Analysis of ring filter and its cascade synthesis method

Abstract

A ring resonator filter with a stub (ring filter) has a band-stop filter characteristic. The attenuation frequencies are at two symmetric locations with respect to the center frequency of the passband. If the range between these two attenuation frequencies is considered as the passband, the loss is low and the group delay is constant in the passband region. In the present paper, the condition of the ripple generation in the passband is derived for the ring filter. Further, the ripple frequencies under the ripple generation conditions are numerically obtained and compared with the measured results. Next, the passband group delay is analytically derived and compared with the measured value. Further, a method of cascading the ring filters is studied. It is found that the transfer function of the cascaded ring filter is expressed in terms of a rational function of the Richard variable . It is shown that a set of the characteristic impedances realizing the desired rational function can be inversely calculated. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 90(3): 9–16, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20298