Solution to Razavi Book Problem 14.5

Including only the gate-source capacitance of M3, explain under what condition the impedance of the composite load (seen at the drain of M3) becomes inductive.

Find KCL equations:

so the output impedance is:

so the equivalent inductance is:

and the output impedance is always inductive.

A transient simulation is conducted to verify the inductive effect of this load: A input step current is initiated and voltage (Vi) is probed. (a 100fF cap is added to make the inductive effect more prominent)

The driving point (voltage) response is shown below (red curve), the inductive effect can be eminently seen (ringing to step response)

The inductive impedance can be intuitively described (in a hand-waving manner) as follows:

When the voltage of the drain of M3 is moving very slow, the gate voltage of M3 follows suit, and only very a quite amount of current will be following into drain of M3. On the other hand, when the drain of M3 is moving very rapidly, the caps at the gate of M3 actually filters out all the high frequency signals, and the voltage at this node basically stays put, and virtually no current will be flowing into the drain of M3, so that means the higher the frequency, the larger the drain impedance, which means it is inductive.


voltage @ /M3/Gate follows current into /M3/Drain,
Current into C leads voltage @ /M3/Gate ( by 90deg )
Current out /M5/Source follows Current into C
voltage @ /M3/Drain follows current out /M5/Source

In summary, voltage @ /M3/Drain leads current into /M3/Drain by 90deg, which results in inductive impedance.