Statistical Electromagnetics

Richard Holland

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000158670
• Edition: 1
• Topic: Ciencias físicas
• Subtopic: Electromagnetismo

This book addresses the problem of treating interior responses of complex electronic enclosures or systems, and presents a probabilistic approach. Relationships for determining the statistics of the driving fields to apply to a circuit analysis code representing part of an enclosed system's writing are worked out. Also addressed are limited spatial and frequency coherence essential to a statistically based field drive model. This text gives examples, different modeling, and describes how to make, interchange, and optimize models.

PART I. THE DEVELOPMENT AND USE OF
STATISTICAL ELECTROMAGNETICS
(STEM)

CHAPTER 1. INTRODUCTION

This book is intended to serve as a monograph in the relatively new and underdocumented field that we call STatistical ElectroMagnetics (STEM). Our subject matter is the probabilistic approach to the response of cables and other conductors inside a complex, enclosed system. Although we shall not always explicitly so state, the STEM acronym in this book carries the implication that the enclosure or problem dimensions are large compared to a wavelength, and that continuous wave (cw) conditions apply. Thus, we presume so many modes are excited in the enclosure that they may be treated statistically, in a thermodynamic-like way, as opposed to mode by mode.

The type of question we ultimately desire to show the reader how to answer is this: for a given threatening or otherwise disturbed ElectroMagnetic (EM) environment, what is the probability that a particular interior wire, pin, or Integrated Circuit (IC) metallization will not carry a current i greater than some acceptable value?

1.1 HISTORICAL BACKGROUND AND RELATION TO OTHER FIELDS OF STUDY

Two of the underlying goals in this work are to consider the shape and frequency separation of the resonances of the enclosure, and to evaluate how energy is statistically distributed among these resonances. Acousticians and mechanical engineers have developed this procedure into a sophisticated protocol, which they refer to as Statistical Energy Analysis (SEA) [1]. However, their task is almost the negative image of ours: it usually develops that most mechanical energy is stored in walls, braces, plates, and other fixed or flexible objects, while EM energy primarily resides in rooms, enclosure interiors, or other three-dimensional voids. Thus, while the concepts of SEA are quite similar to those of STEM, the actual numerics are very different. For example, mechanical oscillators may have just a single resonance, and rods or braces may have just a singly sequenced family of resonances (like a violin string). On the other hand, enclosure volumes almost universally imply a triply infinite number of resonances. Also, the resonant motions of mechanical systems can frequently be explicitly described. We, on the other hand, essentially deal with blackbody (Bose-Einstein) statistics [2], where little may be known about the resonances except their separation as a function of frequency. (The preceding synopsis of acusto-mechanical SEA is not intended to imply that no multidimensional finite-difference/finite-element SEA-related literature exists [3].)

This book documents studies, by us and others, to understand and model statistically the EM field and cable response of an enclosed asset and its wiring during High-Power Microwave (HPM)¹ attack or in the presence of other threatening Radio Frequency (RF) leakage and penetration. Much of this rather meager existent literature has not been readily accessible to the community. For instance, the more generic and exploratory work on the statistics of such EM response has only been informally described ([4] and [5]).

The problem of predicting cable or pin currents in an enclosed system under HPM illumination or RF Interference (RFI) at a frequency where the asset is many (>6) wavelengths on a side (i.e., well overmoded) is all but impossible to treat deterministically. Moreover, even assuming a supercomputer and state-of-the-art Finite-Difference Time-Domain (FDTD) [6,7] or Finite-Volume Time-Domain (FVTD) [8,9] code were available, one could logically claim a deterministic solution would be of no value. This claim could be made because, in such a scenario, a 1° rotation of the asset or a 1% shift in frequency would commonly alter the excitation on any given pin or circuit device by as much as 20 dB.

Additionally, the interior of a satellite, aircraft, or missile has wiring of almost inconceivable complexity as viewed by an FVTD or FDTD practitioner who is used to zero or one (two if he is really heroic) conductors passing through each FVTD or FDTD cell [6,10].

To solve this sort of problem rigorously and deterministically, one not only needs to track the fields in 10⁶ to 10⁹ FVTD or FDTD cells, but also to model the drive these fields impose on each conductor (or even each IC) passing through or located in each cell. The final twist to the complexity is that each of these conductor ...