Optimizing Untunable Matching Elements Sizes in the Transmission Lines

A task is set to determine dimensional tolerances of matching elements of a long line to meet requirements for transmission signal mode. The line is characterized by the standing wave ratio (SWR) while the matching element is characterized by the reactive conductivity. In full matching SWR is equal to unit. Changing conductivity of an element leads to SWR change. An approximate relationship between these changes in vicinity of full matching mode is derived. The approximation error is estimated. At the same time, the matching element design and dimensions define its conductivity. Therefore a SWR deviation from the unit can be expressed through the dimensional tolerances. The appropriate calculation is performed for a rectangular waveguide with a diaphragm as a matching element. Symmetric diaphragms of inductive and capacitor types are considered. Such diaphragms contain only one varied size, i.e. window width. Besides, an important condition for matching is the choice of a point where the matching element is installed in the line. Therefore a variation of the diaphragm coordinate in the waveguide also was taken into account. The paper derives a relationship of the SWR deviation from the unit with dimensional tolerance of window and error of coordinate. Relation analysis showed that the limiting values of tolerance and error drastically depend both on the initial value of SWR before matching, and on its final value after the installation of matching diaphragm. Both types of diaphragms are compared with each other. It is found that the inductive diaphragm is characterized by a greater dimensional tolerance of window than the capacitive one. The results of the work can be used in designing the microwave lines with high requirements for matching