In today's deep submicron technology the coupling capacitances among individual on-chip RC trees have an essential effect on the signal delay and crosstalk, and the interconnects should be modeled as coupled RC trees. We provide simple explicit formulas for the Elmore delay and higher order voltage moments, and a linear order recursive algorithm for the voltage moment computation for lumped and distributed coupled RC trees. By using the formulas and algorithms, the moment matching method can be efficiently implemented to deal with delay and crosstalk estimation, model order reduction and optimal design of interconnects.

In today's deep submicrometer technology the coupling capacitances among individual on-chip RC trees have an essential effect on the signal delay and crosstalk, and the interconnects should be modeled as coupled RC trees. In this paper we provide simple exact explicit formulas for the Elmore delay and higher order voltage moments and a linear order recursive algorithm for the voltage moment computation for lumped and distributed coupled RC trees. By using the formulas and algorithms, the moment-matching method can be efficiently implemented to deal with delay and crosstalk estimation, model order reduction, and optimal design of interconnects. As an application of the algorithm, we provide a new efficient and accurate model for crosstalk estimation in coupled RC trees. Simulation results show it works better than existing methods.

In this paper, we provide a new passive model order reduction algorithm on interconnects, which is based on the Chebyshev expansion of their impulse response. The Chebyshev coefficient matrices of the impulse response of the reduced order model up to a given order remain the same as those of the original network, so that the time domain transient response of the reduced order model matches that of the original network well. Compared with the model order reduction algorithms based on the frequency domain response, it is more efficient in dealing with complicated transient waveforms of interconnects where strong inductance effects are involved.

With the increase in signal speed and the development of process technology, distributed RC line model is found to be more suitable for on-chip interconnects than lumped RC model, especially for interconnects around and below 0.25 /spl mu/m. In this paper, we first describe a new explicit form for crosstalk approximation for coupled RC lines. Then we introduce a novel passive model order reduction technique for distributed RC lines. These two parts serve as two steps in static noise analysis of full on-chip interconnect networks called pruning process and static analysis process.

A new Chebyshev expansion based model for distributed interconnect networks is presented in this paper. Unlike the moment methods, this new model is optimal and it does not require the knowledge of expansion points. An automatic order selection scheme is also included in the new model. By using the integrated congruence transform, we guarantee the passivity of the new model for distributed interconnect networks. Because of the orthogonality of Chebyshev polynomials, the Modified Gram-Schmidt algorithm can be simplified. In the experimental examples, the new model is found to be accurate and efficient.

In this paper, \ve provide a multipoint moment matching model for mult iport distributed interconnect net~vorks.We introd uce a ne~v concept: integratcd-congruence transform ~vhichcan be apphed to the partial differential equations of a distributed line and generate a passive finite order system as its model.Lloreover, ~vedso provide an efficient algorithm b~sed on the L2 Hilbert space theory so that exact moment matching at multiple points can be obtained.

In this paper, we present new moment models for uniform, nonuniform and coupled transmission lines. The moment model of a line is based on the relationships between the two port currents (KCL) and the two port voltages (KVL) of the line. The parameters of the model depend on the mean values of the voltage moments and the weighted voltage moments of the line. Simple formulas are given to compute these mean values efficiently. By using such models and moment matching techniques, interconnects modeled as transmission line networks can be efficiently simulated. In addition, by using moment sensitivities, we demonstrate that wire sizing optimization can be carried out for layout design.

Moment matching methods are widely used in delay estimation of interconnects modeled as transmission line networks. In this paper, we analyze the contribution of a transmission line to the moments of a resistor-transmission line-capacitor (R-T-C) network and provide a method to form a lumped moment matching model of the line. When the transmission lines are replaced by their pth order moment matching models, the network is transformed into a lumped R-L-C network such that these two networks have identical moments up to the order of p for each corresponding output node voltage. We also provide a recursive formula to compute the moments of the R-L-C network so that the moment matching techniques can be efficiently used in the delay estimation.>

A system of coupled transmission lines with frequency-dependent parameters is decoupled into separate, uncoupled lines by a linear transformation, in which each element, being a function of frequency, is modeled as a transfer function of a lumped circuit. Each decoupled line is modeled by its characteristic 2-port. Lumped models of the characteristic impedance and the propagation function are given. For lines with skin effects, we present a new lumped model of /spl radic/s which is scalable, exact at zero frequency and accurate over a wide frequency range. The model of the entire system of coupled lines can be implemented in SPICE using existing circuit elements.>