Influence of coupling coefficient on transmission and reflection zeros of open-ended coupled ideal stubs

This paper investigates the influence of the coupling coefficient on the reflection zero (RZ) and transmission zero (TZ) of the open-ended parallel transmission line (TL). The structure is assumed equivalent to ideal coupled parallel stub (CPS). Theoretical circuit approach is considered to establish the frequency-dependent reflection and transmission coefficient expressions. The CPS RZ and TZ formulas in function of the coupling coefficient are derived. The CPS RZ and TZ characterizations in function of the elementary TL TZs and coupling coefficient are described. The relevance of the established CPS analytical model was effectively verified with microstrip structures operating in the frequency band 0.1 GHz to 10 GHz and the coupling coefficient varied from -20 dB to -0.9 dB. Excellent correlation between the introduced CPS model and the considered ideal CPS structure simulations was found in function of the coupling coefficient. The elaborated circuit theory is potentially useful for the printed circuit board (PCB) design, electromagnetic interference (EMI) and signal integrity engineering.