In this letter, admittance matrix and arbitrary phase delay is investigated for the design of sub-miniaturized Wilkinson power divider (WPD). A theoretical model based on admittance matrix is derived and discussed to find the relationship among arbitrary phase delay, characteristic impedance and electrical length of WPD. The presented method is validated by building a modified configuration which is centered at 500 MHz with 14.18% fractional bandwidth (FBW) using both microstrip lines and lumped elements. The measured results show that the proposed WPD exhibits excellent performances, including less than 0.27 dB insertion loss, better than 26.1 return loss and greater than 39.2 dB isolation. Moreover, more than 85% size reduction is achieved, compared with conventional WPD.Index Terms-Admittance matrix, arbitrary phase delay, subminiaturized, Wilkinson power divider (WPD).

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Abstract-A new out-of-phase power divider (PD) without phase shifter at the output ports is proposed. Based on admittance matrix, a new topology of uniplanar power divider with symmetrical outputs is designed. Under conditions of good matching, perfect isolation, and 180 • phase difference between two output ports, the corresponding design equations and synthesis procedures are derived and given with admittance matrix. To verify the design approach, an out-of-phase power divider operating at 2 GHz with equal power division ratio is designed, fabricated, and measured. Experimental results demonstrate that the input return loss is better than 32 dB, the insertion loss is less than 0.29 dB and the isolation is better than 33 dB. The amplitude imbalance between the output ports is 0.03 dB and the phase difference between the two output ports is 181.6 • at the operation frequency. Further more, 49.9% relative bandwidth of 15 dB return loss and 39.4% relative bandwidth of 20 dB port isolation are achieved.

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