MT24: the 2024 midterm
The Fall 2024 midterm (October 17, 2024; 200 points). Work through it in order: each part gives its question in short and links to the page that solves it. The exam ways of M3, M5 and M6 come with their rebuild in early December.
17 parts: all solved in the guide.
MT24-1
MT24-1a (10 points)
From an inverter’s VTC: the largest DC noise a chain tolerates on a low node and on a high node, with noise on every node.
MT24-1b (10 points)
The same with noise on a single node only.
MT24-1c (10 points)
Make the PFET stronger relative to the NFET: how do the VTC, , , , and the noise margins change?
MT24-1d (10 points)
If the inverter’s peak small-signal gain falls with scaling, what happens to the same quantities?
MT24-2
MT24-2a (10 points)
A chain of N W/W inverters: the energy drawn from the supply per , as a function of N and W.
MT24-2b (10 points)
The subthreshold leakage energy per cycle at 300 K.
MT24-2c (10 points)
With equal to the chain’s delay, the ratio of leakage energy to total energy.
MT24-2d (10 points)
The W that minimizes energy × delay.
MT24-2e (10 points)
The W that minimizes the delay alone (think carefully).
MT24-3
MT24-3a (10 points)
A pass-transistor carry circuit with cross-coupled PFETs: is it static CMOS? Explain.
MT24-3b (15 points)
What logic function does it give at and ?
MT24-3c (10 points)
What do transistors P3 and P4 do?
MT24-3d (10 points)
Draw a complementary static CMOS circuit with the same function.
MT24-4 (15 points)
Draw the schematic of a stick layout and give its logic function.
MT24-5
MT24-5a (15 points)
A dynamic circuit: what functions does it give at Sum and Carry?
MT24-5b (15 points)
The delay of the critical path from A falling to Sum falling, with 500 fF on Sum.
MT24-5c (20 points)
Resize and to minimize that delay; give the new delay.