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A new reflection-type phase shifter with a full 360deg relative phase shift range and constant insertion loss is presented. This feature is obtained by incorporating a new cascaded connection of varactors into the impedance-transforming quadrature coupler. The required reactance variation of a varactor can be reduced by controlling the impedance ratio of the quadrature coupler. The implemented phase shifter achieves a measured maximal relative phase shift of 407deg, an averaged insertion loss of 4.4 dB and return losses better than 19 dB at 2 GHz. The insertion-loss variation is within plusmn0.1 and plusmn0.2 dB over the 360deg and 407deg relative phase shift tuning range, respectively.