Evaluating RC-interconnect using moment-matching approximations

Coping with RC(L) interconnect design headaches

“…But due to the low pass nature of RC circuits, it can be shown that only a small number of lumped segments are required to accurately model a URC, and there is never a need for more than five lumped segments to model any URC for digital circuit applications [9]. Moreover, as inter-…”

“…One conservative estimate for the number of lumped segments (N) required to model a URC, based on the maximum signal frequency of interest, is obtained by solving: (1) for N [9].…”

“…From distribution theory, the 2nd and 3rd central moments of a distribution function, which represent the variance and skewness respectively, are given by: (9) From Fig.11 it is apparent that three central moments may be required to estimate the delay with less relative error. Using the Elmore delay as a dominant time constant scales the delay approximation by 0.7 and can help the relative errors somewhat, but not sufficiently in all cases, and with some of the estimates becoming optimistic [10].…”

A sequential quadratic programming approach to concurrent gate and wire sizing

“…Modeling the gate by a resistor R d driven by a step voltage source and replacing every interconnect branch with its L-section model -lumping techniques allow for accurate and efficient analysis of complex multilevel interconnect structures [13] -we obtain the RC circuit shown in Figure 1b. The interconnect branches may lie on different layers and, therefore, exhibit different parasitics.…”

“…We can write the objective function in (4) as (12) For clarity, in (12), k i = γ i l i for each wire i and k N+1 = g 1 for the driver. The Hessian and the Jacobian of the objective function of (4) are given by (13) Since all diagonal terms of the matrix H are positive and off-diagonal terms zero, H is always positive definite. The sensitivity of the Elmore delay with respect to the transformation variable, x i , is computed by the chain rule as .…”