6.012 Spring 2007 1Lecture 21Frequency Response of Amplifiers (I)Common-Emitter AmplifierOutline• Review frequency domain analysis• BJT and MOSFET models for frequency response• Frequency Response of Intrinsic Common-Emitter Amplifier• Effect of transistor parameters on fTReading Assignment:Howe and Sodini, Chapter 10, Sections 10.1-10.46.012 Spring 2007 2Phasor Analysis of the Low-Pass Filter• Example: • Replacing the capacitor by its impedance, 1 / (jωC), we can solve for the ratio of the phasors• Phasor notationI. Frequency Response ReviewVoutVin=11+ jωRCVoutVin=1/jωCR +1/ jωCVout ≡VoutVinCRVinVout+−+−6.012 Spring 2007 3Magnitude Plot of LPF• --> 1 for “low” frequencies• --> 0 for “high” frequencies• The “break point” is when the frequency is equal to ωo= 1 / RC• The break frequency defines “low” and “high” frequencies.• dB 20 log x ----> 20dB = 10, 40dB = 100, -40dB = .01•At ωothe ratio of phasors has a magnitude of- 3 dB.Vout /VinVout /Vin≡VoutVin10.10.010.0010.00010.01RC0.1RC1RC10RC100RC1000RCωBreak point12= 0.707−20dBdecade0−20−40−60−80dBscale−3dB1/ωlog scaleVoutVinlog scale6.012 Spring 2007 4Phase Plot of LPF•Phase (Vout/ Vin) = 0ofor low frequencies •Phase (Vout/ Vin) = -90ohigh frequencies.• Transition region extends from ωo/ 10 to 10 ωo•At ωoPhase = -45oReview of Frequency Domain Analysis Chap 10.1∠0° −90°−180°ω−45°−135°Break pointlog scaleVoutVin0.01RC0.1RC1RC10RC100RC1000RC6.012 Spring 2007 5II. Small Signal Models for Frequency ResponseBipolar TransistorMOS Transistor - VSB = 0•Replace Cgsfor Cπ•Replace Cgdfor Cµ•Let rπ---> ∞CCµgmVrorBCEE(a)V+−gmVgsGDSSVgs+−Cgd(b)Cgsro6.012 Spring 2007 6III. Frequency Response of Intrinsic CE Current Amplifier• KCL at the output node:• KCL at the input node:• After AlgebraRS---> ∞ & RL= 0Circuit analysis - Short Circuit Current Gain Io/IinIo= gmVπ−VπjωCµIin=VπZπ+VπjωCµwhereZπ= rπ1jωCπ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ IoIin=gmrπ1−jωCµgm⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 1+ jωrπCπ+ Cµ()=βo1−jωCµgm⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ 1+ jωrπCπ+ Cµ()=βo1− jωωz1+ jωωp⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ωZ=gmCµωp=1rπCπ+ Cµ()CCµgmVrV+−IinIo6.012 Spring 2007 7Bode Plot of Short-Circuit Current Gain• Frequency at which current gain is reduced to 0 dB is defined at fT:fT=12π⎛ ⎝ ⎜ ⎞ ⎠ ⎟ gmCπ+ Cµ()1ωIoIin10−45−90−135−180IoIin∠ω(a)log scalelog scale(b)Cµ C + Cµr (C + Cµ)1r (C + Cµ)gmC + Cµgm Cµgm Cµβo = gmr6.012 Spring 2007 8Gain-Bandwidth Product• When we increase βowe increase rπBUT we decrease the pole frequency---> Unity Gain Frequency remains the sameExamine how transistor parameters affect ωT• Recall • The unity gain frequency isCπ=Cje+gmτFωT=IC/VthIC/ Vth()τF+ Cje+ CµIo1Iingmβo1(C + Cµ)gmβo2(C + Cµ)gmC + CµωT =βo1βo2βo1 > βo2ωlog scale6.012 Spring 2007 9• At low collector current fTis dominated by depletion capacitances at the base-emitter and base-collector junctions• As the current increases the diffusion capacitance, gmτF,becomes dominant• Fundamental Limit for the frequency response of a bipolar transistor is set byTo Increase fT• High Current - Diffusion capacitance limited -Shrink basewidth• Low Current - Depletion capacitance limited -Shrink emitter area and collector area - (geometries)τF=WB22 Dn, pωT=IC/VthIC/ Vth()τF+ Cje+ CµIC12 τFfTfT dominated by diffusioncapacitance fT dominated by depletioncapacitances Cµ and
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