[SOLVED] Gain in a diode connected load for a Common Source configuration

[iVenky]

Hello. I have a doubt in a topic in the CMOS book by Razavi. It's in page 57. Anyway I will tell you the question

Consider the drain of the common source is connected to a diode connected NMOS. It can be seen clearly that

Gain Av= gm1/gm2. (approx) and at the same time Av= (W/L)1 / (W/L)2.

If we write gm in terms of W/L and overdrive voltage, we get Av to be inversely proportional to the overdrive of transistor 2 and directly proportional to the overdrive of transistor 1. But if we find Av , by equating the drain current of both the transistors (which is same by the way) then Av seems to be directly proportional to the overdrive of transistor 2 and inversely proportional to the overdrive of transistor 1. Razavi has left for the reader to find out the reason behind this. I couldn't find out the reason.

Could you please help me with this?

Thanks in advance.

 

[goldsmith]

Hello my friend
How are you?!
Can you attach that page here ? i have not that book . thus perhaps i can help you.
Best Wishes
Goldsmith

 

[iVenky]

It's in page number 57.

 

[goldsmith]

No my mean was not the number of page . my mean was the page. as i said i haven't that book .

 

[iVenky]

Okay. I have attached the pages.


Read from the equation that is at the bottom of the first page. Note that: Gain Av is equal to the ratio of aspect ratios and at the same time it is also equal to the ratio of the transconductances.

Thanks in advance.

 

[ninju]

See page 21 of the same book.

there are multiple formulae for the same 'gm'. In one, overdrive is inversely proportional and in one, its directly proportional. Both are equivalent.

 

[iVenky]

See page 21 of the same book.

there are multiple formulae for the same 'gm'. In one, overdrive is inversely proportional and in one, its directly proportional. Both are equivalent.

I got it. If Vov1 is more than Vov2 then W/L2 should be very much greater than W/L1 (i.e., squared) so that Av becomes lesser and hence it is directly proportional to Vov2 and inversely proportional to Vov1.