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between the ground lines of 156 m demonstrated similar improvement. The results from the 60-m-wide microstrip lines suggest that maintaining a constant line width so that the probe pad structure is indistinguishable from the transmission line, if possible, is best. This allows direct probing of the transmission line without introducing error during the removal of probe-pad parasitics or correction for microstrip-width variations.In either situation, it is then possible to implement the calibration-comparison method by inserting an impedance transformer to map the reference impedance of the measurement into the reference impedance Z 0 of the multiple, redundant line standards and the following the procedure given in [7][8][9]. Investigations continue to determine if following this approach results in a more accurate characteristic impedance determination.The author thanks Dr. Mark Gouker from MIT Lincoln Laboratory for fabricating the transmission-line structures and providing all of the scattering-parameter measurements. More recent works show the importance of achieving ever narrower bandwidths (up to 0.11%) and higher out-of-band rejection required in the wireless communications industry [13][14][15], and even in radio astronomy [16]. An HTS microstrip filter with lumped-element realization has been reported to achieve FBW of 0.014% at a midband frequency of 700 MHz [15]. A previous recent work [17], showed a possible FBW of up to 0.05% achieved at wireless frequencies using a new version of folded spiralmicrostrip geometry, where the current directions in all adjacent sections of a resonator are forced to be opposite to each other so as to minimize parasitic internal couplings and hence reduce the overall coupling coefficient. However, the design of planar ultranarrowband filters with FBW of less than 0.1% generally still face the following constraints: a very weak coupling with a reasonably smaller separation between resonators in order to maintain a small circuit size. The other challenge is to identify and control the required electric and magnetic nonadjacent cross-couplings in or- der to achieve a highly selective elliptic function response with transmission zeros near the passband. Also, it was found that the standard model used for extracting the coupling coefficient between two resonators or two degenerate modes (in dual-mode filters) can not be accurate when the quality factor Q is not too high. Thus, a more accurate model for the coupling coefficient is required to take the circuit losses into account when designing narrowband filters.In this paper, a method for accurate calculation of the coupling coefficient between two degenerate modes (in dual-mode filters) or two resonators in standard filters is presented and compared with the standard model using two example filters with different configurations and coupling types: one is fabricated and tested using a conventional conductor, the other is designed and simulated using a fictitious HTS. The idea for improving the narrowband performance to achiev...

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