Analysis of magnetically coupled all-pass network for phase-shifter design

An all-pass network with magnetic coupling between its two inductors is analyzed in the context of phase-shifter design. Using even-odd mode analysis, the scattering parameters of the magnetically coupled all-pass network (MCAPN) are derived. Criteria for the network to provide an all-pass frequency response are obtained. Two switched-network phase-shifter topologies based on the MCAPNs are investigated. The results show that positive magnetic coupling between the inductors within the network boosts the amount of phase shift, whereas negative magnetic coupling broadens the bandwidth over which the phase shift remains constant. By using the MCAPNs for phase-shifter design, the tradeoff between the amount of phase shift and the bandwidth can be exploited, which not only adds to the design freedom, but suggests potential performance enhancement. For experimental verification, a 1-bit 22.5^° phase shifter and a 4-bit 360^° phase shifter are designed based on the analyzed MCAPNs with negative coupling factor. The measured phase error of the 1-bit phase shifter is less than 5% of the target phase shift from 2.38 to 4.80 GHz, corresponding to a bandwidth of 67%. The measured root mean square phase error of the 4-bit phase shifter is less than 3^° from 1.62 to 3.89 GHz, which translates into a bandwidth of 82%.