A General Design Procedure Inhomogeneous Impedance for Quarter-Wavelength Transformers Having Approximately Equal-Ripple Performance

• Published in: IEEE transactions on microwave theory and techniques Vol. 13; no. 5; pp. 622 - 629
• Main Author: Riblet, H.J.
• Format: Journal Article
• Language: English
• Published: IEEE 01.09.1965
• Subjects: Cutoff frequency; Design for experiments; Difference equations; Frequency locked loops; Impedance; Polynomials; Transformers; Transmission line matrix methods
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.1965.1126056

A general design procedure for quarter-wavelength inhomogeneous impedance transformers having approximately equal-ripple performance is presented, based on the simplifying assumptions that the relative impedance of two waveguides of slightly different widths is a constant and that tan /spl Theta//sub i/= k/sub i/ tan /spl Theta//sub 0/ in the vicinity of /spl Theta//sub i/ and /spl Theta//sub 0/ = 90/spl deg/. The calculation of the design parameters depends on the fact that the insertion-loss function can be expressed, in closed form, in terms of the unknown parameters. When this is identified with the permissible equal-ripple function, a set of simultaneous equations in the unknown parameters results. The solution of these equations is approximated by the solution to the corresponding homogeneous transformer problem. Thus a set of simultaneous linear equations in the small differences can be obtained which provides an approximate solution to the problem. An experimental design is described and the resulting data are presented.