Basic question: Dependence of Av on (Vgs-Vt) for an amplifier?

Hello,

Upon reading Willy Sansens excellent book "Analog Design Essentials" I was struck with one thing he mentioned on pg. 14:

"A single transistor amplifier will give a large amount of gain provided its L is large and its Vgs - Vt is small. This will apply
to all applications where high gain, low noise and low offset are most important, such as in operation amplifiers."

My issue is this:

Av = gm * Rout.

- Rout propto L ... Therefore increases in L lead to increases in Rout and hence Av. No problems here.
- However gm propto (Vgs - Vt) ... Therefore, small Vgs-Vt gives small gm and hence small Av.

Am I missing something here? To me it makes intuitive sense that by increasing Vgs or decreasing Vt we make the FET more responsive
i.e. increase its gm, resulting in increases in Av ... not decreases.

I know gm can alternatively be expressed as [2Id / (Vgs-Vt)] which is the same as stating gm propto [(Vgs-Vt)squared/(Vgs-Vt)] or simply propto (Vgs-Vt).

Am I correct in thinking large (Vgs-Vt) gives large Av i.e. large Vov gives large gain? Or have I missed something in the text?

Any feedback most appreciated!

Thanks in advance,

Diarmuid

Hello diarmuid,
Normally in Analog design you start with deciding the current in each branch. hm has 3 equations depending on what parameters are available to tweak:

gm = u Cox W/L (Vgs-Vth) = sqrt(2 u Cox W/L Id) = 2 Id/(Vgs-Vt)

if you use the 1st one and increase your L to get a large rout then increase Vgs-Vt then you would not be totally increasing your gain since Vgs-Vt also increases the current which decreases your rout. Using the second one gives you no idea on the dependance of Vgs-Vt so the 3rd one is the right one to tell you the Vgs-Vt dependance of gm once you have set the Id and the L (i.e. the transistor size). So decreasing Vgs-Vt on the same current increases gm which can be visualized if you have Id vs Vgs graph for different Vds. For a same Ids if you reduce the Vgs you will move towards curve of higher vds which have higher slopes for the same Id and hence more gm.

Excellent answer. Was forgetting to fix Id. Thanks very much ... am all clear now!

gain primarily depends on current flowing in the applied voltage talking that into consideration the answer is solved