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Berkeley ELENG 105 - Lecture Notes

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4/17/2008EE105 Fall 2007 1Lecture 21OUTLINE• Frequency Response– Review of basic concepts– high‐frequency MOSFET model– CS stageEE105 Spring 2008 Lecture 21, Slide 1Prof. Wu, UC Berkeley– CG stage– Source follower– Cascode stage• Reading: Chapter 11• The impedance of CLdecreases at high frequencies, so that it shunts some of the output current to ground.AvRoll‐Off due to CLLDpCR1=ω0=λ1⎛⎞EE105 Spring 2008 Lecture 21, Slide 2Prof. Wu, UC Berkeley• In general, if node j in the signal path has a small‐signal resistance of Rjto ground and a capacitance Cjto ground, then it contributes a pole at frequency (RjCj)‐11||1vmDLDmDLAgRjCRgjRCωω⎛⎞=−⎜⎟⎝⎠=−+Pole Identification Example 10=λEE105 Spring 2008 Lecture 21, Slide 3Prof. Wu, UC BerkeleyinGpCR11=ωLDpCR12=ωPole Identification Example 20=λEE105 Spring 2008 Lecture 21, Slide 4Prof. Wu, UC BerkeleyinmGpCgR⎟⎟⎠⎞⎜⎜⎝⎛=1||11ωLDpCR12=ωDealing with a Floating Capacitance• Recall that a pole is computed by finding the resistance and capacitance between a node and (AC) GROUND. • It is not straightforward to compute the pole due to CFin the circuit below, because neither of its terminals is grounded.EE105 Spring 2008 Lecture 21, Slide 5Prof. Wu, UC BerkeleygMiller’s Theorem • If Av is the voltage gain from node 1 to 2, then a floating impedance ZF can be converted to two grounded impedances Z1 and Z2:vFFFAZVVVZZZVZVV−=−=⇒=−11 21111121EE105 Spring 2008 Lecture 21, Slide 6Prof. Wu, UC BerkeleyvFFFAZVVVZZZVZVV111 21222221−=−−=⇒−=−4/17/2008EE105 Fall 2007 2Miller Multiplication• Applying Miller ’s theorem, we can convert a floating capacitance between the input and output nodes of an amplifier into two grounded capacitances. • The capacitance at the input node is larger than the original floating capacitance. 1EE105 Spring 2008 Lecture 21, Slide 7Prof. Wu, UC Berkeley()FvvFvFCAjACjAZZ−=−=−=111111ωωFvvFvFCAjACjAZZ⎟⎠⎞⎜⎝⎛−=−=−=111111112ωωApplication of Miller’s Theorem0=λEE105 Spring 2008 Lecture 21, Slide 8Prof. Wu, UC Berkeley()FDmGinCRgR +=11ωFDmDoutCRgR⎟⎟⎠⎞⎜⎜⎝⎛+=111ωMOSFET Intrinsic CapacitancesThe MOSFET has intrinsic capacitances which affect its performance at high frequencies:1. gate oxide capacitance between the gate and channel,2. overlap and fringing capacitances between the gate and the source/drain regions, and3. source‐bulk & drain‐bulk junction capacitances (CSB& CDB).EE105 Spring 2008 Lecture 21, Slide 9Prof. Wu, UC BerkeleyHigh‐Frequency MOSFET Model• The gate oxide capacitance can be decomposed into a capacitance between the gate and the source (C1) and a capacitance between the gate and the drain (C2). – In saturation, C1≅ (2/3)×Cgate, and C2 ≅ 0. ( Cgate=CoxWL )– C1in parallel with the source overlap/fringing capacitance Æ CGSCi ll l ith th di l/fii itÆCEE105 Spring 2008 Lecture 21, Slide 10 Prof. Wu, UC Berkeley–C2in parallel with the drain overlap/fringing capacitance ÆCGDExampleCS stage…with MOSFET capacitancesexplicitly shownSimplified circuit for high-frequency analysisEE105 Spring 2008 Lecture 21, Slide 11 Prof. Wu, UC BerkeleyTransit Frequency• The “transit” or “cut‐off” frequency, fT, is a measure of the intrinsic speed of a transistor, and is defined as the frequency where the current gain falls to 1.Conceptual set-up to measure fTI⎟⎞⎜⎛1VIEE105 Spring 2008 Lecture 21, Slide 12 Prof. Wu, UC BerkeleyGSmTCgf =π2inmTinTminminoutCgCjgZgII=⇒=⎟⎟⎠⎞⎜⎜⎝⎛==ωω11inininZVI =inmoutVgI=4/17/2008EE105 Fall 2007 3Small‐Signal Model for CS Stage0=λEE105 Spring 2008 Lecture 21, Slide 13 Prof. Wu, UC Berkeley… Applying Miller’s Theorem 1EE105 Spring 2008 Lecture 21, Slide 14 Prof. Wu, UC Berkeley()()GDDminThevinpCRgCR ++=11,ω⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛++=GDDmoutDoutpCRgCR111,ωNote that ωp,out> ωp,inDirect Analysis of CS Stage• Direct analysis yields slightly different pole locations and an extra zero:XYmzCg=ωEE105 Spring 2008 Lecture 21, Slide 15 Prof. Wu, UC Berkeley() ( )() ( )()outinXYoutXYinDThevoutXYDinThevThevXYDmpoutXYDinThevThevXYDmpCCCCCCRRCCRCRRCRgCCRCRRCRg++++++=++++=11121ωωI/O Impedances of CS Stage0=λEE105 Spring 2008 Lecture 21, Slide 16 Prof. Wu, UC Berkeley()[]GDDmGSinCRgCjZ++≈11ω[]DDBGDoutRCCjZ ||1+=ωCG Stage: Pole FrequenciesXmSXpCgR⎟⎟⎠⎞⎜⎜⎝⎛=1||1,ωCG stage with MOSFET capacitances shown0=λEE105 Spring 2008 Lecture 21, Slide 17 Prof. Wu, UC BerkeleySBGSXCCC+=YDYpCR1,=ωDBGDYCCC +=AC Analysis of Source Follower• The transfer function of a source follower can be obtained by direct AC analysis, similarly as for the emitter follower0=λEE105 Spring 2008 Lecture 21, Slide 18 Prof. Wu, UC Berkeley()() ()112+++=ωωωjbjagCjvvmGSinout()mSBGDGDSSBGSSBGDGSGDmSgCCCRbCCCCCCgRa++=++=4/17/2008EE105 Fall 2007 4Example()() ()112+++=ωωωjbjagCjvvmGSinoutEE105 Spring 2008 Lecture 21, Slide 19 Prof. Wu, UC Berkeley[]12211122111111))((mDBGDSBGDGDSDBGDSBGSGDGSGDmSgCCCCCRbCCCCCCCgRa++++=++++=Source Follower: Input Capacitance• Recall that the voltage gain of a source follower isSmSvRgRA+=1Follower stage with MOSFET capacitances shown0=λ• CXYcan be decomposed into CXand CYat the input and output nodes respectively:EE105 Spring 2008 Lecture 21, Slide 20 Prof. Wu, UC BerkeleySmGSGDinRgCCC++=1()SmGSGSvXRgCCAC+=−=11output nodes, respectively:Example0≠λEE105 Spring 2008 Lecture 21, Slide 21 Prof. Wu, UC Berkeley()12111||11GSOOmGDinCrrgCC++=Source Follower: Output Impedance• The output impedance of a source follower can be obtained by direct AC analysis of small‐signal model, similarly as for the i fll0=λEE105 Spring 2008 Lecture 21, Slide 22 Prof. Wu, UC BerkeleymGSGSGXXgCjCRjiv++=ωω1emitter followerSource Follower as Active InductorCASE 1: RG< 1/gmCASE 2: RG> 1/gmmGSGSGoutgCjCRjZ++=ωω1EE105 Spring 2008 Lecture 21, Slide 23 Prof. Wu, UC Berkeley• A follower is typically used to lower the driving impedance, i.e. RGis large compared to 1/gm,so that the “active inductor” characteristic on the right is usually observed. Example03=λEE105 Spring 2008 Lecture 21, Slide 24 Prof. Wu, UC Berkeley()333211||mGSGSOOoutgCjCrrjZ++=ωω4/17/2008EE105 Fall 2007 5MOS Cascode Stage• For a cascode stage, Miller multiplication is smaller than in the CS stage.111−≈⎟⎟⎞⎜⎜⎛−=≡mXXYvgvAEE105 Spring 2008 Lecture 21, Slide 25 Prof. Wu, UC


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Berkeley ELENG 105 - Lecture Notes

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