Lecture 8ANNOUNCEMENTS•A summary of frequently misunderstood/missed concepts is•A summary of frequently misunderstood/missed concepts is now posted on the class website, and will be updated regularly.• Graded HW assignments can be picked up in lab (353 Cory). OUTLINEÆ Please indicate your lab section on your HW assignments!OUTLINE• BJT Amplifiers (cont’d)– Common‐emitter topology–CE stage with emitter degeneration– Impact of Early effect (ro)EE105 Fall 2007 Lecture 8, Slide 1Prof. Liu, UC BerkeleyReading: Finish Chapter 5.3.1Emitter Degeneration• By inserting a resistor in series with the emitter, we “degenerate” the CE stage. g g• This topology will decrease the gain of the amplifier but improve other aspects, such as linearity, and input dimpedance. EE105 Fall 2007 Lecture 8, Slide 2Prof. Liu, UC BerkeleySmall‐Signal Analysis• The gain of a degenerated CE stage = the total load resistance seen at the collector divided by 1/gplusresistance seen at the collector divided by 1/gm plus the total resistance placed in series with the emitter. RRg−−EmCEmCmvRgRRgRgA+=+=11mgEE105 Fall 2007 Lecture 8, Slide 3Prof. Liu, UC BerkeleyEmitter Degeneration Example 1Note that the input impedance of Q2is in parallel with RE. 2||1πrRRAECv+−=EE105 Fall 2007 Lecture 8, Slide 4Prof. Liu, UC Berkeley21||πgEmEmitter Degeneration Example 2Note that the input impedance of Q2is in parallel with RC.ECvRrRA+−=21||πEE105 Fall 2007 Lecture 8, Slide 5Prof. Liu, UC BerkeleyEmg1Input Impedance of Degenerated CE Stage• With emitter degeneration, the input impedance is increased fromrtor+ (β+1)R―a desirable eff ectincreased from rπto rπ+ (β+1)RE a desirable eff ect.AiRiV)1()(∞=βExinxExxRrvRiRirv)1()1(++=≡++=ββππEE105 Fall 2007 Lecture 8, Slide 6Prof. Liu, UC BerkeleyExini)(βπOutput Impedance of Degenerated CE Stage• Emitter degeneration does not alter the output impedance if the Early effect is negligibleimpedance, if the Early eff ect is negligible.ARvV⇒⎞⎜⎜⎛++∞=00)(πxEminRvRvRvgrvv=⇒⎠⎜⎜⎝++==00πππππEE105 Fall 2007 Lecture 8, Slide 7Prof. Liu, UC BerkeleyCxxoutRiR=≡Degenerated CE Stage as a “Black Box”AV ∞= )(EinmoutRgrvgi++=−)(11• If gmRE>> 1, Gmis more linear.moutmEmRgiGRgr+≈≡++1)(1πEE105 Fall 2007 Lecture 8, Slide 8Prof. Liu, UC BerkeleygmE,mEminRgv+1Degenerated CE Stage with Base Resistance)( ∞=AV.=βAoutinAinoutvvvvvv)1( +++−=ββπBECinoutRRrRvv1++−≈BECvRRRAEE105 Fall 2007 Lecture 8, Slide 9Prof. Liu, UC Berkeley1+++βEmRgDegenerated CE Stage: Input/Output ImpedancesInput/Output Impedances • Rin1is more important in practice, because RBis often the output impedance of the previous stagethe output impedance of the previous stage.AV ∞=)(EinARRRRrR+++++=)1()1(1ββπCoutEBinRRRrRR=+++=)1(2βπEE105 Fall 2007 Lecture 8, Slide 10 Prof. Liu, UC BerkeleyEmitter Degeneration Example 3211)||(RRRRABCv++−=22)1(1RRrRgBinm+++=+ββπEE105 Fall 2007 Lecture 8, Slide 11 Prof. Liu, UC Berkeley1||RRRCout=Output Impedance of Degenerated CE Stage withVA<∞with VA• Emitter degeneration boosts the output impedance.–This improves the gain of the amplifier and makes theThis improves the gain of the amplifier and makes the circuit a better current source. [])||)(1(||)||(1πππrRrgrRrRrrRgREOmOoutEOEmout++=++=EE105 Fall 2007 Lecture 8, Slide 12 Prof. Liu, UC Berkeley[])||(1ππrRgrREmOoutEOmOout+≈Two Special CasesStage with explicit depiction of ro:OmOoutErrgrRrR )1( : )1≈+≈>>ππβOEErRgRrR)1(:)2+≈<<EE105 Fall 2007 Lecture 8, Slide 13 Prof. Liu, UC BerkeleyOEmoutErRgRrR)1( :)2+≈<<πAnalysis by Inspection• This seemingly complicated circuit can be greatly simplified by first recognizing that the capacitor creates an AC short to ground, and gradually transforming the circuit to a known topology.[][]EE105 Fall 2007 Lecture 8, Slide 14 Prof. Liu, UC Berkeley[]12||)||(1RrrRgROmoutπ+=[]OmoutrrRgR)||(121π+=11||outoutRRR=Example: Degeneration by Another BJT[]1121)||(1OOmoutrrrgRπ+=• Called a “cascode”, this circuit offers many advantages EE105 Fall 2007 Lecture 8, Slide 15 Prof. Liu, UC Berkeley, y gthat we will study later...Bad Input Connection• Since the microphone has a very low resistance (connecting the base of Q1to ground), it attenuates (g1g)the base voltage and renders Q1 with a very small bias current.EE105 Fall 2007 Lecture 8, Slide 16 Prof. Liu, UC BerkeleyUse of Coupling Capacitor• A capacitor is used to isolate the DC bias network from the microphone and to short (or“couple”) thefrom the microphone , and to short (or couple ) the microphone to the amplifier at higher frequencies. EE105 Fall 2007 Lecture 8, Slide 17 Prof. Liu, UC BerkeleyDC and AC Analysis• The coupling capacitor is replaced with an open circuit for DC analysis, and then replaced with a shortcircuit for DC analysis, and then replaced with a short circuit for AC analysis.BinOCmvRrRrRgA||)||(=−=πOCoutrRR ||=EE105 Fall 2007 Lecture 8, Slide 18 Prof. Liu, UC BerkeleyBad Output Connection• Since the speaker has an inductor with very low DC resistance, connecting it directly to the amplifier , g y pwould ~short the collector to ground, causing the BJT to go into deep saturation mode.EE105 Fall 2007 Lecture 8, Slide 19 Prof. Liu, UC BerkeleyUse of Coupling Capacitor at Output• The AC coupling indeed allows for correct biasing. However due to the speaker’s small inputHowever, due to the speaker s small input impedance, the overall gain drops considerably.EE105 Fall 2007 Lecture 8, Slide 20 Prof. Liu, UC BerkeleyCE Stage with Voltage‐Divider BiasingOCmvrRgA)||(−=OCoutinrRRRRrR||||||21==πEE105 Fall 2007 Lecture 8, Slide 21 Prof. Liu, UC BerkeleyCE Stage with Robust Biasing ∞=V∞AV)(∞=AVCvRRA+−=1)(∞AV[]EinEmRRRrRRg++=+21||||)1(βπEE105 Fall 2007 Lecture 8, Slide 22 Prof. Liu, UC BerkeleyCoutRR =Elimination of Emitter Degeneration for AC Signalsfor AC Signals• The capacitor C2shorts out REat higher frequencies to eliminate the emitter degenerationto eliminate the emitter degeneration.)(∞=AViCmvRRrRRgA=−=21||||)(ACoutinRRRRrR=21||||πEE105 Fall 2007 Lecture 8, Slide 23 Prof. Liu, UC BerkeleyComplete CE StagessLCvRRRRRRRRRRRA+⋅++−=212121||||||||1||EE105 Fall 2007 Lecture 8, Slide 24 Prof. Liu, UC BerkeleyssEmRg +++2121||1βSummary of CE ConceptsEE105 Fall 2007 Lecture 8, Slide 25 Prof. Liu, UC
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