Block latency insertion method (Block-LIM) for fast transient simulation of tightly coupled transmission lines

Abstract

This paper describes a block matrix formulation of latency insertion method (LIM) for the fast transient simulation of the circuit which includes the elements such as mutual inductance and mutual capacitance. First, the basic formulation of LIM is shown. Next, the block-LIM formulation for the network with mutual inductance and mutual capacitance is described. Then, the block-LIM algorithm is applied to the tightly coupled transmission lines which are connected each other by a number of mutual inductors and capacitors. Finally, some numerical results are shown and it is confirmed that the proposed technique is useful and efficient for the simulations of the tightly coupled transmission lines.

Locally implicit block leapfrog scheme for PDN simulation

“…Since all of the terms in the right hand sides of the updating formulas (1) and (2) can be given as the ones at the (n+1)-th or the (n+1/2)-th time step, each variable is updated explicitly, in other words, by substituting only the values at the past time steps. For these years, a variety of studies related to LIM have been done and several kinds of skillful techniques, namely, multi-rate LIM [7], cloud and GPU-LIM [11] [12], block-LIM [13], ADE-LIM [14] and parallel-distributed block-LIM [15], have been proposed, which exploit the multi-rate behavior in the time domain, the cloud/GPU computing environment, the characteristics of strongly coupled multi-conductor transmission lines, alternating-direction explicit scheme and the parallelism of the block-LIM, respectively.…”

“…First, the original LIM is described briefly, and the block-LIM, which is regarded as one of the locally implicit methods, is reviewed [13], which is useful for the efficient simulation of tightly coupled multi-conductor transmission lines, in which each segment with mutual couplings is defined as a block circuit and leapfrog method is applied at the block level, where each block is locally solved by using the implicit method. Next, the locally implicit block leapfrog method, which is applicable to the arbitrarily shaped PDN meshed by unstructured triangular cells, is suggested, where the subdomain composed of small values of reactance is defined as a block circuit and the leapfrog method is applied at the block level in which each block is also locally solved by using the implicit method.…”

Transient simulation of multilayered power distribution network based on block-type alternating direction implicit scheme

“…Because the above block-type leapfrog scheme is locally implicit, but globally explicit method, it is restricted by a numerical stability condition [2]. Due to this condition, we have to choose a sufficiently-small time step size to produce numerically stable solutions.…”

“…Although Meanwhile, a block-type leapfrog scheme has been pro posed to perform a fast simulation for coupled network such as multiconductor transmission lines [2]. Although the block type leapfrog scheme is substantially more efficient than conventional SPICE-like simulators, it is conditionally stable and the upper bound of a time step size is strictly limited by a numerical stability condition.…”

Hybrid modeling method for transient simulation of multilayered power/ground planes

“…To overcome this limitation, the Block-LIM algorithm has been proposed [5], [6].In the Block-LIM, a large linear circuit is described by the RLGC-MNA formulation as follows,…”