# Is this small-signal gain correct?

All MOSFETs (not JFETS)

Have I calculated the small-signal gain correctly?

IGNORE body effect etc. but not channel length modulation

I was basically able to get rid of M2 apart from its resistance.

• Quick analysis in my head: if $r_{o1}, r_{o2}, r_{o3}$ are infinitely high impedances I expect the gain to be $-g_{m1} / g_{m3}$. Your formula has an extra "1 +" in the denominator which I do not expect.Since the $r_o$ only make the gain lower I do not expect their values to be present in the numerator. Also: draw the small signal equivalent circuit. – Bimpelrekkie Oct 2 '18 at 11:36

This is common source amplifier for which the gain is given by $$\-g_{1} * Resistance_{seen by the small signal VCCS }\$$
The small signal resistance seen by the small signal VCVS of $$\M_{1}\$$ is $$\r_{o1}||r_{o2}||r_{o3}||\frac{1}{g_{3}}\$$
So the small signal gain of the system is $$\-g_{1}(r_{o1}||r_{o2}||r_{o3}||\frac{1}{g_{3}})\$$
And for sanity check $$\r_{o1}=r_{o2}=r_{o3}=infinity\$$ the gain is equal to $$\\frac{-g_{1}}{g_{3}}\$$