Left half and right half plane zeros

In the common-source on the left, one can solve for the transfer function and see that there's a right-half plane zero at $$\s_z = +g_m/C_{gd}\$$. For the source-follower on the right, similarly you can solve for the transfer function and see that this time there's a left-half plane zero at $$\ s_z = -g_m/C_{gs} \$$.

A couple things I'm wondering about:

1. How could one look at these circuits and reason about whether or not there's a zero (without explicitly solving for the transfer function)?
2. How could one reason about whether a zero is in the right-half plane or left-half plane (again intuitively)?
3. At a high level, why do RHP and LHP zeros have opposite phase behavior?

• Answer to a similar question. It probably covers one of the two circuits above.
– AJN
Mar 7, 2021 at 7:10
• You can often infer the presence of a zero if bringing a considered energy-storing element in its high-frequency state (a short for a cap. and an open circuit for an inductor), the stimulus finds its way to the output. In other words, if there is coupling between the input and output because of one element set in HF, then this element brings a zero. You see that if $G_{GS}$ and $G_{DB}$ are replaced by a short, there are no HF gains while if you short $G_{GD}$, then you have gain. FACTs state that a zero generates a null in the response (no current in $R_D$ for $s=s_z$). Mar 7, 2021 at 7:29