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Design >> RF Design >> RF microelectronics book, equation (2.90)
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Message started by mix on Mar 16^th, 2011, 12:50am

Title: RF microelectronics book, equation (2.90)
Post by mix on Mar 16^th, 2011, 12:50am

Hello everyone,

I would be happy to receive your feedback about my comments on equation (2.90) of this precious book by Razavi. This equation gives the Rout of a feedback amplifier with input match.

I cannot find the same result for the output impedance. Small signal modeling gives me a totally different result, i.e. a very small Rout vs a big one predicted in (2.90).
But before doing the math, intuitive analysis also predicts a small Rout:

1. Shunt-Shunt Feedback:
I see shunt at the output node (i.e. voltage sampling) and shunt at the input (current mixing). Thus the feedback will tend to reduce the input impedance (to make it a more ideal input for current) and it will ALSO tend to REDUCE the output impedance (the ideal voltage output stage has zero Rout).
So, equation 2.89 indeed predicts a small Rin. BUT equation 2.90 predicts a quite BIG Rout, which seems inconsistent to me.

2. M1 is effectively diode connected in AC
M2 is a source follower so practically vg2=vs2. Due to the gain of M2 source follower = 1, the gate and drain of M1 are effectively shorted in AC.
This means that M1 is DIODE CONNECTED in AC. Thus, the Rout should be 1/gm1 (in parallel with the bigger Rd which can be ignored). That's exactly the result I take after doing the math on the small signal model.

Any comment on my thinking is welcome.

Regards

Title: Re: RF microelectronics book, equation (2.90)
Post by aaron_do on Mar 16^th, 2011, 8:00am

Hi,

I've gone over the equation in my head - I don't have a pen and paper with me - and it looks correct. Take note of the sentence "assuming Rin = Rs". Use that to calculate Rin, and Rout, and you will be able to rearrange Rout to get equation 2.9. Also for your intuitive comments, point (1) is correct, but in equation 2.9, (1+gm2Rs) is not the loop gain. Your answer is probably correct, but its just not in the correct form. (1 + gm2Rs) will increase Rout as long as Rs is large and as long as Rin is equal to Rs...

cheers,
Aaron