Exact Synthesis of Two‐Section Schiffman Phase Shifters With Equal‐Ripple Phase Response

ABSTRACT

This letter presents an exact synthesis procedure for two‐section Schiffman phase shifters with an equal‐ripple phase response. By analytically formulating the phase response in terms of impedance ratios and electrical length, the resulting transcendental equations are solved numerically to obtain the circuit parameters as initial design values, which are subsequently translated into physical dimensions and refined through full‐wave EM optimization to obtain the final practical design. To validate the proposed synthesis method, two broadside‐coupled strip‐line prototypes were fabricated. The first achieves an ultra‐wideband (UWB) performance from 1 to 6 GHz (142.8% FBW) with a phase shift of 90° ± 15°, an insertion loss below 0.4 dB, and a return loss greater than 19 dB. The second demonstrates high‐precision phase control from 2 to 7 GHz (111.1% FBW) with a significantly reduced deviation of 90° ± 3.5°, an insertion loss below 0.17 dB, and a return loss exceeding 20 dB. Both theoretical and experimental results confirm that this exact synthesis approach provides a deterministic design trade‐off, enabling either ultrawide bandwidth or high‐precision phase control.