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329lect27 - 27 Guided TEM waves on TL systems x An x...

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27 Guided TEM waves on TL systems An ˆ x polarized plane TEM wave propagating in z direction is depicted in the margin. A pair of conducting plates placed at x = 0 and x = d would not perturb the fields except that charge and current density variations would be induced on plate surfaces at x = 0 and x = d (on both sides) to satisfy Maxwell’s boundary condition equations. z x y E × H E H Unguided uniform plane wave propagation in a homogeneous medium W d z x y Plate 2 Plate 1 E × H E H I I If charge and currents were confined only to interior surfaces of the plates facing one another, fields E and H accompanying them would be restricted to the region in between the plates, constituting what we would call guided waves . Such a guided wave field confined to the region between the plates will sat- isfy Maxwell’s equations including a minor fringing component that can be neglected when the plate width W is much larger than plate separation d . In the following discussion of guided waves in parallel-plate transmission lines (TL) we will assume W d and neglect the e ff ects of fringing fields. Guided waves produce wavelike surface charge and current variations on plate surfaces. Conversely, wavelike charge and current variations on plate surfaces would produce guided wave fields. It is su ffi cient to apply a time-varying current and/or charge density at some location z on a parallel-plate TL — e.g., by a time-varying voltage or current source — in order to “excite” the TL with propagating guided fields. How such excitations propagate away from their “source points” on TL systems will be our main subject of study for the rest of the semester. 1
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In a parallel-plate TL we ignore any fringing fields and assume that TEM wave fields W d z x y Plate 2 Plate 1 E × H E H I I E = ˆ xE x ( z, t ) and H = ˆ yH y ( z, t ) occupy the region between the plates. For these fields uniform in x and y , Faraday’s and Ampere’s laws reduce to scalar expressions ∇ × E = - μ H t E x z = - μ H y t and ∇ × H = σ E + E t - H y z = σ E x + E x t . Now, multiply both equations by d and let Note that voltage drop V = 1 2 E · d l = E x d is uniquely defined — inde- pendent of integration path — on constant z surfaces be- cause with TEM fields B z = μH z = 0 , and consequently circulation C E · d l = - d dt S B · d S = 0 when C is on constant z plane and d S = ± dxdy ˆ z .
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