1 / 23

Prof. David R. Jackson Dept. of ECE

ECE 5317-6351 Microwave Engineering. Fall 2011. Prof. David R. Jackson Dept. of ECE. Notes 9. Waveguides Part 6: Coaxial Cable. Coaxial Line: TEM Mode. y. T o find the TEM mode fields We need to solve. b. a. z. x. Zero volt potential reference location (  0 = b ). .

idra
Download Presentation

Prof. David R. Jackson Dept. of ECE

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ECE 5317-6351 Microwave Engineering Fall 2011 Prof. David R. Jackson Dept. of ECE Notes 9 Waveguides Part 6: Coaxial Cable

  2. Coaxial Line: TEM Mode y To find the TEM mode fields We need to solve b a z x Zero volt potential reference location (0 = b).

  3. Coaxial Line: TEM Mode (cont.) y Hence b a Thus, z x

  4. Coaxial Line: TEM Mode (cont.) y b a z x Hence Note: This does not account for conductor loss.

  5. Coaxial Line: TEM Mode (cont.) y Attenuation: b a Dielectric attenuation: z x Conductor attenuation: (We remove all loss from the dielectric in Z0lossless.)

  6. Coaxial Line: TEM Mode (cont.) Conductor attenuation: y b a z x

  7. Coaxial Line: TEM Mode (cont.) Conductor attenuation: y b a z x Hence we have or

  8. Coaxial Line: TEM Mode (cont.) y Let’s redo the calculation of conductor attenuation using the Wheeler incremental inductance formula. b Wheeler’s formula: a z x The formula is applied for each conductor and the conductor attenuation from each of the two conductors is then added. In this formula, dl (for a given conductor) is the distance by which the conducting boundary is receded away from the field region.

  9. Coaxial Line: TEM Mode (cont.) y b a z x so Hence or

  10. Coaxial Line: TEM Mode (cont.) y We can also calculate the fundamental per-unit-length parameters of the coaxial line. b a From previous calculations: z x (Formulas from Notes 1) where (Derived as a homework problem)

  11. Coaxial Line: Higher-Order Modes y We look at the higher-order modes of a coaxial line. b The lowest mode is the TE11 mode. a y z x x Sketch of field lines for TE11 mode

  12. Coaxial Line: Higher-Order Modes (cont.) y We look at the higher-order modes of a coaxial line. b TEz: a z x The solution in cylindrical coordinates is: Note: The value n must be an integer to have unique fields.

  13. Plot of Bessel Functions n =0 n =1 n =2 Jn (x) x

  14. Plot of Bessel Functions (cont.) n =0 n =1 n =2 Yn (x) x

  15. Coaxial Line: Higher-Order Modes (cont.) y We choose (somewhat arbitrarily) the cosine function for the angle variation. b Wave traveling in +z direction: a z x The cosine choice corresponds to having the transverse electric field E being an even function of, which is the field that would be excited by a probe located at  = 0.

  16. Coaxial Line: Higher-Order Modes (cont.) y Boundary Conditions: b a z x Note: The prime denotes derivative with respect to the argument. Hence

  17. Coaxial Line: Higher-Order Modes (cont.) y b a In order for this homogenous system of equations for the unknowns A and B to have a non-trivial solution, we require the determinant to be zero. z x Hence

  18. Coaxial Line: Higher-Order Modes (cont.) y b Denote a z x The we have For a given choice of n and a given value of b/a, we can solve the above equation for x to find the zeros.

  19. Coaxial Line: Higher-Order Modes (cont.) A graph of the determinant reveals the zeros of the determinant. Note: These values are not the same as those of the circular waveguide, although the same notation for the zeros is being used. xn3 x xn1 xn2

  20. Coaxial Line: Higher-Order Modes (cont.) Approximate solution: n = 1 Exact solution Fig. 3.16 from the Pozar book.

  21. Coaxial Line: Lossless Case Wavenumber: TE11 mode:

  22. Coaxial Line: Lossless Case (cont.) At the cutoff frequency, the wavelength (in the dielectric) is Compare with the cutoff frequency condition of the TE10 mode of RWG: b so a or

  23. Example Page 129 of the Pozar book: RG 142 coax:

More Related