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# Circuit Models for Communication Channels

Module by: Don Johnson. E-mail the author

Summary: Maxwell's equations govern th propagation of electromagnetic signals in both wireline and wireless channels.

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## Point of Interest:

You will hear the term tetherless networking applied to completely wireless computer networks.

Maxwell's equations neatly summarize the physics of all electromagnetic phenomena, including circuits, radio, and optic fiber transmission.

curlE=(μH)t E t μ H
(1)
divεE=ρ ε E ρ
(2)
curlH=σE+(εE) t H σ E t ε E
(3)
divH=0 H 0
(4)
where EE is the electric field, HH the magnetic field, εε dielectric permittivity, μμ magnetic permeability, σσ electrical conductivity, and ρρ is the charge density. Kirchoff's Laws represent special cases of these equations for circuits. We are not going to solve Maxwell's equations here; do bear in mind that a fundamental understanding of communications channels ultimately depends on fluency with Maxwell's equations. Perhaps the most important aspect of them is that they are linear with respect to the electrical and magnetic fields. Thus, the fields (and therefore the voltages and currents) resulting from two or more sources will add.

## Point of Interest:

Nonlinear electromagnetic media do exist. The equations as written here are simpler versions that apply to free-space propagation and conduction in metals. Nonlinear media are becoming increasingly important in optic fiber communications, which are also governed by an elaboration of Maxwell's equations.

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