M2 M1 Vbb Vin CL M4 M3 Vyy Vxx VDD VDD Vo<Vxx+|Vt3| flip up-down

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M2 M1 Vbb Vin CL M4 M3 Vyy Vxx VDD VDD Vo<Vxx+|Vt3| flip up-down for source Rb M2 Vbb CL M1 Vin connecting D1 to S2 cascoding Vo> Vbb-Vt2 ro = rop||ron, Av=-gm1*ro

VDD VDD flip left-right to get this differential telescopic cascoded amplifier M7 M5 Vyy Vxx Vo<Vxx+|Vt3| M8 M6 vo- vo+ CL M3 M4 Vbb CL M1 M2 vin+ vin- Vs Vo> Vbb-Vt2 Tail current to change gnd to virtual gnd

Let vin+ = Vic + ½ vid, vin- = Vic - ½ vid The cross source: Vs = Vic – VGS1Q. Left half circuit same as two slides back, but with vin = ½ vid. So vo- = - gm1ro-(½ vid), where ro- = ro5,7||ro1,3. Similarly, vo+ = - gm1ro+(-½ vid), where ro+ = ro6,8||ro2,4. Hence: vod = gm1rovid Av = vod/vid = gm1ro where ro = ro- = ro+

Slew rate For Vo+: SR+ = I8Q/CL SR- = (I2max-I8Q)/CL But I2max=Itail, I8Q=Itail/2 So, SR+ = SR- =Itail/2CL Similarly for Vo-, SR+ = SR- =Itail/2CL For Vod, SR+ = SR- =Itail/CL

ICMR M3 M4 Vbb What is Vicmax? VD1 = Vbb-Vt3-Veff3 For M1 in saturation, need VD1>VG1Q–Vt1 =Vic–Vt1. So, Vic<Vbb-Vt3-Veff3+Vt1 Vicmax=Vbb-Veff3 What is Vicmin? Vs>Veff9 for M9 in saturation. Vic>Veff9+Veff1+Vt1 Vicmin=Veff9+Veff1+Vt1 M1 M2 vin+ vin- Is M1 M2 vin+ vin- M9

VDD VDD ICMR: Vicmin=Veff5+Veff1+Vt1 Vicmax=VDD-Veff3+Vt1 Total range: VDD-Veff3-Veff1-Veff5 Vyy M3 M4 Vo<VDD-Veff4 vo- vo+ CL CL M1 M2 OSR: Vic-Vt2 to VDD-Veff4 Total range: VDD-Vic-Veff4+Vt2 vin+ vin- Vs M5 Vo>Vic-Vt2

VDD VDD Diode connection to turn diff out to single-ended output  M7 M5 M8 Vo<VG6+|Vt6| M6 vo Same ICMR. But Vo range is different. VG6=VDD-2Vtp-2Veff M3 M4 CL Vbb M1 M2 vin+ vin- Vo>Vbb-Vt2 Same Av, ro

VDD VDD ICMR: Vicmin=Veff5+Veff1+Vt1 Vicmax=VDD-Veff3-Vt3+Vt1 Total range: VDD-Vt3-Veff3-Veff1-Veff5 Vyy M3 M4 Vo<VDD-Veff4 vo- vo+ CL CL M1 M2 OSR: Vic-Vt2 to VDD-Veff4 Total range: VDD-Vic-Veff4+Vt2 vin+ vin- Vs M5 Vo>Vic-Vt2

VDD VDD Vo Vo Folded cascode

VDD Vin CL Vbb flip up-down for I sources VDD M1 Vin CL M2 Vbb connecting n-D to p-S

VDD VDD folded cascode amp Vbb Vin+ Vin- CL

Output swing range and input common mode range are now decoupled. OSR: VDD-4Veff ICMR: 2Veff+Vt1 to VDD-Veff +Vt1 VDD-3Veff But, if Vic cannot exceed VDD, ICMR: 2Veff+Vt1 to VDD VDD-2Veff-Vt1

Miller equivalent circuit I2 =Y(V2-V1) =Y(V2+V2/A) =(1+1/A)YV2  Y2=(1+1/A)Y Y Chapter 4 Figure 15 I1=I=Y(V1-V2) =Y(V1+AV2) =(1+A)YV1 Y1=(1+A)Y

v2 = -Av1 v2 Agm1R2