Transmission Characteristics of Helix Waveguide
A simple frequency transformation method to obtain propagation constant and mode coupling coefficients of a helix waveguide is introduced. Theoretical TE/sub 01/ mode losses agree well with measured results. Also the transmission characteristics of 5,700 of helix waveguide recently manufactured are described. The inner diameters of them are 51 mm and 60 mm and their unit length is 5 meters.
Normal modes and mode conversion in helix waveguide
Helix waveguide, composed of closely wound insulated copper wire covered with an absorptive or reactive jacket, transmits circular electric waves with low loss. Mechanical imperfections, such as curvature and deformation, cause coupling between the circular electric waves and unwanted modes and degrade the transmission. In designing a helix waveguide for a particular application, a jacket must be found that minimizes the transmission degradation. Unwanted mode characteristics and their coupling coefficients must be known; these quantities are given by the roots of a transcendental equation involving complex Bessel functions. A program has been set up for automatically finding the complex roots by iterative approximation. Starting from the known roots at infinite jacket conductivity, the characteristic equation is solved for all practical values of wall impedance of the jacket and all modes of interest. The representation of the mode characteristics as a function of wall impedance leads to a definite designation of modes in heterogeneous waveguide. The TE pn modes of helix waveguide with n ≠ 1 can have only a limited attenuation. These limits determine the design of mode filters. Manufacturing imperfections increase the average TE 01 loss independently of the wall impedance. Random curvature with large correlation distance is produced by laying tolerances, but its contribution to the average loss is minimized in a helix waveguide with very large wall impedance.
Iustitia Dei: A History of the Christian Doctrine of Justification
Preface Acknowledgements 1. Prolegomena 2. The fountainhead: Augustine of Hippo 3. The development of the doctrine in the medieval period 4. The medieval schools of thought on justification 5. The transition from the medieval to the modern period 6. The development of the doctrine in the Reformation period 7. The Tridentine decree of justification 8. The legacy of the English Reformation 9. The modern period Appendix: a glossary of medieval soteriological terms Abbreviations Notes Bibliography Index.