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Here is the circuit:

enter image description here

Here is the solution (taken from the book RF microelectronics by Behzad Razavi):

enter image description here

My attempt:

First i tried to find the gain expression for this circuit, i noticed that M2 is in diode configuration so in the small signal model M2 is equivalent to a resistor (= 1/gm2).

I would say everything is ok here as i got the same gain as the solution.

enter image description here

Now for the total noise at the output:

enter image description here

The noise i got at the output by the contribuition of IdM1 is not the same as the solution.

In the solution it's Id^2 * gm2 while i got Id^2 * 1/gm2 . Also in the solution there's a term somewhat related to the Vm1,Rs noise i computed but instead it has a id^2/gm1 factor. I dont know where that came from.

What am i doing wrong here?

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1 Answer 1

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A few things to note that are probably the cause of the mismatch with the solution:

  • Your equations do not seem to include the noise of M2. I bet that this is the term with the \$\cdot g_{m2}\$ that you don't seem to be able to match.
  • The solution avoids dealing with \$r_{ds1}\$ as it is likely negligible compared to \$g_{m2}^{-1}\$ (i.e. \$r_{ds1}//g_{m2}^{-1}\approx g_{m2}^{-1}\$). You probably already saw this however.
  • The first line of the solution does not include the noise term for the resistor \$R_s\$. They probably consider that noise source as part of the input, i.e. for computing the input SNR for the noise figure.

[edit] after seeing your other post, it seems that there is also indeed a mistake in the solution. You can see that it is a mistake because the units of the two terms in the addition don't match.

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  • \$\begingroup\$ About the gm2 term, i made another post about that: electronics.stackexchange.com/questions/639640/… . The noise of M2 i did it (idM2) \$\endgroup\$
    – Scipio
    Commented Oct 23, 2022 at 20:51
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    \$\begingroup\$ Yep that turns out to be a mistake in the solution. \$\endgroup\$
    – Sven B
    Commented Oct 23, 2022 at 21:28

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