In the circuit, \( I_{DC} \) is an ideal current source. The transistors \( M_1 \) and \( M_2 \) are assumed to be biased in saturation, wherein \( V_{in} \) is the input signal and \( V_{DC} \) is fixed DC voltage. Both transistors have a small signal resistance of \( r_{ds} \) and transconductance of \( g_m \). The small signal output impedance of this circuit is:
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In a cascode amplifier, the small-signal output resistance is significantly increased due to the multiplication effect from the transconductance and output resistance of the upper transistor: \( R_{out} \approx g_m r_{ds}^2 + 2r_{ds} \).
This is a cascode amplifier structure. The small signal output impedance of a cascode circuit can be approximated using the following expression:
\[
R_{out} \approx r_{ds2} + \left(1 + g_{m2}r_{ds2} \right)r_{ds1}
\]
Assuming \( r_{ds1} = r_{ds2} = r_{ds} \) and \( g_{m1} = g_{m2} = g_m \), we substitute:
\[
R_{out} \approx r_{ds} + (1 + g_m r_{ds})r_{ds} = r_{ds} + r_{ds} + g_m r_{ds}^2 = 2r_{ds} + g_m r_{ds}^2
\]
So the total small signal output impedance is:
\[
R_{out} = g_m r_{ds}^2 + 2r_{ds}
\]
