A synthesis procedure is developed in this paper for the design of N-step coplanar waveguide-to-microstrip transitions. An equivalent circuit approach is adopted to model the structure in terms of N cascaded ABCD matrices relative to the N coplanar waveguide sections forming the transition. A constrained optimization problem is formulated as the minimum finding of a proper functional to accurately determine the transition dimensions by imposing an upper bound to the return loss within a prescribed frequency band. An iterative N-step procedure is developed to find the optimization problem solution. Numerical results on millimeter-wave transition configurations are provided to demonstrate the effectiveness of the proposed synthesis method. A back-to-back transition prototype with N=3 sections is then fabricated and characterized in terms of measured S-parameters to experimentally demonstrate a return loss better than 10 dB in the frequency range from 1 GHz up to 40 GHz.
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