Module 5 a - Module 5 Lecture 1 Field solutions of uniform...

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page 1 Module 5 Lecture 1 Field solutions of uniform waveguides
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page 2 Contents Waveguide types: TEM and Non-TEM Generalities Examples of TEM waveguides: Coax line Microstrip line Waveguide modes: generic properties Field solutions from Maxwell’s equations TE and TM waves in waveguides
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page 3 Two broad categories of waveguides (1) Waveguides that support TEM waves: Twisted pair, coaxial cable, microstrip (and the idealized case of the infinitely wide parallel conducting planes) Wavelength is proportional to frequency (unique wavelength associated with a source frequency) Phase velocity does not depend strongly on frequency (only through dispersion of material properties) As the name implies, the guided EM fields have no components along the propagation direction. There is no ‘cut - off’: waves can propagate at all frequencies down to DC. All these waveguides have two physically separated conductors
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page 4 Two broad categories of waveguides (2) Waveguides that do not support TEM waves: Hollow metallic waveguides, all-dielectric waveguides Wavelength is not proportional to frequency Several waves with different wavelengths may propagate at a given source frequency. Phase velocity depends strongly on frequency in certain ranges and depends on which one of the allowed waves propagates at a given frequency. The guided EM fields have some components along the propagation direction. There is a cut-off frequency below which a wave cannot be propagated.* *there are 2 exceptions to this rule, for dielectric waveguides that have a certain symmetry)
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page 5 Why can’t these types of waveguides support TEM waves In hollow waveguide or all dielectric waveguides a completely transverse magnetic field must form closed loop in the transverse plane; Since there is no conduction current inside these loops, there must be a displacement current crossing the plane of the loop, i.e. a time-varying E field with an axial component! (see next slide) This is a heuristic argument. The impossibility of TEM waves in such waveguides can be proven rigorously using Maxwell’s equations.
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page 6 Graphical demonstration of the impossibility for TEM waves in hollow or all-dielectric waveguides Cross-section view Side view H field lines By Ampère’s law, some sort of current must flow through the closed H loop. Since there is no conductor there, it must be a dE/dt term.
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page 7 So TEM waveguides are characterized by having two separate conductors This way a current can flow inside the closed H loops in the transverse plane and the E field can also be transverse. However, to remain TEM, the frequency must be such that the wavelength is much larger than the guide dimensions. Otherwise the E field “sees” the charge differences along the axis and acquires a longitudinal component (see next slide).
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page 8 Wavelengths for TEM operation In the bottom case, l is too short for TEM (i.e. f is too high) Waveguide axis
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Module 5 a - Module 5 Lecture 1 Field solutions of uniform...

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