Lucia Cascio, Giampaolo Tardioli and Wolfgang J.R. Hoefer
The increase in clock rate and integration density in modern IC technology leads the designer to deal with problems for which traditional lumped circuit design methodology fails to accurately account for the complex interactions among different parts of the circuit. Traditional CAD tools, such as SPICE, provide very accurate models for a large variety of active devices, but their description of the passive part of the circuit is progressively becoming insufficient as the frequencies of the signals increase. Problems such as dispersion, crosstalk and package effects require a full electromagnetic approach in order to predict their impact on the final response of the circuit. The TLM method is particularly suitable for interfacing lumped circuits to distributed structures: the electromagnetic fields are directly related to the voltages and currents propagating in the TLM transmission lines, and it is straightforward to interpret the connection between the distributed electromagnetic problem and the lumped devices in terms of circuit theory. Moreover, unlike FDTD, the TLM method is very stable at low frequencies, particularly in the presence of one-way absorbing boundary conditions. We have thus developed a technique for introducing lumped elements in a set of TLM-SC nodes. To incorporate the circuit into the TLM mesh, we consider an equivalent region extending over the device volume, and we assume that the behavior of the device depends on the local field in all the cells in that volume. This is particularly important in the case of nonlinear active elements, such as Tunnel diodes, because the connection of the cells in the direction of the feeding voltage would have the effect of a series of diodes, which is DC-unstable. A second advantage is that when modeling nonlinear devices such as pn-junction diodes or bipolar transistors, we will need to solve only a single nonlinear equation at each iteration. To connect the device to the TLM mesh we add n series-connected capacitive stubs in the direction of the feeding voltage. The inclusion of the circuit into the TLM mesh is performed by expressing the equation relating the voltage across the element, v, and the current flowing into it, i, as a function of the voltages traveling in the TLM stubs:
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Further details can be found in: L. Cascio, G. Tardioli and W. J. R. Hoefer, "Modeling of Nonlinear Active and Passive Devices in Three-Dimensional TLM Networks", in IEEE Intl. Microwave Symp. Dig, pp. 383-386, Denver, Colorado, June 8-13, 1997.
