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Lecture 21 Frequency Response of Amplifiers (I) Common-Emitter Amplifier Outline • • • • Review frequency domain analysis BJT and MOSFET models for frequency response Frequency Response of Intrinsic Common-Emitter Amplifier Effect of transistor parameters on fT Reading Assignment: Howe and Sodini, Chapter 10, Sections 10.1-10.4 6.012 Spring 2009 1 I. Frequency Response Review Phasor Analysis of the Low-Pass Filter • Example: R + Vin + − C Vout − ω • Replacing the capacitor by its impedance, 1 / (jωC), we can solve for the ratio of the phasors Vout Vin Vout 1/ jωC = V in R + 1/ j ωC Vout 1 = V in 1+ jωRC • Vout ≡ Phasor notation 6.012 Spring 2009 2 Magnitude Plot of LPF • • Vout /Vin Vout /Vin --> 1 for “low” frequencies --> 0 for “high” frequencies Vout Vin log scale 1 Vout Vin Break point 0 −3dB 0.1 0.01 1 = 0.707 2 1/ω dB −20 decade 0.001 0.0001 dB scale −20 −40 −60 0.01 RC 0.1 RC 1 RC 10 RC 100 RC 1000 RC −80 ω log scale (a) • • • • 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 ωo the ratio of phasors has a magnitude of - 3 dB. 6.012 Spring 2009 ≡ 3 Phase Plot of LPF • Phase (Vout / Vin ) = 0o for low frequencies • Phase (Vout / Vin ) = -90o high frequencies. V ∠ out V in Break point 0° −45° −45° −90° −135° −180° 0.01 RC 0.1 RC 1 RC 10 RC 100 RC 1000 RC ω log scale • Transition region extends from ωo / 10 to 10 ωo • At ωo Phase = -45o Review of Frequency Domain Analysis Chap 10.1 6.012 Spring 2009 4 II. Small Signal Models for Frequency Response Bipolar Transistor Cµ B C + rπ π Vπ Cπ π− π gmVπ ro π E E (a) MOS Transistor - VSB = 0 Cgd G D + Vgs Cgs gmVgs ro − S S (b) • Replace Cgs for Cπ • Replace Cgd for Cµ • Let rπ ---> ∞ 6.012 Spring 2009 5 III. Frequency Response of Intrinsic CE Current Amplifier RS ---> ∞ & RL = 0 Circuit analysis - Short Circuit Current Gain Io/Iin Cµ Io + Iin rπ Vπ gmVπ Cπ − • KCL at the output node: Io = gmVπ − Vπ j ωCµ • KCL at the input node: V Iin = π + Vπ j ωCµ where Zπ Zπ = rπ 1 jω Cπ • After Algebra jω Cµ jωCµ ω 1− j gm rπ 1− β o 1− gm gm ωz Io = = = βo ω Iin 1+ j ωrπ (Cπ + Cµ ) 1+ jω rπ (Cπ + Cµ ) 1+ j ω p gm ωZ = Cµ 6.012 Spring 2009 1 ωp = rπ (Cπ + Cµ ) 6 Bode Plot of Short-Circuit Current Gain Io I in βo = gmrπ 1 Cµ Cπ + Cµ 1 r(π Cπ + Cµ) gm Cπ + Cµ gm Cµ ω log scale (a) I ∠ o Iin 0 −45 −90 −135 −180 gm Cµ 1 rπ(Cπ + Cµ) ω log scale (b) • Frequency at which current gain is reduced to 0 dB is defined at fT: 1 gm fT = 2π (Cπ + Cµ ) 6.012 Spring 2009 7 Gain-Bandwidth Product • When we increase βo we increase rπ BUT we decrease the pole frequency---> Unity Gain Frequency remains the same Io Iin βo1 βo2 1 gm βo1(Cπ + Cµ) gm βo2(Cπ + Cµ) ωT = gm Cπ + Cµ ω log scale βo1 > βo2 Examine how transistor parameters affect ωT • Recall Cπ = C je + gmτ F • The unity gain frequency is I C / Vth ωT = (IC / Vth )τF + C je + Cµ 6.012 Spring 2009 8 I C / Vth ωT = (IC / Vth )τF + C je + Cµ fT dominated by diffusion capacitance fT 1 2πτF fT dominated by depletion capacitances Cµ and Cje IC • At low collector current fT is dominated by depletion capacitances at the base-emitter and basecollector junctions • As the current increases the diffusion capacitance, • gmτF ,becomes dominant • Fundamental Limit for the frequency response of a bipolar transistor is set by WB 2 τF = 2 Dn, p To Increase fT • High Current - Diffusion capacitance limited Shrink basewidth • Low Current - Depletion capacitance limited Shrink emitter area and collector area - (geometries) 6.012 Spring 2009 9 MIT OpenCourseWare http://ocw.mit.edu 6.012 Microelectronic Devices and Circuits Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.