ECE137B: High-Frequency Amplifier Crib Sheet, Page 1Basics: Transistor small-signal high-frequency models VbeCCRgmVbeRoCBEHybrid-pi model: Cm= Cbc Cp= Cbe= Cp,depl+ Cp,diff Cp,diff= gmtf ft= gm2pCp+ Cm()() gm=are= IcVT Rp=b+1()re Ro= VAICCCRoCBEregmVebVeb"T"-modelMakes common-base analysis much easier.Both these models are only approximate,being "good" up to ft. Additionally Rb©b isoften an important parasitic (not discussedmuch in 137B.Simplification of Emitter Degeneration REapproximate only; check notes for boundson validity ÄCp= Cprere+ RE()() Ägm= gmrere+ RE()()=are+RE() ÄCm= Cm ÄRp= Rpre+ RE()re()=b+1()re+RE()Common-Emitter StageCBCCgmVbeVbeRLeqRiIiCL VoutVgen= VoutVgen()MB1 + stzero1 + a1s + a2s2 a1= RiCp+ Cm1 + gmRLeq()()+RLeqCm+ CL() a2= RiRLeqCmCL+ CmCp+ CpCL() tzero=-CmgmECE137B: High-Frequency Amplifier Crib Sheet, Page 2Emitter-Follower StageBECCgmVbeVbeRLeqRiIiCLR VoutVgen= VoutVgen()MB1 + stzero1 + a1s + a2s2given that Avmb= rere+ RLeq()(): a1= CpRpreRLeq+ Ri1 - Avmb()()() +CmRitransistor input resistance() +CLRLeqtransistor output resistance() a2= Ritransistor input resistance()RLeqre() ´ CmCp+ CmCL+ CLCp() tzero= gmCpGeneral Solutions of Problems: Nodal analysis (Know how to do this!)1)Write the nodal equations (sum of thecurrents=0) at each circuit node, and putthe resulting equations in matrix form (theY's being various combinations of gm's,1/R's, and sC's): Y11Y12Y13Y14Y21Y22Y23Y24Y31Y32Y33Y34Y41Y42Y43Y44éëêêêêùûúúúúV1= VinV2V3V4= Voutéëêêêêùûúúúú=Iin000éëêêêêùûúúúú2) Use Cramer's rule to solve: Y11Y12Y13IinY21Y22Y230Y31Y32Y330Y41Y42Y430Y11Y12Y13Y14Y21Y22Y23Y24Y31Y32Y33Y34Y41Y42Y43Y44= Vout3) This comes out as: VoutIin= ksmc0+ c1s + c2s2+Ld0+ d1s + d2s2+L,which is divided through to get:(if present, m is the number of zeros,minus the number of poles, in the transferfunction)4) VoutIin=VoutIinæèçöø÷mbsm1 + b1s + b2s2+L1 + a1s + a2s2+L...and the poles and zeroes are found byfactoring the numerator and denominator.The separated-pole approximation, ifapplicable, makes this factoring easy.5) To find the impulse response, do apartial-fraction expansion and then take theinverse LaPlace transform.6) To find the sinusiodal frequencyresponse, set s = jw.ECE137B: High-Frequency Amplifier Crib Sheet, Page 3General Solutions of Problems: Method of Time ConstantsCircuit withoutCapacitors orInductorsport 1port 2port 4C1C2C3C4Circuit withoutCapacitors orInductorsport 1port 2port 3port 4R211R110Circuit withoutCapacitors orInductorsport 1port 2port 3port 4R211 VoutVgen=VoutVgenæèçöø÷mb1 + b1s + b2s2+L1 + a1s + a2s2+L a1= R110C1+ R220C2+ R330C3+ R440C4 a2= R110R221C1C2+ R110R331C1C3+ R110R441C1C4 +R220R332C2C3+ R220R442C2C4+ R330R443C3C4notethat Rxx0Ryyx= RxxyRyy0R0xxRiRLeq Rxx0= RpreRLeq+ Ri1 - Avmb()() Avmb= RLeqre+ RLeq()()R0yyRxRLeq Ri= RxRp Ryy0= Ri1 +
or
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