# chapter4_ex - 1 Chapter 4 Problem Set Chapter 4 Problems 1....

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1 Chapter 4 Problem Set Chapter 4 Problems 1. [M, None, 4.x] Figure 0.1 shows a clock-distribution network. Each segment of the clock net- work (between the nodes) is 5 mm long, 3 µ m wide, and is implemented in polysilicon. At each of the terminal nodes (such as R ) resides a load capacitance of 100 fF. a. Determine the average current of the clock driver, given a voltage swing on the clock lines of 5 V and a maximum delay of 5 nsec between clock source and destination node R . For this part, you may ignore the resistance and inductance of the network b. Unfortunately the resistance of the polysilicon cannot be ignored. Assume that each straight segment of the network can be modeled as a Π -network. Draw the equivalent cir- cuit and annotate the values of resistors and capacitors. c. Determine the dominant time-constant of the clock response at node R . 2. [C, SPICE, 4.x] You are designing a clock distribution network in which it is critical to mini- mize skew between local clocks ( CLK 1, CLK 2, and CLK 3). You have extracted the RC net- work of Figure 0.2, which models the routing parasitics of your clock line. Initially, you notice that the path to CLK 3 is shorter than to CLK 1 or CLK 2. In order to compensate for this imbalance, you insert a transmission gate in the path of CLK 3 to eliminate the skew. a. Write expressions for the time-constants associated with nodes CLK 1, CLK 2 and CLK 3. Assume the transmission gate can be modeled as a resistance R 3 . b. If R 1 = R 2 = R 4 = R 5 = R and C 1 = C 2 = C 3 = C 4 = C 5 = C , what value of R 3 is required to balance the delays to CLK 1, CLK 2, and CLK 3? c. For R = 750 and C = 200fF, what ( W / L )’s are required in the transmission gate to elimi- nate skew? Determine the value of the propagation delay. d. Simulate the network using SPICE, and compare the obtained results with the manually obtained numbers. 3. [M, None, 4.x]Consider a CMOS inverter followed by a wire of length L . Assume that in the reference design, inverter and wire contribute equally to the total propagation delay t pref . You may assume that the transistors are velocity-saturated. The wire is scaled in line with the ideal wire scaling model . Assume initially that the wire is a local wire . a. Determine the new (total) propagation delay as a a function of t p ref , assuming that technol- ogy and supply voltage scale with a factor 2. Consider only first-order effects. b. Perform the same analysis, assuming now that the wire scales a global wire , and the wire length scales inversely proportional to the technology.

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## chapter4_ex - 1 Chapter 4 Problem Set Chapter 4 Problems 1....

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