Analysis of Cylindrical Waveguide Structures with Noncircular Cross - - PowerPoint PPT Presentation

▶
analysis of cylindrical waveguide structures with
SMART_READER_LITE
LIVE PREVIEW

Analysis of Cylindrical Waveguide Structures with Noncircular Cross - - PowerPoint PPT Presentation

Jan 10, 2024 695 likes •920 views

Analysis of Cylindrical Waveguide Structures with Noncircular Cross Sections Marcos. V. T. Heckler and Achim Dreher Folie 1 > GeMiC 2008 > Marcos Heckler Dokumentname > Heckler_Dreher_COST_2008.ppt Outline Possible applications of the

slide-1
SLIDE 1

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 1 > GeMiC 2008 > Marcos Heckler

Analysis of Cylindrical Waveguide Structures with Noncircular Cross Sections

  • Marcos. V. T. Heckler and Achim Dreher
slide-2
SLIDE 2

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 2 > GeMiC 2008 > Marcos Heckler

Outline

Possible applications of the present formulation Theory Application 1: dielectric elliptical waveguide Application 2: stripline with elliptical top ground Application 3: conformal microstrip antennas Conclusions

slide-3
SLIDE 3

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 3 > GeMiC 2008 > Marcos Heckler

Introduction

Possible applications Dielectric waveguides with quasi- circular cross sections Transmission lines with quasi- circular cross sections

slide-4
SLIDE 4

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 4 > GeMiC 2008 > Marcos Heckler

Extension of the DMM to 2D Cylindrical Problems with Quasi-Circular Cross Sections

Wave equation within every layer (normalized to k0)

  • ,

,

2 2 2

  • z

k

k

k

  • where

2 2 z r r

k k

k k k

  • z

jk i i e k k z

z k i i k i i k

e k Y B k J A z E

  • )

, ( ) , , (

  • Modal expansions

k

  • r
  • z

jk i i h k k z

z k i i k i i k

e k Y D k J C z H

  • )

, ( ) , , (

  • k

z

E

k

z

H

slide-5
SLIDE 5

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 5 > GeMiC 2008 > Marcos Heckler

Extension of the DMM to 2D Cylindrical Problems with Quasi-Circular Cross Sections

The other field components may be obtained by

  • z

z z r r z z r r z

H E k k k k j H E H E k

2

  • z

jk i i e z

z i i

e k J A z E

  • )

, ( ) , , (

  • Inner layer
  • z

jk i i h z

z i i

e k J C z H

  • )

, ( ) , , (

  • Outer layer
  • z

jk i i e M z

z M i i M

e k H A z E

  • )

, ( ) , , (

) 2 (

  • z

jk i i h M z

z M i i M

e k H C z H

  • )

, ( ) , , (

) 2 (

slide-6
SLIDE 6

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 6 > GeMiC 2008 > Marcos Heckler

Extension of the DMM to 2D Cylindrical Problems with Quasi-Circular Cross Sections

Discretization Ez, H and H are sampled on the e-lines Hz, E and E are sampled on the h-lines Each line system has N lines, which governs the truncation of the infinite expansions:

  • z

jk i i i i e z

z i i

e k J A z E

  • )

, ( ) , , (

  • final

initial

with iinitial = -(N-1)/2 and ifinal = (N-1) /2

slide-7
SLIDE 7

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 7 > GeMiC 2008 > Marcos Heckler

Extension of the DMM to 2D Cylindrical Problems with Quasi-Circular Cross Sections

Matching of the fields in the k-th non-circular interface Using the short notation

  • k

k B k A k zk

B A E L L

  • cos

, sin , ,

k k k

E E Et

  • cos

, sin , ,

k k k

H H Ht

  • k

k D k C k zk

D C H L L where

  • T

i k i k i k k

A A A

final inicial

  • A
  • T

e N z e i z e z z

k k k k

E E E ) , ( ) , ( ) , (

1

  • E
slide-8
SLIDE 8

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 8 > GeMiC 2008 > Marcos Heckler

Extension of the DMM to 2D Cylindrical Problems with Quasi-Circular Cross Sections

Arranging the expressions for Et, Ez and for Ht and Hz, results in

  • k

k k k B k A k D k C k B k A k z t

k k

D C B A E E L L Q Q Q Q

  • k

k k k D k C k B k A k D k C k t z

k k

D C B A H H G G G G L L

k

E

M

k

H

M

slide-9
SLIDE 9

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 9 > GeMiC 2008 > Marcos Heckler

Extension of the DMM to 2D Cylindrical Problems with Quasi-Circular Cross Sections

Adopting the notation

  • k

k

z t k

E E E

  • k

k k k k

D C B A C The elimination of the coefficients results in

  • k

k

t z k

H H H we can write

k E k

k C

! M E

k H k

k C

! M H

  • !
  • k

k E H k k

k k

E E H H

1 1 1

M M

k

Y

  • k

k

E E ~ ~

k-1 k k-2 k+1 k k1 k+1

k

F

1

  • k

F

slide-10
SLIDE 10

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 10 > GeMiC 2008 > Marcos Heckler

Extension of the DMM to 2D Cylindrical Problems with Quasi-Circular Cross Sections

Considering the boundary condition at the interfaces an equivalent circuit can be obtained

  • k

k

E E

k k k

J H H

  • Yk

Yk+1

1 k-

E

1 k-

J

  • 1

k

H

  • 1

k

H

k

E

  • k

H

  • k

H

  • 1

k

H

  • 1

k

H

1

  • k

E

k

J

1

  • k

J

slide-11
SLIDE 11

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 11 > GeMiC 2008 > Marcos Heckler

Extension of the DMM to 2D Cylindrical Problems with Quasi-Circular Cross Sections

Relation between current and electric field in the interfaces where

1 1 , , 1 1 ,

  • k

k k k k k k k k k

E L E L E L J E L J !

  • M

k

J J J J

  • 1
  • M

k

E E E E

  • 1
  • MM

L L L L L L L L L L L L

  • 44

43 34 33 32 23 22 21 12 11

slide-12
SLIDE 12

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 12 > GeMiC 2008 > Marcos Heckler

1st Application – Analysis of Elliptical Dielectric Waveguides

Geometry

2B 2A r = 2.37 air rod

System equation

  • !E

L

air rod

Y Y L

  • det
  • L

For non-trivial solutions where

slide-13
SLIDE 13

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 13 > GeMiC 2008 > Marcos Heckler

1st Application – Analysis of Elliptical Dielectric Waveguides

Modes in elliptical dielectric waveguides

Determinant of the system equation Normalized propagation constant

2B 2A

Modes in ellipical dielectric waveguides with different B/A ratios (B was kept constant)

slide-14
SLIDE 14

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 14 > GeMiC 2008 > Marcos Heckler

1st Application – Analysis of Elliptical Dielectric Waveguides

Numerical results

B/A = 0.5

Variation of the propagation constant with the aspect ratio Variation of the propagation constant with the dimension B

air rod

  • B

VB

slide-15
SLIDE 15

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 15 > GeMiC 2008 > Marcos Heckler

2nd Application – Stripline with elliptical upper GND

Cross-sectional view

2B 2A

Electrical Parameters r = 3.00 t = 0.762 mm f0 = 5 GHz 0 = 10.98 mm W/t = 5.37 1 = 11.75 mm B = 16.23 mm A = 11.94 – 15.28 mm

slide-16
SLIDE 16

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 16 > GeMiC 2008 > Marcos Heckler

2nd Application – Stripline with elliptical upper GND

Convergence of the solution with the discretization refinement

slide-17
SLIDE 17

Dokumentname > Heckler_Dreher_COST_2008.ppt

3rd Application – Conformal Microstrip Antennas

Conformal microstrip patch Use of symmetry H-wall E-wall

slide-18
SLIDE 18

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 18 > GeMiC 2008 > Marcos Heckler

3rd Application – Conformal Microstrip Antennas

Discretization scheme e-lines (sampling of Ez) h-lines (sampling of Hz) Cross section

slide-19
SLIDE 19

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 19 > GeMiC 2008 > Marcos Heckler

3rd Application – Conformal Microstrip Antennas

Complex resonant frequency for different discretization criteria

  • Cyl. radius = 10 mm; t = 0.762 mm; diel. const.= 2.2; L = 35 mm; W = 27 mm
slide-20
SLIDE 20

Dokumentname > Heckler_Dreher_COST_2008.ppt

Folie 20 > GeMiC 2008 > Marcos Heckler

Conclusion

The discrete mode matching method has been applied to the analysis of waveguides with noncircular cross sections One application of this new formulation is the analysis of elliptical dielectric waveguides Striplines with an upper elliptical top ground have been analyzed Validation of the DMM results was done with data found in the literature

  • r predicted by commercial software

Good agreement has been verified