Wideband 4×4 Nolen Matrix with 360° Continuously Tuned Differential Phase and Low In-Band Phase Deviation Error

Abstract

In the paper, a wideband tunable $4\times 4$ Nolen matrix is proposed. By using the presented topology of the Nolen matrix, tunable output port phase differences can be realized by inserting one type of tunable phase shifters (T-PS). Besides, the in-band phase deviation error is minimized by adding compensation phase shifters (C-PSs) to the output ports of the Nolen matrix. Analytical design methods based on signal flow graphs and complex exponential signal are given to obtain the rigorous relationships of the coupling and phase shifts in the Nolen matrix. Besides, a detailed method for output ports phase slope compensation is provided. For validation, a prototype centered at 5.8 GHz is designed and fabricated. Measurement results agree well with the simulated ones. By using only one voltage to control the phase shifts of the T-PS in a 90° range for each input excitation of the Nolen matrix, a full 360° range of the progressive phase difference is realized by switching four input ports. The measured fractional bandwidth under 10 dB return loss and isolation is larger than 24.5% with the $\text{in}-\text{band}\pm 1.5$ dB amplitude imbalance and ±15° phase deviation error for ports 1-4 excitations. Besides, for a more strict criterion of ±1 dB amplitude imbalance and 10° phase deviation error, the measured bandwidths are larger than 15% for all port excitations.