Y.I. Ismail, E. G. Friedman, J.L. Neves, "Equivalent Elmore delay for RLC trees", IEEE Trans. CAD 19(1) (2000), pp. 83-97.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....For long wire lengths or for narrow lines the line tends to be more resistive (RC dominant) and Bakoglu s model produces matching results with HSPICE. However, when delay is more LC dominated (i.e. large inductance value) this model underestimates delay by more than 10 . Ismail et al. s model [24] matches well with SPICE Typically, the design guidelines will define the amount of overshoot and undershoot allowed in a response. These can be translated into a condition between the first and second moments of the interconnect transfer function, which are in turn functions of driver and ....

Y.I. Ismail, E.G. Friedman, J.L. Neves, "Equivalent Elmore delay for RLC trees," IEEE Transactions on CAD, 19(1), 2000, pp. 83-97.

....by 25 50 75 100 125 150 175 200 225 3.04.05.06.07.08.09.010.0 Interconnect Length (mm) Interconnect Delay (ps) RC Bakoglu RLC Friedman RLC Kahng M uddu HSP CE Figure 1. Comparison of RC RLC delay models LC dominated Case (b 1 2 4b 2 0) more than 10 . Friedman s model [18] matches well with SPICE for LC dominated cases but overestimates delay by up to 30 in RC dominated cases. Finally, the two pole model of Kahng and Muddu [17] described above matches SPICE for both RC and RLC cases within 10 error. Given its very acceptable accuracy, we use the two pole model ....

Y.I. Ismail, E. G. Friedman, J.L. Neves, "Equivalent Elmore delay for RLC trees", IEEE Trans. CAD 19(1) (2000), pp. 83-97.

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Y. I. Ismail, E. G. Friedman, and L. N. Jose, "Equivalent Elmore delay for RLC trees," in Proc. ACM/IEEE Design Automation Conf., June 1999, pp. 715--720.

....The linear analysis method used to evaluate the delays and of the two trees resulting from the saturation and linear region approximations, respectively, is described in this subsection. A second order transfer function that approximates the transfer function at a node of an tree is introduced in [34] and is (7) The variables and that characterize the second order approximation of the transfer function at node are (8) 9) where is the common resistance (inductance) from the input to nodes and . For example, in Fig. 6, and . The summation variable operates over all of the capacitors in the ....

....that the second order approximation exhibits as compared to AS X simulations for the case of a balanced tree. If the tree is unbalanced, the second order approximation is less accurate. The accuracy characteristics of this solution is similar to the Elmore [36] Wyatt [37] delay model for trees [34]. The 50 propagation delay and the 10 90 rise time of the signal at node of an tree are given in closed form in [34] for a step input and are (10) 11) The error in these expressions is less than 3 for balanced trees. The error can exceed 20 for highly unbalanced trees [34] Referring to ....

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Y. I. Ismail, E. G. Friedman, and J. L. Neves, "Equivalent Elmore delay for RLC trees," in Proc. ACM/IEEE Design Automat. Conf., June 1999, pp. 715--720.

....respectively. The square root dependence can be compared to the linear dependence of the delay expressions on the resistance since any RC constant has the dimensions of time, where R is any resistance of the circuit. For example, according to the equivalent Elmore delay for RLC trees introduced in [19], the 50 delay of the signal at node i of an RLC tree is = k ik k k ik k pdi R C e L C t 695 . 0 047 . 1 85 0 , 1) where is the damping factor at node i and is 2 1 = k ik k k ik k i L C R C . 2) The summation variable k operates over all of the ....

Y. I. Ismail, E. G. Friedman, and Jose L. Neves, "Equivalent Elmore Delay for RLC Trees," Proceedings of the ACM/IEEE Design Automation Conference, pp. 715-720, June 1999.

....repeaters are inserted in a tree to decouple capacitance from the critical path. The effect of capacitance decoupling on improving the critical path delay is less significant when inductance effects increase. This trend is due to the LC time constant at node i of a tree, k ik k L C [10], which has a square root behavior as compared to the linear behavior of the RC time constant, k ik k R C . Reducing the capacitance coupling has less effect on the LC time constant as compared to the RC time constant due to this square root behavior. As inductance effects increase, the square ....

....repeater positions is 20 sec on an S 490 IBM machine with one gigabyte of RAM. For typical trees with less than fifty possible repeater positions, the CPU time is below one second. Hence, the second order algorithm is used in the work presented here. Appendix B: Delay Model The method [9] [10] used to evaluate the delays at the sinks of a buffered RLC tree is briefly discussed here. The proposed method approximates the nonlinear transistor characteristics by combining two piecewise linear regions describing the linear and saturation regions of operation [9] Thus, delays are found for ....

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Y. I. Ismail, E. G. Friedman, and Jose L. Neves, "Equivalent Elmore Delay for RLC Trees," Proceedings of the ACM/IEEE Design Automation Conference, pp. 715-720, June 1999.

....used to evaluate the delays t pdsat and t pdlin of the two RLC trees resulting from the saturation and linear region approximations, respectively, is described in this subsection. A second order transfer function that approximates the transfer function at a node i of an RLC tree is introduced in [34] and is 2 2 2 2 ) ni ni i ni s s s g w w z w = 7) The variables z i and w ni that characterize the second order approximation of the transfer function at node i are 2 1 = k ik k k ik k i L C R C z , 8) 1 = k ik k ni L C w , 9) where R ik (L ik ) is the ....

....the second order approximation exhibits as compared to AS X simulations for the case of a balanced tree. If the tree is unbalanced, the second order approximation is less accurate. The accuracy characteristics of this solution is similar to the Elmore [36] Wyatt [37] delay model for RC trees [34]. Fig. 7. AS X simulations of the RLC tree shown in Fig. 6 as compared to the second order approximation and the Wyatt RC model. C 1 R 1 L 1 V in C 3 R 3 L 3 C 2 R 2 L 2 C 5 R 5 L 5 C 4 R 4 L 4 C 7 R 7 L 7 C 6 R 6 L 6 1 2 3 4 5 6 7 time (ns) V 7 (volts) AS X RLC Tree ....

[Article contains additional citation context not shown here]

Y. I. Ismail, E. G. Friedman, and Jose L. Neves, "Equivalent Elmore Delay for RLC Trees," Proceedings of the ACM/IEEE Design Automation Conference, pp. 715-720, June 1999.

....The square root dependence can be compared to the linear dependence of the delay expressions on the resistance since any RC constant has the dimensions of time, where R is any resistance of the circuit. For example, according to the equivalent Elmore delay for RLC trees that was introduced in [19], the 50 delay of the signal at node i of an RLC tree is = k ik k k ik k pdi R C e L C t i 695 . 0 047 . 1 85 . 0 z , 1) where z is the damping factor at node i and is 2 1 = k ik k k ik k i L C R C z . 2) The summation variable k operates over all of the capacitors ....

Y. I. Ismail, E. G. Friedman, and Jose L. Neves, "Equivalent Elmore Delay for RLC Trees," Proceedings of the ACM/IEEE Design Automation Conference, pp. 715-720, June 1999.

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Y.I. Ismail, E. G. Friedman, J.L. Neves, "Equivalent Elmore delay for RLC trees", IEEE Trans. CAD 19(1) (2000), pp. 83-97.

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