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 6.012 Spring 2009 1 Reading Assignment:Howe and Sodini, Chapter 10, Sections 10.1-10.4ωI. Frequency Response Review Phasor Analysis of the Low-Pass Filter • Example: C R Vin Vout + − + − • Replacing the capacitor by its impedance, 1 / (jωC), we can solve for the ratio of the phasors • Phasor notation Vout Vin = 1 1+ jωRC Vout Vin = 1/ jωC R + 1/ jωC Vout ≡ Vout Vin 6.012 Spring 2009 2(a)Magnitude Plot of LPF • Vout /Vin --> 1 for “low” frequencies • --> 0 for “high” frequencies Vout /Vin Vout Vin Break pointlog scale 01 −3dB0.1 −20 1 = 0.707 2 −400.01 1/ω dB −20 decade 0.001 −60 Vout Vin dB scale • The “break point” is when the frequency is equal to ω o = 1 / RC • The break frequency defines “low” and “high” frequencies. • dB 20 log x ----> 20dB = 10, 40dB = 100, -40dB = .01 • At ω o the ratio of phasors has a magnitude of - 3 dB. ≡ 0.0001 0.01 RC 0.1 RC 1 RC 10 RC 100 RC 1000 RC ω−80 log scale 6.012 Spring 2009 3−45°Phase Plot of LPF • Phase (Vout / Vin ) = 0o for low frequencies • Phase (Vout / Vin ) = -90o high frequencies. V ∠ out V in Break point −45° 0° • Transition region extends from ω o / 10 to 10 ω o • At ω o Phase = -45o Review of Frequency Domain Analysis Chap 10.1 −90° −180° ω −135° log scale 0.01 RC 0.1 RC 1 RC 10 RC 100 RC 1000 RC 6.012 Spring 2009 4(a)ππππ(b)II. Small Signal Models for Frequency Response Bipolar Transistor Cπ C µ gm Vπ r o rπ B C E E Vπ + − MOS Transistor - VSB = 0 • Replace Cgs for Cπ • Replace Cgd for Cµ • Let rπ ---> ∞ gm V gs G D S S V gs + − Cgd C gs r o 6.012 Spring 2009 5III. Frequency Response of Intrinsic CE Current Amplifier RS---> ∞ & RL= 0 Circuit analysis - Short Circuit Current Gain Io/Iin Cπ C µ gm Vπrπ Vπ + − Iin I o • KCL at the output node: • KCL at the input node: • After Algebra I o = gm Vπ − Vπ jωCµ Iin = Vπ Zπ + Vπ jωCµ where Zπ = rπ 1 jωCπ I o Iin = gm rπ 1− jωCµ gm 1+ jωrπ Cπ + Cµ( ) = β o 1− jωCµ gm 1+ jωrπ Cπ + Cµ( ) = β o 1− j ω ω z 1+ j ω ω p ωZ = gm Cµ ω p = 1 rπ Cπ + Cµ( ) 6.012 Spring 2009 6π πππ π ππBode Plot of Short-Circuit Current Gain I o I in β o = gmrπ 1 C µ Cπ + C µ 1 gm gm ω r(πCπ + C µ) Cπ + C µ C µ log scale (a) I ∠ o Iin • Frequency at which current gain is reduced to 0 dB is defined at fT: fT = 1 2π gm Cπ + Cµ( ) 0 −45 −90 −135 −180 ω log scale (b) 1 rπ(Cπ + C µ) gm C µ 6.012 Spring 2009 7π ππGain-Bandwidth Product • When we increase β o we increase rπ BUT we decrease the pole frequency---> Unity Gain Frequency remains the same I o Iin β o1 β o2 Examine how transistor parameters affect ωT • Recall • The unity gain frequency is Cπ = Cje + gm τ F ωωωωT = IC / Vth IC / Vth( )ττττF + C je + Cµµµµ1 gm β o1(Cπ + C µ) gm β o2(Cπ + C µ) gm Cπ + C µ ωT = β o1 > β o2 ω log scale 6.012 Spring 2009 8•ωωωωT = IC / Vth (IC / Vth )ττττF + Cje + CµµµµIC 1 2πτF fT fT dominated by diffusion capacitance fT dominated by depletion capacitances C µ and Cje • At low collector current fT is dominated by depletion capacitances at the base-emitter and base-collector junctions • As the current increases the diffusion capacitance,As the current increases the diffusion capacitance, gm τF ,becomes dominant • Fundamental Limit for the frequency response of a bipolar transistor is set by To Increase fT • High Current - Diffusion capacitance limited -Shrink basewidth • Low Current - Depletion capacitance limited -Shrink emitter area and collector area - (geometries) ττττF = WB 2 2 Dn, p 6.012 Spring 2009 9MIT OpenCourseWarehttp://ocw.mit.edu 6.012 Microelectronic Devices and Circuits Spring 2009 For information about citing these materials or our Terms of Use, visit:
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