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Prof. D. R. Wilton

ECE 3317. Prof. D. R. Wilton. Notes 19 Waveguiding Structures. [Chapter 5]. Waveguiding Structures. A waveguiding structure is one that carries a signal (or power) from one point to another. There are three common types:. Transmission lines Fiber-optic guides Waveguides.

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Prof. D. R. Wilton

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  1. ECE 3317 Prof. D. R. Wilton Notes 19 Waveguiding Structures [Chapter 5]

  2. Waveguiding Structures A waveguiding structure is one that carries a signal (or power) from one point to another. There are three common types: • Transmission lines • Fiber-optic guides • Waveguides

  3. Transmission lines Properties • Has two conductors running parallel • Can propagate a signal at any frequency (in theory) • Becomes lossy at high frequency • Can handle low or moderate amounts of power • Does not have signal distortion, unless there is loss • May or may not be immune to interference • Does not have Ez or Hz components of the fields (TEMz) (always real:  = 0) Lossless:

  4. Fiber-Optic Guide Properties • Has a single dielectric rod • Can propagate a signal only at high frequencies • Can be made very low loss • Has minimal signal distortion • Very immune to interference • Not suitable for high power • Has both Ez and Hz components of the fields

  5. Fiber-Optic Guide (cont.) Two types of fiber-optic guides: 1) Single-mode fiber Carries a single mode, as with the mode on a waveguide. Requires the fiber diameter to be small relative to a wavelength. 2) Multi-mode fiber Has a fiber diameter that is large relative to a wavelength. It operates on the principle of total internal reflection (critical angle effect).

  6. Multi-Mode Fiber Higher index core region http://en.wikipedia.org/wiki/Optical_fiber

  7. Waveguide Properties • Has a single hollow metal pipe • Can propagate a signal only at high frequency: >c • The width must be at least one-half of a wavelength • Has signal distortion, even in the lossless case • Immune to interference • Can handle large amounts of power • Has low loss (compared with a transmission line) • Has either Ez or Hz component of the fields (TMz orTEz) http://en.wikipedia.org/wiki/Waveguide_(electromagnetism)

  8. Waveguides (cont.) Cutoff frequency property (derived later) In a waveguide: (wavenumber of material inside waveguide) (wavenumber of material at cutoff frequency c ) We can write (propagation) (evanescent decay)

  9. Field Expressions of a Guided Wave Statement: All six field components of a wave guided along the z-axis can be expressed in terms of the two fundamental field components Ez and Hz. "Guided-wave theorem" Assumption: (This is the definition of a guided wave. Note for such fields, ) A proof of the “statement” above is given next.

  10. Field Expressions (cont.) Proof (illustrated for Ey) or Now solve for Hx:

  11. Field Expressions (cont.) Substituting this into the equation for Ey yields the result Next, multiply by

  12. Field Expressions (cont.) This gives us Solving for Ey, we have: The other three components Ex, Hx, Hy may be found similarly.

  13. Field Expressions (cont.) Summary of Fields

  14. Field Expressions (cont.) TMz Fields TEz Fields

  15. TEMz Wave TEMz Assume a TEMz wave: To avoid having a completely zero field, Hence,

  16. TEMz Wave (cont.) z S plane wave E H y H E x coax Examples of TEMz waves: • A wave in a transmission line • A plane wave In each case the fields do not have a z component!        

  17. TEMz Wave (cont.) Wave Impedance Property of TEMz Mode Faraday's Law: Take the x component of both sides: The field varies as Hence, Therefore, we have

  18. TEMz Wave (cont.) Now take the y component of both sides: Hence, Therefore, we have Hence,

  19. TEMz Wave (cont.) Summary: These two equations may be written as a single vector equation: The electric and magnetic fields of a TEMz wave are perpendicular to one another, and their amplitudes are related by . The electric and magnetic fields of a TEMz wave are transverse to z, and their transverse variation as the same as electro- and magneto-static fields, rsp.

  20. TEMz Wave (cont.) z coax S plane wave y H E x microstrip Examples         z y The fields look like a plane wave in the central region. d x

  21. Waveguide y PEC boundary A E C x B waveguide In a waveguide, the fields cannot beTEMz. Proof: Assume a TEMz field (property of flux line) contradiction! (Faraday's law in integral form)

  22. Waveguide (cont.) In a waveguide, there are two types of fields: TMz: Hz = 0, Ez 0 TEz: Ez = 0, Hz 0

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