Page 152 - Maxwell House

132 Chapter 3

operating ones. It is possible to show that Maxwell’s equations and Poynting’s theorem
forecasts the infinite number of such resonances of different magnitude. The classical circuit
theory generally keeps silence on this subject.

We have shown above that the EM energy is stored in electric and magnetic fields surrounding
the field sources. Suppose, some physical body is located nearby. Since body consists of the
countless number of atoms carrying positively charged nucleus and cloud of negatively charged
electrons, these fields disturb more or less the initial spreading of such charged particles. As a
result, the moving material charges induce some currents inside the body. Consequently, these
currents will cause the secondary EM fields not only inside but also outside the body. As well,
the secondary fields should change the primary source distribution that in turn changes the
secondary fields, and so on. The described effect is called the EM mutual influence or EM
mutual coupling. Poynting’s theorem demonstrates that the EM energy can migrate through the
free space. Therefore, the whole universe is “mutual coupled” not only by the gravitation but
also by electromagnetic forces. In principle, it is impossible to hide from EM radiation. We can
shield devices or whole building and minimize such radiation but cannot escape it entirely. The
anechoic chambers shown in Figure 2.2.13 of Chapter 2 are exemplary.

The power transforms considered in Chapter 2 are exemplary of the “useful” application of
mutual coupling. We can say the same about mutual couplings in electric motors, generators,
microwave directional coupler and many other devices. Unfortunately, the list of “harmful”
mutual coupling is much longer: crosstalk in communication systems, potentially hazardous
voltages induced by overhead power lines, interference between different systems such as
powerful radars and high-speed broadband communication systems, interactions between
elements in highly packed integrated circuits, undesired radiation received from such sources
as doorbell transformer, cars, airplanes, ovens, walkie-talkies, garage-door openers, cordless
phones, electric motors and generators, switched-mode power supplies, lighting, Sun, and so
on and so on. All aspects of such “mutual coupling” or interferences are investigated by the
particular branch of electromagnetic science named ElectroMagnetic Compatibility (EMC). All
developed countries incorporate an extensive list of mandatory EMC standards requiring that
manufactured products must not emit unwanted electromagnetic pollution (interference) and
must be immune to a reasonable level of interference. EMC as a subject is out of reach in our
book, but some additional examples of mutual coupling will be considered later in different
chapters of this book.

3.1.15 Why did We Pay so Much Attention to the Lumped Circuit Elements?

The answer is obvious, due to the beauty, perfection, and maturity of the modern circuit theory.
The approach with interconnected lumped elements allows not only analytical, and relative
simple numerical analysis of millions of active and passive, linear and nonlinear elements
combined into very complex networks, but it is the basis for the circuitry optimization and
synthesis. The latter is the process by which we can find both the topology and numerical values
of all or part of the circuit’s components in a particular device that satisfies the specified design
goals. A straight application of Maxwell’s equations to such problems especially for circuit
synthesis is mostly impracticable because of the extreme complexity of their analytical or