Due Fri, Feb 2 at the start of class.

Use single-sided pages only. You will be asked to re-draw/write if you use the back side of your paper sheets. We can discuss financial assistance for paper if necessary :).

1. Schematics for 3NAND gate

Start with the book’s example of a 3-input NAND gate in Figure 4.6 and Example 4.2 (p. 147-148).

Re-do that example for a 3-input NOR gate. Remember, the transistor widths are scaled by the factor written next to the channel in order to keep the same (DC) equivalent resistance of the ON paths the same. Use the same _prototype inverter_sizing as the example which uses a 1-unit width nMOS and a 2-unit width pMOS (implying a μn/μp electron / hole mobility ratio of about 2).

  • Draw three 5 schematics in the same progression as Figure 4.6 a—​e. Either draw this series of schematics on at least 2 pages or provide a magnifying glass.

  • Why does Figure 4.7 (b) include only a 3C value capacitor at each of the two internal nMOS S-D nodes instead of 6C capacitors to account for the fact that there are two sources/drains connected?

2. RC network responses

vlsi rc delays
Figure 1. RC networks

2.1. Calculations

  • Find the propagation delay \(t_{pdr}\) (in ECE 340 this was named \(t_{pLH}\)) of Figure 1, “RC networks” (a) using the circuit equations.

  • Find the propagation delay \(t_{pdr}\) of Figure 1, “RC networks” (b) by using a similar technique as book section 4.3.4 and equation (4.13) to approximate as a single time constant system. This is the Elmore delay. There will still be a \((\ln 2)\) factor in your math, we are not dropping it yet like the book’s equation (4.9).

2.2. Simulations

Simulate the transient response of the two networks of Figure 1, “RC networks” using LTspice. Be sure the input waveform’s rise time is less than 1/10th of the output’s rise time.

  • Find the propagation delay \(t_{pdr}\) of Figure 1, “RC networks” (a). This should be exactly the same as your calculated value.

  • Find the propagation delay \(t_{pdr}\) of Figure 1, “RC networks” (b). Compare this to your Elmore-estimated value. Do you think it will always be an over/under estimate?