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Compact dual-mode dual-band bandpass fllters are realized with a single periodic stepped-impedance ring resonator. Neither extra resonator nor substrate layer is required for implementing the second passband. Based on the transmission line theory, a transmission zero design graph consisting of the transmission zeros together with the resonant frequencies of the resonator is developed against the space separation angle between the input and output ports. Based on this graph, when the line-to-ring feed structure is implemented, the space angle can be determined for the dual-mode dual-band design with designated zeros near the two passbands. It is believed that this is the flrst design graph for designating the transmission poles and zeros of a dual-mode ring resonator fllter before the excitation structure is realized. Three dual-mode dual-band bandpass fllters are carried out for demonstration. All circuits occupy only 60% of the area of the conventional ring resonator bandpass fllter

TRANSMISSION ZERO DESIGN GRAPH FOR DUAL-MODE DUAL-BAND FILTER WITH PERIODIC STEPPED-IMPEDANCE RING RESONATOR