formula in small signal analysis

[Yuya_O]

I’m studying analog circuit design and reading Design of Analog CMOS Integrated Circuit written by Behzad Razavi. I found a formula that
δVth/δVin = η(δVout/δVin). It doesn’t make sense. Someone could you explain it to me ?

 

[FvM]

The formula is meaningless if you don't tell us which transistor circuit it describes, To ask a usefull question, please tell in which chapter you are seeing the formula.

 

[Yuya_O]

Thanks for your reply. I'm seeing the formula at chapter 3.2.2. . It is just after formula (3.31) if my Japanese textbook is same with yours.

 

[FvM]

o.k. it's on p.54 in the first edition (international 2001 edition).
Do you understand that they are analyzing nonlinearity of the a diode connected load circuit caused by variation of gm/gmb (vaiation of bulk effect)? At first sight it makes sense for me.

 

[Yuya_O]

You are talking about gain Av right ? I understood about it.

 

[JackLin063]

You can find a diode connected NMOS (M2) and a common source NMOS (M1) in your textbook.

The source of M2 is connected to Vout, so there is body effect in the M2 device. In this configuration, Vin will affect both Vout and Vth2, and the Body effect is related to the value of VSB, so it can be said that Vth2 and Vin are dependent.

This formula "δVth/δVin = η(δVout/δVin)" tells us that if the body effect is ignored, the gain of this configuration is δVout/δVin=sqrt(W1/L1)/sqrt(W2/L2); if the body effect is considered, the gain of this configuration is δVout/δVin=(sqrt(W1/L1)/sqrt(W2/L2)) * ((1/(1+η)), the gain will be decreased.