Design of Continuously Tunable Phase Shifter and Its Application to Butler Matrix With 360° Continuous Progressive Phase Shift

This article presents a design method for a continuously tunable phase shifter (PS) based on a varactor-loaded slot line structure. The equivalent capacitance of the varactor is varied to achieve phase changes, and quarter-wavelength open-circuit microstrips are used to achieve loading and phase slope tuning for low in-band phase errors. The equivalent transmission line model and closed-form equations of the proposed structure are given, and from the theoretical analysis, we find that the proposed structure has the advantage of achieving ideal matching and transmission in a number of varactor and slot line impedance states. In order to verify the practicality of the proposed PS, it is cascaded at the output ports of the Butler matrix to achieve 360° continuous progressive phase shifts, and the Butler matrix also includes hybrid slot line-microstrip couplers and slot line crossovers. In order to validate the proposed design approach, a 90° PS, a 360° PS, and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$</tex-math> </inline-formula> Butler matrix are simulated, fabricated, and measured. From the measurement results, the operating frequency band, return loss, rms phase error, and circuit size of the proposed 360° PS are 1.7–2.3 GHz, 10 dB, 5°, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.104\lambda _{g}^{2}$</tex-math> </inline-formula>, respectively. The proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$</tex-math> </inline-formula> Butler matrix realizes 360° continuous progressive phase shifts with a circuit size of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.92\lambda _{g}^{2}$</tex-math> </inline-formula>.