Lecture 24 ANNOUNCEMENTS The last HW assignment HW 12 will be due 12 6 Prof Liu will be away on Tuesday 12 4 no office hour that day OUTLINE MOSFET Differential Amplifiers Reading Chapter 10 3 10 6 EE105 Fall 2007 Lecture 24 Slide 1 Prof Liu UC Berkeley Common Mode CM Response Similarly to its BJT counterpart a MOSFET differential pair produces zero differential output as VCM changes V X VY VDD EE105 Fall 2007 Lecture 24 Slide 2 I SS RD 2 Prof Liu UC Berkeley Equilibrium Overdrive Voltage The equilibrium overdrive voltage is defined as VGS VTH when M1 and M2 each carry a current of ISS 2 VGS VTH equil EE105 Fall 2007 Lecture 24 Slide 3 I SS W n Cox L Prof Liu UC Berkeley Minimum CM Output Voltage In order to maintain M1 and M2 in saturation the common mode output voltage cannot fall below VCM VTH This value usually limits voltage gain VDD EE105 Fall 2007 Lecture 24 Slide 4 I SS RD VCM VTH 2 Prof Liu UC Berkeley Differential Response EE105 Fall 2007 Lecture 24 Slide 5 Prof Liu UC Berkeley Small Signal Response For small input voltages V and V the gm values are equal so the increase in ID1 and decrease in ID2 are equal in magnitude Thus the voltage at node P is constant and can be considered as AC ground I EE I D1 I 2 I D2 I EE I 2 VP 0 I D1 g m V I D 2 g m V EE105 Fall 2007 Lecture 24 Slide 6 Prof Liu UC Berkeley Small Signal Differential Gain Since the output signal changes by 2gm VRD when the input signal changes by 2 V the small signal voltage gain is gmRD Note that the voltage gain is the same as for a CS stage but that the power dissipation is doubled EE105 Fall 2007 Lecture 24 Slide 7 Prof Liu UC Berkeley Large Signal Analysis I D1 I D 2 EE105 Fall 2007 4 I SS 1 W 2 n Cox Vin1 V in 2 Vin1 Vin 2 W 2 L n Cox L Lecture 24 Slide 8 Prof Liu UC Berkeley Maximum Differential Input Voltage There exists a finite differential input voltage that completely steers the tail current from one transistor to the other This value is known as the maximum differential input voltage Vin1 Vin 2 EE105 Fall 2007 max 2 VGS VTH equil Lecture 24 Slide 9 Prof Liu UC Berkeley MOSFET vs BJT Differential Pairs In a MOSFET differential pair there exists a finite differential input voltage to completely switch the current from one transistor to the other whereas in a BJT differential pair that voltage is infinite MOSFET Differential Pair EE105 Fall 2007 Lecture 24 Slide 10 BJT Differential Pair Prof Liu UC Berkeley Effect of Doubling the Tail Current If ISS is doubled the equilibrium overdrive voltage for each transistor increases by 2 thus Vin max increases by 2as well Moreover the differential output swing will double EE105 Fall 2007 Lecture 24 Slide 11 Prof Liu UC Berkeley Effect of Doubling W L If W L is doubled the equilibrium overdrive voltage is lowered by 2 thus Vin max will be lowered by 2as well The differential output swing will be unchanged EE105 Fall 2007 Lecture 24 Slide 12 Prof Liu UC Berkeley Small Signal Analysis When the input differential signal is small compared to 4ISS nCox W L the output differential current is linearly proportional to it 4 I SS 1 W W I D1 I D 2 n Cox Vin1 Vin 2 n Cox I SS Vin1 Vin 2 W 2 L L n Cox L We can use the small signal model to prove that the change in tail node voltage vP is zero g m1v1 g m 2 v2 0 vin1 vin 2 v1 vP v2 vP EE105 Fall 2007 v1 v2 Lecture 24 Slide 13 Prof Liu UC Berkeley Virtual Ground and Half Circuit Since the voltage at node P does not change for small input signals the half circuit can be used to calculate the voltage gain vP 0 Av g m RD EE105 Fall 2007 Lecture 24 Slide 14 Prof Liu UC Berkeley MOSFET Diff Pair Frequency Response Since the MOSFET differential pair can be analyzed using its half circuit its transfer function I O impedances locations of poles zeros are the same as that of the half circuit s EE105 Fall 2007 Lecture 24 Slide 15 Prof Liu UC Berkeley Example p X 1 RS CGS 1 1 g m1 g m3 CGD1 p Y p out EE105 Fall 2007 1 g m3 C DB1 CSB 3 CGS 3 CGD1 1 g m1 1 RD CGD 3 C DB 3 1 g m3 Lecture 24 Slide 16 Prof Liu UC Berkeley Half Circuit Example 1 0 Half circuit for small signal analysis 1 Av g m1 rO 3 rO1 g m3 EE105 Fall 2007 Lecture 24 Slide 17 Prof Liu UC Berkeley Half Circuit Example 2 0 Half circuit for small signal analysis RDD 2 Av 1 g m RSS 2 EE105 Fall 2007 Lecture 24 Slide 18 Prof Liu UC Berkeley MOSFET Cascode Differential Pair Half circuit for small signal analysis Av g m1rO 3 g m3 rO1 EE105 Fall 2007 Lecture 24 Slide 19 Prof Liu UC Berkeley MOSFET Telescopic Cascode Amplifier Half circuit for small signal analysis Av g m1 g m3 rO 3 rO1 g m5 rO 5 rO 7 EE105 Fall 2007 Lecture 24 Slide 20 Prof Liu UC Berkeley CM to DM Conversion Gain ACM DM If finite tail impedance and asymmetry are both present then the differential output signal will contain a portion of the input common mode signal VCM VGS 2 I D RSS I D I D 2 I D RSS gm VCM 1 2 RSS gm Vout1 I D RD Vout 2 I D RD RD Vout Vout1 Vout 2 I D RD Vout RD 1 g m 2 RSS VCM EE105 Fall 2007 Lecture 24 Slide 21 Prof Liu UC Berkeley MOS Diff Pair with Active Load Similarly to its BJT counterpart a MOSFET differential pair can use an active load to enhance its single ended output EE105 Fall 2007 Lecture 24 Slide 22 Prof Liu UC Berkeley Asymmetric Differential Pair Because of the vast difference in magnitude of the resistances seen at the drains of M1 and M2 the voltage swings at these two nodes are different and therefore node P cannot be viewed as a virtual ground EE105 Fall 2007 Lecture 24 Slide 23 Prof Liu UC Berkeley Thevenin Equivalent of the Input Pair vThev g mN roN vin1 vin 2 RThev 2roN EE105 Fall 2007 Lecture 24 Slide 24 Prof Liu UC Berkeley Simplified Diff Pair w Active Load vout g mN rON rOP vin1 vin 2 EE105 Fall 2007 Lecture 24 Slide 25 Prof Liu UC Berkeley
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