MT21: the 2021 midterm

The Fall 2021 midterm (October 21, 2021; 150 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 MT21-5 come with their rebuild in early December.

10 parts: all solved in the guide.

MT21-1

MT21-1a (10 points)

An NFET pass-transistor multiplexer: what constraint on $S_1$–$S_4$ makes it a static CMOS circuit?

Full solution

MT21-1b (10 points)

What output high level does it reach, relative to $V_{DD}$VDD​? Explain.

Full solution

MT21-1c (10 points)

Draw a complementary static CMOS circuit with the same function.

Full solution

MT21-2 (25 points)

The FO4 delay in terms of $\tau_{tr}$ and $\eta = C_g/C_d$Cg​/Cd​, with the PFET exactly as strong as the NFET.

Full solution

MT21-3 (25 points)

The six-transistor XOR is not static CMOS: how could it be sized so that it gives a wrong result?

Full solution

MT21-4

MT21-4a (10 points)

Four inverters sized $n$ µm/1 µm (2/1 gives equal edges): the delay from A to B for $n = 2$2.

Full solution

MT21-4b (10 points)

The dynamic energy of one transition for $n = 2$2.

Full solution

MT21-4c (15 points)

The $n$ that minimizes the delay, and why it is below 2; the answer with equal-strength devices.

Full solution

MT21-5

MT21-5a (15 points)

With $C_B = 0$ and each input limited to 1 fF, size the path for minimum delay.

Full solution

MT21-5b (20 points)

With a 500 fF branch $C_B$CB​, find a sizing close to the minimum delay.

Full solution