VDD M3 M1 Vbb Vin CL Rb Vo VDD Vo Vb3 Both share the same small signal model. gm2 may include gs2, rds1 may include rp-source Cs2 include all caps at S2

vg1/vin =1/(1+sRsaCgs1) KCL at Vo: KCL at Vs2:

ro  rds1*Av2 || RL Av(0)  - gm1ro p1 = - w-3dB = -1/roCout GBW = gm1/Cout z1 = +gm1/Cgd1 p2  -1/{(rds1|| rincg)Cs2} p3  -1/RsaCgs1

Veff1 + |Veff2| = VDD – OSR For VDD = 5, OSR>=4, Vomin = Veff1 Vomax = VDD – |Veff2| Output swing range: VDD – Veff1 – |Veff2| Veff1 + |Veff2| = VDD – OSR For VDD = 5, OSR>=4,  Veff1 + |Veff2| <= 1 M2 vo 10m CL M1 Vin For transistor in signal path, small Veff -> large gm For current mirror transistors, large Veff -> robust So take: Veff1 ~ 0.3, |Veff2| ~0.7

Positive slew rate SR+ = I2Q/CLtot Negative slew rate SR- = (I1max-I2Q)/CLtot I1max can be very large when Vin is very large. So, SR- is unknown but is not the limit. From SR+, I2Q = SR+ * CLtot To accommodate parasitics: I2Q = SR+ * 1.2CLtot 40*1.2*5=240m Current mirror ratio: 1:24 For M2: ID2 = K’ (W/L) (Veff2)^2 -240 = -20 (W/L) 0.7^2  W/L  24. The diode connection: W/L = 1. For both transistors, use larger L, e.g. L=2Lmin.

GBW = gm1 / CLtot gm1 = GBW * CLtot = GBW * 1.2CL =40*2*10^6*1.2*5*10^-12  0.0015 gm1^2 = K’ (W/L) 4*I1Q = K’ (W/L) 4*I2Q W/L = 0.0015^2/(60e-6*4*240e-6)  39 For input transistor, use L = 1.5*Lmin = 0.9 W=39*0.9  35 Can use W/L = (6m/0.9m) x 6 Check Veff: {240/(60)/(36/0.9)}^0.5=0.1^0.5, OK

So Vin has to be very accurately selected to have the right Q-point. VDD VDD Since the amplifier is supposed to have high gain from Vin to Vo, a small error in Vin can cause large change in Vo, thus pushing Vo to be either very high (M2 in triode) or very low (M1 in triode). So Vin has to be very accurately selected to have the right Q-point. Two ways for this: M2 10 vo CL VoQ – + M1 VinQ

Use a high gain in VCVS, eg, 10^4. VDD VDD You can either do a fine step sweep near the computed VinQ = Veff+Vt, to find the right VinQ that make VoQ near middle of OSR; Or use the VCVS feedback on the previous page to automatically generate VinQ. Use a high gain in VCVS, eg, 10^4. After generation, replace by the connection on this page. M2 vo 10 CL M1 ~ VinQ With this, do DC, AC, and transient analysis.

VDD VDD VDD M2 M2 10 vo- vo+ CL CL M1 M1 VoQ Voc vin+ vin- – + 2*M1