cascode_biasing.mcd 9/1/2009

High-Swing Cascode Biasing

M4M2

M1

IS

X

B

A

IS

Y

M3

Assume M1, M2, M4 are in saturation, and M3 in triode region.Vds1 is set to slightly above Vov1 by controlling Vds3 (sizing M3).Also assume square-law behavior and ignore CLM effect.

M1 --> Cox (W1/L1), Vov1 = Vgs1 - Vth1M2, M4 --> , Vov2M3 --> n, Vov3

Sizing:

KVL: Vgs2 Vds1 Vgs4 Vds3= Vgs3=

The goal is to establish the gatevoltages of M1 and M2 properly.

Is1

21 Vov1

2=

1

22 Vov2

2=

nVov3 Vds3

1

2Vds3

2

=

If M2 and M4 are matched devices of the same size, Vgs2 = Vgs4, and we have,

Vds1 Vds3=

Also, Vds3 Vgs4 Vgs3= So, Vov3 Vov4 Vth4 Vds3 Vth3= Vov2 Vds1 Vth=

where, Vth is the threshold voltage difference between the cascode (M4) and bottom device (M3)

So,1

n

1

2Vov1 Vds1 Vth

Vds11

2Vds1

2

1

21 Vov1

2=

Let, 1

2

Vth

Vov1= So,

1

n Vov1 Vds1 Vds1

1

2Vds1

2

1

21 Vov1

2=

Solve to obtain Vds1 Vds3= 2

n

Vov1= Vov1=

Conclusion

If Vth

Vov1 is small compared to

1

2, then

1

2n

1

2= is largely determined by sizing only,

i.e., Vds1 will track Vov1.

E.x., for = 1.25 and = 1, we obtain n ~ 4. Usually, n is set by SPICE simulation due to CLM andother second-order effects.

1