# Question about cascode amplifier problem

The Rout in the circuit below is stated by my textbook to be Rout = [1 + gm2(r01||rπ2)]r02 + r01.

However, I thought the equation for Rout was Rout = [1 + gm2(r01||rπ2)]r02 + (r01||rπ2) for a cascode amplifier.

What happened to the rπ2 in parallel with the r01?

• And the book name is?
– G36
Sep 26, 2020 at 5:54
• @G36 Problem 9.23 from Fundamentals of Microelectronics (2nd edition) by Behzad Razavi. Sep 26, 2020 at 17:01
• Well but you have a correct equation on page 396 and 397 (eq 9.1 and 9.5)
– G36
Sep 26, 2020 at 22:36
• @G36 Yeah that was the one I mentioned in my question. I was just confused because the textbook provided the different equation for the solution to the problem. Sep 26, 2020 at 23:31

Notice that $$\R_{OUT} = g_{m2}r_{o2}(r_{\pi_2}||r_{o1}) + r_{o2} + r_{\pi_2}||r_{o1}\$$

The proof can be found here:

finding the output resistance of bjt folded cascode

Thus, if we collect in terms of $$\r_{o2}\$$ we will end up with this:

$$\R_{OUT} = \left(1 + g_{m2}(r_{\pi_2}||r_{o1})\right)r_{o2} + r_{\pi_2}||r_{o1}\$$

but we can collect in terms of $$\r_{\pi_2}||r_{o1}\$$ therefore:

$$\R_{OUT} = (1 + g_{m2}r_{o2})\cdot r_{\pi_2}||r_{o1} + r_{o2}\$$

Conclusion there is an error in the book equation but numerically not a big error.