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?
The book Microelectronic circuits by sedra and smith,7e, OUP gives the equation for output resistance of a BJT cascode amplifier as:
\$R_{out} = r_{02} + (g_{m2} r_{02})(r_{01} || r_{π2}) \$ as the term \$(1+ g_{m2} r_{02}) \$ is nearly equal to \$(g_{m2} r_{02})\$ assuming \$(g_{m2} r_{02}) >>1 \$.
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.
