UNIVERSITY OF CALIFORNIA



UNIVERSITY OF CALIFORNIA

College of Engineering

Department of Electrical Engineering and Computer Sciences

Last modified on February15, 2002 by Josie Ammer (mjammer@eecs.berkeley.edu)

Jan M. Rabaey, Andrei Vlademirescu Homework #5 EECS 141

Due Friday 03/1/02 5pm, in 558 Cory

Problem #1

Calculate the Elmore delay from node A to node B using the values for the resistors and capacitors given in the table below.

[pic]

|Resistor |Value (Ohms) |Capacitor |Value (fF) |

|R1 |0.25 |C1 |250 |

|R2 |0.25 |C2 |750 |

|R3 |0.50 |C3 |250 |

|R4 |100 |C4 |250 |

|R5 |0.25 |C5 |1000 |

|R6 |1.00 |C6 |250 |

|R7 |0.75 |C7 |500 |

|R8 |1000 |C8 |250 |

Problem #2

a. Compute the 0%-50% delay of a 500um x 0.5um wire with resistance of 0.08 Ohms/sq, with area capacitance of 30aF/um2, and fringe capacitance of 40aF/um. Assume the driver has a source resistance of 100 ohms and negligible output capacitance.

i. Using a lumped model for the wire.

ii. Using a PI model for the wire, and the Elmore equations to find tau. (see Chapter 4, figure 4.26).

iii. Using the distributed RC line equations from Chapter 4, section 4.4.4.

b. Compare your results in part a. using spice (be sure to include the source resistance). For each simulation, measure the 0%-50% time for the output

i. First, simulate a step input to a lumped R-C circuit.

ii. Next, simulate a step input to your wire as a PI model.

iii. Unfortunately, our version of spice does not support the distributed RC model as described in the book (Chapter 4, section 4.5.1). Instead, simulate a step input to your wire using a PI3 distributed RC model.

Problem #3

A standard CMOS inverter drives an aluminum wire on the first metal layer. Assume Rn=4Kohms, Rp=6Kohms. Also, assume that the output capacitance of the unloaded gate is negligible compared to the wire we are driving. The wire is .5um wide, and the resistivity is 0.08 Ohms/sq.

a. What is the "critical length" of the wire (see Chapter4)?

b. What is the equivalent capacitance of a wire of this length? (For your capacitance calculations, use Chapter 4 Table 4.2, assume field underneath, nothing above, and nothing on either side of the wire.)

Problem #4

A two-stage buffer is used to drive a metal wire of 1 cm. The first inverter is a minimum size with an input capacitance Ci=10 fF and a propagation delay tp=150 ps when loaded with an identical gate, and assume gamma =1. The width of the metal wire is 2.5 (m. The sheet resistance of the metal is 0.08 (/(, the capacitance value is 0.03 fF/(m2 and the fringing field capacitance is 0.04 fF/(m.

a. What is the propagation delay of the metal wire?

b. Compute the optimal size of the second inverter. What is the minimum delay through the buffer (i.e. the sum of the delays through both inverters)?

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