Input-referred thermal noise voltage (Razavi exercise)

[emdezla]

Homework Statement

Calculate the input-referred thermal noise voltage of the circuit assuming lambda equal zero.

Relevant Equations

Both the equations and the solutions are attached

So this is a problem from the legendary Razavi book "Design of Analog CMOS Integrated Circuits" (Specifically, it is the problem 7.7 (c)). I got the solutions online but when I try to calculate the noise expression myself, I don't arrive at the same result. Lambda is assumed zero for neglecting Ro of the transistors

I know the circuit voltage gain Av=Vout/Vin has to be computed and I can to do that.
Then I know that every element of the circuit has to be assumed as a source of current noise. I also can do that, and for this case, we have the 4 following current noise:

• Current noise from Rd = 4KT/Rd
• Current noise from M1 = 4KT*(2/3)*gm_1
• Current noise from M2 = 4KT*(2/3)*gm_2
• Current noise from RS = 4KT/Rs

So far so good, but here is where the problem comes: I have to transform current noise into voltage noise by multiplying by a resistance (V^2 = R^2*I^2) And I don't really know what's the correct method or procedure to obtain the suitable resistance expression for the current noise of each circuit component. These are my guesses after doing many exercises so far:

• Resistance for M1 noise: if this transistor is used for amplification then R = Av/gm_1
• Resistance for M2 noise: if this transistor is used as an active load then R = Rout (output resistance of the whole circuit)
• Resistance for Rd noise: no idea, but usually is R = Rd
• Resistance for Rs noise: no idea at all

So yes, that is basically my question: how do we compute the resistance for transforming the current noise of a circuit component to a voltage noise. Thank you very much in advance!

 

[emdezla]

Thank you