[Moved]: Book Common source problem

[MahmoudHassan]

Dear All
I am attaching problem from razavi book I thought it should be a simple common source with gain of gm (RD//ro) as the current source connected to the source of MOS is bypassed by a capacitor so it should be shorted in AC analysis. But in solution manual he didn't bypass it !!!!
I don't know why? I think he is wrong but I want to make sure

attached problem and solution


Solution
1

2

3

4


Best Regards

 

[Dominik Przyborowski]

Re: Book Common source problem

Those four pages of hand calculations are made by You or are taken it from "solution book"?

For the first look: 2mW of total power with 1.8V supply gives ≈1mA of drain current. With reasonable DC op point of amplifier (Vout_dc=Vdd/2) it gives 900Ω for Rd. To achieve gain of 6V/V in interest band, transconductance of mosfet should be equal to 6.667 mS. For Id=1mA it results with gm/Id=6.667 and ideally fit to Vod=200mV.

One important remark here to the page 2 of solution: there is an equation that gm should be equal 100mS. In room temperature and any CMOS/FDSOI technology, it is impossible to achieve higher transconductance than 38×Id. Maybe with some very experimental technologies, uses quantum effects and providing devices with SS«60mV/dec it could be possible to get higher value but not in conventional ones.

 

[sarge]

Re: Book Common source problem

Hello,

This solution looks strange for me:

1. C1 - even if we calculate F3dB frequency of such high pass filter we comes to ~8pF
2. How was value of Vd achieved? I don't get this Vds = (Vd-Vth)+0.2 and that's why Vd is 1.6, in my opinion Vd = Vg - Vth + 0.2, but we don't know value of Vth.
3. Tricky things with setting of Rs

 

[MahmoudHassan]

Re: Book Common source problem

Thanks a lot for your reply
The four pages are from the solution manual.
I was asking about the gain he used as (RD/ (1/gm + RS)) I think RS shouldn't appear in gain because it's shorted already in AC using this capacitor CB
Why it is impossible to achieve higher transconductance than 38×Id at room temp ?

 

[Dominik Przyborowski]

Re: Book Common source problem

Why it is impossible to achieve higher transconductance than 38×Id at room temp ?

Physics ;-)
I forgot all solid-state theory so I can give You an engineering answer.
From all types of transistors, the higher gm/Id ratio You can obtain for bipolar ones which is constant and equal to 1/nVt, where n is slope factor and Vt=kT/q is a thermal voltage. In mosfets, gm/Id=1/nVt is an asymptotic value for transistors working in weak inversion (Vgs«Vth; Id«Ispec, whatever) if we avoid any leakage.
For very ideal case with n=1, inverse of Vt in room temperature is equal to 1/25.7m = 38.91. For silicon BJT, n=1.2 so gm≈32.5×Ic.

BTW Look on the numbers from above solution. W/L=363; K=200µA/V²; Vod=1.8-0.022-0.4=1.3778V.
Has it any sense by putting it into a square law drain current which results for those numbers of 68.9mA and compare it to previously calculated 1.11mA?