley•VCEfor Q2can be as low as ~0.4V (“soft saturation”)Maximum Cascode Output Impedance• The maximum output impedance of a cascode is limited byrlimited by rπ1.rrrgRβ≈: If12πrrO>>1111max,1OOmoutrrrgRβπ=≈EE105 Fall 2007 Lecture 11, Slide 12 Prof. Liu, UC BerkeleyPNP Cascode Stage()121121||||)]||(1[ππRrrrrrgROOOmout++=EE105 Fall 2007 Lecture 11, Slide 13 Prof. Liu, UC Berkeley()1211||πrrrgROOmout≈False Cascodes• When the emitter of Q1is connected to the emitter of Qit’s not a cascode sinceQis a diode‐connectedQ2, it s not a cascode since Q2is a diodeconnected device instead of a current source. 11⎤⎡⎞⎜⎛1122112211||||1||||11OmOOmmoutgrrgrrrggR⎞⎜⎛+⎥⎦⎤⎢⎣⎡⎟⎠⎞⎜⎜⎝⎛+=ππEE105 Fall 2007 Lecture 11, Slide 14 Prof. Liu, UC Berkeley12121211OmOmmoutrgrggR≈+⎟⎠⎞⎜⎜⎝⎛+≈Short‐Circuit Transconductance• The short‐circuit transconductance of a circuit is a measure of its strength in converting an inputmeasure of its strength in converting an input voltage signal into an output current signal. i0=≡outvinoutmviGEE105 Fall 2007 Lecture 11, Slide 15 Prof. Liu, UC BerkeleyVoltage Gain of a Linear Circuit• By representing a linear circuit with its Norton equivalent the relationship betweenVandVcanequivalent, the relationship between Vout and Vin can be expressed by the product of Gm and Rout.Norton Equivalent CircuitRvGRiv==outminoutoutinmoutoutoutRGvvRvGRiv−=−=−=Computation of short-circuit output current:EE105 Fall 2007 Lecture 11, Slide 16 Prof. Liu, UC BerkeleyExample: Determination of Voltage Gain
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