Noise interview question

[yolande_yj]

2 NMOS connected as current mirror with 1:5 ratio. 1 being the source side and 5 being the load side.
Question: which one has more contribution to the load and why?

My answer was the 1, or source side NMOS. Any noise will copy 5 times to the load.
The interviewer gave me a hint that the thermal noise is 4KTrGm, ask me if I would like to change my mine.
I said Gm is proportional to sqrt(Ids), so the load side NMOS contributes sqrt(5) of noise, still less than x5 from the source side.


after the interview I think a little more, the thermal noise is proportional to sqrt(Ids*W/L), so does it mean the load side NMOS also contribute sqrt(5*5)=5x noise, same as the source NMOS?
what do you think?

 

[jjx]

I would go with your first answer too. In a current mirror, they have the same effective gate voltage, so (arguably) simpler to use gm = 2 I / Veff. This would be my argument:

A transistor has 4kT r gm of noise current PSD, means from the secondary side you have

Is^2(f) = 4kT r gms = 4kT r (2 * 5 * I / Veff)​

The noise current on the input would be

Ip^2(f) = 4kT r gmp = 4 kT r (2 * I / Veff)​

and on the gates, the noise voltage PSD would be

Vg^2(f) = 4kT r gmp / gmp^2 (assuming gds << gm) = 4kT r / gmp​

Which is transferred to output as per

4kT r / gmp * gms^2 = 4kT r gms^2/gmp = 4kT r gms * (gms/gmp) = Is^2(f) * (2*5*I/Veff) / (2*I/Veff) = 5 Is^2(f)​

However, in this hypothetical question the bandwidth limitation was not mentioned at all. The primary transistor, for example, would potentially see a larger capacitive load than the secondary, etc.

 

[sutapanaki]

On the load side you have five 1x transistors in parallel, each having the same gm as the transistor on the source side. We can consider these 5 parallel transistors as uncorrelated for noise purposes. So, the noise PSD current from them is 5x4kTrgm. The PSD of the source transistor is 4kTrgm and is multiplied by 5^2 contributing to the output noise PSD. So, obviously the source transistor contributes 5x more noise power.