1. Prof. David R. Jackson Notes 19 Waveguiding Structures Waveguiding Structures ECE 3317 1 Spring 2013

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 2

3. Transmission lines Lossless:  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 E z or H z components of the fields (TEM z ) Properties (always real:  = 0 ) 3

4. Fiber-Optic Guide Properties  Has a single dielectric rod  Can propagate a signal at any frequency (in theory)  Can be made very low loss  Has minimal signal distortion  Very immune to interference  Not suitable for high power  Has both E z and H z components of the fields (“hybrid mode”) 4

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

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

7. 7 Multi-Mode Fiber (cont.) At left end of rod: Assume cladding is air

8. 8 Multi-Mode Fiber (cont.) At top boundary with air:

9. Waveguide  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 E z or H z component of the fields (TM z or TE z ) Properties http://en.wikipedia.org/wiki/Waveguide_(electromagnetism) 9 Inside microwave oven

10. Waveguides (cont.) Cutoff frequency property (derived later) (wavenumber of material inside waveguide) (definition of cutoff frequency) (propagation) (evanescent decay) In a waveguide: We can write 10

11. Field Expressions of a Guided Wave All six field components of a guided wave can be expressed in terms of the two fundamental field components E z and H z. Assumption: (This is the definition of a guided wave.) A proof of this statement is given next. Statement: "Guided-wave theorem" 11

12. Field Expressions (cont.) Proof (illustrated for E y ) or Now solve for H x : 12

13. Field Expressions (cont.) Substituting this into the equation for E y yields the result Next, multiply by 13

14. Field Expressions (cont.) Solving for E y, we have: This gives us The other three components E x, H x, H y may be found similarly. 14 or

15. Field Expressions (cont.) Summary of Fields 15

16. TEM z Wave To avoid having a completely zero field, Assume a TEM z wave: TEM z Hence, 16

17. TEM z Wave (cont.) Examples of TEM z waves: In each case the fields do not have a z component!  A wave in a transmission line (no conductor loss)  A plane wave E H         Coax x y z E H S Plane wave 17

18. TEM z Wave (cont.) Wave Impedance Property of TEM z Mode Faraday's Law: Take the x component of both sides: The field varies as Hence, Therefore, we have 18

19. TEM z Wave (cont.) Now take the y component of both sides: Hence, Therefore, we have Hence, 19

20. TEM z Wave (cont.) These two equations may be written as a single vector equation: The electric and magnetic fields of a TEM z wave are perpendicular to each other, and the amplitudes of them are related by . Summary: 20

21. TEM z Wave (cont.) Examples E H         Coax x y z E H S Plane wave Microstrip The fields look like a plane wave in the central region. E H 21 “Quasi-TEM” (TEM-like at low frequency)

22. Waveguide In a waveguide, the fields cannot be TEM z. (property of flux line) (Faraday's law in integral form) contradiction! 22 Proof: Assume a TEM z field y x waveguide E PEC boundary A B C

23. Waveguide (cont.) In a waveguide (hollow pipe of metal), there are two types of fields: TM z : H z = 0, E z  0 TE z : E z = 0, H z  0 23