Supervisor: Dr. Jens Borncmann, Professor ABSTRACT Continued advancement in microwave telecommunications generates an ever increasing need for the further development of computer-aided analysis and design tools. The objective of this thesis is to develop computer-aided design algorithms for the construction of original and innovative components in an all-metal nonstandard rectangular waveguide technology, and to do so employing accurate electromagnetic field analysis. Nevertheless, the principles derived from this relatively narrow field of research are applicable to other waveguide technologies. Through the examination of a variety of ways to accomplish this, a mode- matching method is found best suited to this purpose. A building block approach, involving the separate analysis of smaller discrete discontinuities leading to the cascading and combining of them through the Generalized S-matrix Method, is selected as having the greatest potential for universal application. Two nonstandard discontinuities arc selected for further pursuit: as an example of two-port discontinuities, the T-scptum waveguide; and, as an example of multi-ports, the discontinuity-distorted T-junction. To facilitate the discussion of these nonstandard discontinuities, mode-matching is reviewed by solving a double-plane step and a simple E-plane T-Junction. The first objective, when applying mode-matching to nonstandard rectangular waveguide discontinuities, is to determine the propagation characteristics or eigenmodes of each subregion of the discontinuity. The standing wave formulation in conjunction with a minimum singular value decomposition algorithm is employed to determine the cut-off frequencies of a T-scptum waveguide. The results arc then employed in the application of mode-matching to a rectangular-to-T-scptum waveguide TABLE OF CONTENTS A b s t r a c t ii Ta b l e o f C ontents iv List o f F ig u r es V A CKNO WLEDGMENTS x i D e d ic a tio n xii 1. OVERVIEW I 1.1. Introduction 1 1.2. Waveguide Discontinuities: Modeling and Analysis 4 1.2.1. Theoretical Background 4 1.2.2. Two-Port Junctions with Nonstandard Waveguide Cross-sections 9 1.2.3. Multi-port Junctions with Nonstandard Resonator Regions 11 1.3. Passive Microwave Rectangular Waveguide Components 12 1.3.1. Two-Port Components 1 2 1.3.2. Waveguide Comers and Three-port Components 13 1.4. Methodology and Organization 1 5 2. THE M o d e -M a t c h in g M e th o d 17 2.1. Introduction 17 2.2. Theoretical Background 18 2.3. Two-Port Waveguide Junction: A Double-Plane Step 21 2.4. Three-Port W aveguide J unction : An E-PI ane T-Junction 24 3. T -Se pt u m W a v e g u id e 28 3.1 Introduction 28 3.2 Eigenvalue Problem 28 TABU-: OF CONTFJFrS v 3.3 Rectangular-to-T-Septum Waveguide Discontinuity 40 3.4 Component Design 44 3.4.1. Bandpass Filters 44 3.4.2. Transformers 51 3.4.3. Diplexers 54 4. discontinuitv -D ist o r t e d T -Ju n c tio n s 61 4.1. Introduction 61 4.2. T-junction with Discontinuity-Distorted Resonator Region 65 4.2,1 Theoretical Formulation 6 6 4.3. T-Junction with Stepped Resonator Region 82 4.4. Waveguide Comers 87 4.4.1. 90° Waveguide Comers 89 4.4.2. 180° Waveguide Comers 91 4.5. Component Design 92 4.5.1. Power Divider 93 4.5.2. Orthomode Transducer 97 5. C o n c lu sio n s AND R ecommendations 103 5.1. Conclusions 103 5.2. Recommendations 106 References 108 APPENDIX A : GENERALIZED S-M A T R K M E T H O D 117 A.I. Introduction 117 A.2. Two Two-Ports 117 A 3. Two-Port and Homogeneous Waveguide 118 A.4. Two-Port and Its Inverse Structure 119 A.5. Two-port and Three-port 120 APPENDIX B : E LECTRIC FIELD DISTRIBUTION 122 APPENDIX C: ALTERNATIVE MATRIX INVERSION 125 M LIST OF FIGURES F ig u r e l.l Examples of standard rectangular waveguide discontinuities: (a) asym­ metrical double-plane step waveguide junction (two-port); (b) waveguide comer (two-port); (c) E-plane T-junction (three-port); (d) Magic T (four- port). 8 F ig u r e 1.2 Examples of rectangular waveguides with a nonstandard cross-section: (a) double ridge septum; (b) double T-septum. 9 FIGURE 1.3 Examples of multi-ports junctions with a nonstandard resonator region: (a) stepped mitered waveguide comer; (b) ridged E-planc T-junction. 12 FIGURE 1.4 (a) Evanescent-mode T-septum filter; (b) Stepped T-scptum transformer. 14 F ig ur e 1.5 (a) Integrated T-septum diplexer; (b) Compact power divider; (c) Compact orthomode transducer. 15 F ig u r e 2.1 Double-plane step discontinuity: (a) end view; (b) side view. (cf. Figure 1 .1 for a three-dimensional view). 2 1 F ig u r e 2.2 Simple E-plane T-junction of three rectangular waveguides: (a) end view; (b) side view. (cf. Figure i.l for a three-dimensional view). 24 F ig u r e 3.1 T-septum waveguide cross-section (quarter section); (a) dimensions and subregions for the transverse-resonance method (TRM); (b) dimensions and subregions for the standing wave formulation (SWF). 29 F ig u r e 3.2 Typical behavior of system determinant and minimum singular value versus frequency: (a) transverse resonance method (TRM); (b) standing wave formulation (SWF). Dimensions (mm): a = 22.86, 6 = 11.425, a, = 5.7125, a, =10.2825, =0.8569 and 62 =1.1425 (cf. Figure 3.1). 37 F ig u r e 3.3 Convergence analysis and comparison with [35]: (a) normalized cut-off wavelength of fundamental-mode; (b) normalized cut-off wavelength of first higher mode. Dimensions same as in Figure 3.2. 39 LIST OF F/GURFS vu F ig ur e 3.4 Geometry of a rcctangular-io-T-septum waveguide discontinuity: (a) end view; (b) side view. 40 F ig u r e 3.5 Structure of an evanescent-mode bandpass filter: (a) end view; (b) side view (cf. Figure 1.4(a) for a cut-away view of the filter). 45 F ig u r e 3.6 (a) Calculated transmission and reflection of an X-band three-resonator evanescent-mode T-septum wav guide filter; (b) stopband response. Dimensions (mm); a,-=22.86, =10.16, a = 7.06, 6 = 6.98, a, =1.0, On = 2.556, 6 , = 0.5, 6 , =1-5, 1^=1, = 0.49, 6 =/& =0.51, l^= =1.60 and 4 = 1.20 (cf. Figures 3.1 and 3.5). 47 F igure 3.7 (a) Calculated transmission and reflection of an X-band five-resonator evanescent-mode T-septum waveguide filter; (b) stopband response. Dimensions (mm); =22.86, 6 , =10.16, a = 7.06, 6 = 6.98, a, = 1.0, a, =2.53, 6 ] = 0.49, 6 , =1.49, 4 — Ai = 0.47, 4 - =0-488, 4 = 4 = 7.85, 4=4= 0.983, 4=4= 8.59 and 4 = 0.983 (cf.Figures3.1 and 3.5). 48 FIGURE 3.8 (a) Calculated transmission and reflection of a Ka-band three-resonator evanescent-mode T-septum waveguide filter; (b) stopband response. Dimensions (mm): a,-= 7.112, 6 , =3.161, a = 2.1964, 6 = 2.1716, a, =0.3111, a , =0.7952, 6j =0.1556, 6^ =0.4667, 4 = 4 = 0.1524, 4 = 4 = 0.1587 , 4 = 4 = 2.2644 and 4 = 0.3174 (cf. Figures 3.1 and 3.5). 49 F ig u re 3.9 (a) Comparison between the measured and calculated response of an X- band three-resonator filter prototype; (b) stopband response. Dimensions (mm): a, =22.86, 6 ^ = 10.16, a = 7.0, 6 = 6.95, a, = 0.94, a , = 2.49, 6[ = 0 .3 , 6, =1.32, 4=4 = 0.54, 4 =4 = 0.5, 4 =4 =7.68 and 4 =0.9 (cf. Figures 3.1 and 3.5). 50 F ig u r e 3.10 Photograph of the opened evanescent-mode T-septum waveguide filter prototype with feeding X-band waveguide. 51 FIGURE 3.11 Structure of a T-septum waveguide transformer: (a) end view; (b) side view (cf. Figure 1.4(b) for a cut-away view of the transformer). 52 F ig ur e 3.12 input return loss of an optimized three-section transformer. 53 F ig u r e 3.13 Structure of a T-septum waveguide diplexer: (a) end view; (b) side view (cf. Figure 1.5(a) for a cut-away view of the diplexer). 54 F ig u r e 3.14 (a) Transmission and input reflection behavior of an integrated T-septum X-band waveguide diplexer; (b) stopband response. Dimensions (mm); LIST OF FiGURFJ viti 0 ; = 22.86, a = 1.112, 6 = 3.5. Main waveguide filler: = l.O. Oj = 2.556, 6 ; = 0.5, 6 , = 1.5, /,= /? = 0.905, 6 = /^ = 0.895, Z; = = 7.73 and = 1.17. Branch waveguide filler: «, = 1.0. «2=2.556, 6 , = 0.5, b2=l.5, Z, =Z, =0.3750. L=l(,=2.\l. Z3 = Zj = 7.15 and Z^ = 2.836 (cf. Figures 3.1 and 3.12). 56 F ig u r e 3.15 (a) Transmission and inpul refleclion behavior of an iniegraicd T-sepium Ka-band waveguide diplexer; (b) siopha'nd response. Dimensions (mm): «; = 7.112, « = 2.2126, 6 = 1.089. Main waveguide filler: «,=0.3111. « 2 =0.7952, 6 , =0.1556, 6 2 =0.4667, Z, =Z2 =0.2815, Z2 =Z, =0.2784.