Lecture 21 REMINDERS Review session Fri 11 9 3 5PM 3 5PM in 306 Soda HP Auditorium Midterm 2 Thursday 11 15 3 30 5PM in Sibley Auditorium OUTLINE Frequency Response Review of basic concepts high frequency MOSFET model CS stage CG stage Source follower Cascode stage Reading Chapter 11 EE105 Fall 2007 Lecture 21 Slide 1 Prof Liu UC Berkeley Av Roll Off due to CL The impedance of CL decreases at high frequencies so that it shunts some of the output current to ground ground 0 p 1 RD C L 1 Av g m RD j C L In general if node j in the signal path has a small signal resistance of Rj to ground and a capacitance Cj to ground d th then it contributes t ib t a pole l att ffrequency RjCj 11 EE105 Fall 2007 Lecture 21 Slide 2 Prof Liu UC Berkeley Pole Identification Example 1 0 p1 EE105 Fall 2007 1 RG Cin p2 Lecture 21 Slide 3 1 RD C L Prof Liu UC Berkeley Pole Identification Example 2 0 p1 1 1 Cin RG gm EE105 Fall 2007 p2 Lecture 21 Slide 4 1 RD C L Prof Liu UC Berkeley Dealing with a Floating Capacitance Recall that a pole is computed by finding the resistance and capacitance between a node and AC GROUND GROUND It is not straightforward to compute the pole due to CF in the circuit below because neither of its terminals is grounded EE105 Fall 2007 Lecture 21 Slide 5 Prof Liu UC Berkeley Miller 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 V1 V2 V1 V1 1 Z1 Z F ZF ZF Z1 V1 V2 1 Av V1 V2 V2 V2 1 Z 2 Z F ZF ZF Z2 V1 V2 1 1 EE105 Fall 2007 Lecture 21 Slide 6 Av Prof Liu UC Berkeley Miller Multiplication Applying Miller s theorem we can convert a floating capacitance p between the input p and output p nodes of an amplifier into two grounded capacitances The capacitance at the input node is larger than the originall fl floating capacitance ZF Z2 1 1 1 1 j C F 1 1 j 1 1 C F Av Av Av 1 ZF 1 j C F Z1 1 Av 1 Av j 1 Av C F EE105 Fall 2007 Lecture 21 Slide 7 Prof Liu UC Berkeley Application of Miller s Theorem 0 1 ini RG 1 g m RD C F EE105 Fall 2007 out Lecture 21 Slide 8 1 1 C F RD 1 g m RD Prof Liu UC Berkeley MOSFET Intrinsic Capacitances The MOSFET has intrinsic capacitances which affect its performance at high p g frequencies q 1 gate oxide capacitance between the gate and channel 2 overlap and fringing capacitances between the gate and the source drain regions regions and 3 source bulk drain bulk junction capacitances CSB CDB EE105 Fall 2007 Lecture 21 Slide 9 Prof Liu UC Berkeley High 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 C1 in parallel with the source overlap fringing capacitance CGS C2 in parallel with the drain overlap fringing capacitance CGD EE105 Fall 2007 Lecture 21 Slide 10 Prof Liu UC Berkeley Example CS stage EE105 Fall 2007 with MOSFET capacitances explicitly shown Lecture 21 Slide 11 Simplified circuit for high frequency analysis Prof Liu UC Berkeley Transit Frequency The transit or cut off frequency fT is a measure of the intrinsic speed of a transistor transistor and is defined as the frequency where the current gain falls to 1 C Conceptual t l set up t t measure fT to I out g mVin Vin I in Zin 1 I out 1 g m Zin g m I in j T Cin g T m Cin gm 2 fT CGS EE105 Fall 2007 Lecture 21 Slide 12 Prof Liu UC Berkeley Small Signal Model for CS Stage 0 EE105 Fall 2007 Lecture 21 Slide 13 Prof Liu UC Berkeley Applying Miller s Theorem p in 1 RThev Cin 1 g m RD CGD p out 1 1 CGD RD Cout 1 g R m D Note that p out p in EE105 Fall 2007 Lecture 21 Slide 14 Prof Liu UC Berkeley Direct Analysis of CS Stage Direct analysis yields slightly different pole locations and an extra zero gm z C XY 1 p1 1 g m RD C XY RThev RThevCin RD C XY Cout 1 g m RD C XY RThev RThev Cin RD C XY Cout p2 RThev RD Cin C XY Cout C XY Cin Cout EE105 Fall 2007 Lecture 21 Slide 15 Prof Liu UC Berkeley I O Impedances of CS Stage 0 Z in j CGS EE105 Fall 2007 1 1 g m RD CGD Z out Lecture 21 Slide 16 1 j CGD CDB RD Prof Liu UC Berkeley CG Stage Pole Frequencies CG stage with MOSFET capacitances shown p X 0 1 1 C X RS gm C X CGS CSB p Y 1 RDCY CY CGD C DB EE105 Fall 2007 Lecture 21 Slide 17 Prof Liu UC Berkeley AC Analysis of Source Follower 0 vout vin CGS 11 j gm 2 a j b j 1 EE105 Fall 2007 The transfer function of a source follower can be obtained by direct AC analysis similarly as for th emitter the itt follower f ll f ref Lecture 14 Slide 6 RS CGD CGS CGD C SB CGS C SB a gm b RS CGD Lecture 21 Slide 18 CGD C SB gm Prof Liu UC Berkeley Example vout vin CGS 1 j gm 2 a j b j 1 RS C GD 1C GS 1 C GD 1 C GS 1 C SB 1 C GD 2 C DB 2 a g m1 C GD 1 C SB 1 C GD 2 C DB 2 b R S C GD 1 g m1 EE105 Fall 2007 Lecture 21 Slide 19 Prof Liu UC Berkeley Source Follower Input Capacitance Recall that the voltage gain of a source follower is Av Follower stage with MOSFET capacitances shown 0 RS 1 RS gm CXY can be decomposed into CX and d CY at the h input i and d output nodes respectively C X 1 Av CGS CGS 1 g m RS CGS Cin CGD 1 g m RS EE105 Fall 2007 Lecture 21 Slide 20 Prof Liu UC Berkeley Example 0 1 Cin CGD1 CGS 1 1 g m1 rO1 rO 2 EE105 Fall 2007 Lecture 21 Slide 21 Prof Liu UC Berkeley Source Follower Output Impedance 0 The output impedance of a source follower f ll can be b obtained by direct AC analysis similarly as for the emitter follower ref Lecture 14 Slide 9 j RG CGS 11 vX iX j CGS g m EE105 Fall 2007 Lecture 21 Slide 22 Prof Liu …
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