On a transmission line lowpass filter fabricated on a printed circuit board using open-circuited microstrip straight-line stubs, the frequency at the edge of a passband or stopband tends to be higher than the frequency determined by the filter synthesis theory. One of the reasons for this is thought to be the interconnection of a low-impedance straight-line stub and transmission lines. The length of a constituent transmission line cannot be determined precisely because of the finite width. Therefore, as a means of avoiding the frequency shift between a trial circuit and a theoretical one, we first introduce a radial-line stub, and then show the equivalency of a radial-line stub to a straight-line stub in a range of zero to the first resonant frequency from the view point of their input impedances. Dimensional data of radial-line stubs corresponding to low-impedance straight-line stubs are investigated with respect to examples of three-, five- and seven-element Butterworth and Chebyshev filters. It was found that frequency characteristics of trial lowpass filters using radial-line stubs agree well with theoretical characteristics known as the Butterworth or Chebyshev.

This study proposes a 3 dB branch-line coupler using radial stubs to achieve reduced coupler size and simplified stub arrangement. As the electrical lengths of stubs used here are less than 90at center frequency, a method of comparing input impedances to obtain radial stubs that are equivalent to straight stubs is discussed. The frequency characteristics of the proposed coupler are derived by combining classical transmission line theory with the computed data of radial stub input impedances. The methods presented here increase possibilities for realizing reduced branch-line couplers by means of stub design. Experimental results agree well with theoretical results except for slight differences in the high frequency region.