1. For a differential amplifer: vin+=vic+vid/2, vin-=vic-vid/2
As vid change, Vs=const
Vs is virtual ground.
left half = -(right half)
Can use half circuit: M2
vin- CL M8 M1
vin+ M7
Vyy
vo+
vo- Vs
VDD
VDD
VDD
Vyy M7
R,C
vo+
vo+ CL CL M1 M1
Can further use quarter circuit for analysis with suitable parasitic R, C:

2. VDD
VDD
Telescopic
cascode
amplifier
Quarter circuit: M7 M5
Vyy
Vxx M8 M6
VDD M3 M1
Vbb
Vin CL Rb Vo
vo-
vo+ CL M3 M4
Vbb CL M1 M2
vin+
vin- Vs

3. VDD
VDD
VDD Vo
Vb3
folded cascode amp
Vb2
Vb2
Vb3
Vin+
Vin- CL
Vb4
Vb1
Vb5
Quarter circuit

4. Both have the same small signal model
VDD M3 M1
Vbb
Vin CL Rb Vo
VDD Vo
Vb3
Both have the same small signal model

5. a a >1 First take Rs = 0, find TF from vg1 to vo
then from TF from vin to vg1,
Finally, multiply the two together.
Include gs2
Include Cgs2,
Cdb1, Csb2
Include ro of I-source if folded a
a >1
vg1/vin =1/(1+sRsaCgs1)

6. To find TF from vg1 to vo:
Write KCL at vs,
KCL at vo,
Two equations, eliminate vs, and solve for vo in terms of vg1
 vo/vg1

7. 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

8. Design steps:
SR, CL  IQ
OSR  Veff ranges
Ibias or Iref  size current source
GBW, CL  gm
IQ, gm  (W/L)1, round to nice numbers
Feedback to generate VinQ
Check Veff, if too large, increase W1, (this leads to over design of gm and GBW)
Check Av or ro, if not sufficient, use larger L, and adjust W accordingly to keep the same W/L
For cascode structures, modify the steps a little.