Chapter 3Review of Electromagnetic Field and Circuit Representations

Before analyzing the power distribution networks that connect the power converters to the silicon (and are distributed within the silicon), it is usually a good idea to review the governing field equations and the circuit representations, as are approximated from those fields. All of the passive elements that are used for first principles analyses and SPICE modeling come from these fundamental electromagnetic equations, called Maxwell's equations.

Virtually all of the values in the distribution networks analyses are approximations. However, the approximations are usually sufficient to enable one to gain insight to the problems at hand. It is critical, though, that the warnings presented in Chapter 1 be heeded, since it is too easy to fall into the trap of believing that the approximations yield the exact result or even highly accurate results. Nonetheless, approximations are excellent starting points for bounding difficult problems prior to embarking on a serious numerical study. Thus, a discussion of where these approximations tend to fall short and where they are usually “good enough” for a first pass analysis will be presented here. Other ways in which extractions for passive elements may be obtained are through numerical programs, or field solvers. There are many good extraction tools that exist today, and texts that explain how they work; a few examples are given at the end of the chapter [1, 2]. In most ...

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