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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?

enter image description here

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  • \$\begingroup\$ And the book name is? \$\endgroup\$
    – G36
    Sep 26, 2020 at 5:54
  • \$\begingroup\$ @G36 Problem 9.23 from Fundamentals of Microelectronics (2nd edition) by Behzad Razavi. \$\endgroup\$ Sep 26, 2020 at 17:01
  • \$\begingroup\$ Well but you have a correct equation on page 396 and 397 (eq 9.1 and 9.5) \$\endgroup\$
    – G36
    Sep 26, 2020 at 22:36
  • \$\begingroup\$ @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. \$\endgroup\$ Sep 26, 2020 at 23:31

1 Answer 1

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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.

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