A circuit model for vertical transitions between different coplanar waveguide systems using via-holes is presented. The model is directly extracted from the geometry of the transition using closed expressions. Additionally, it can be used to find suitable initial dimensions for the transition in a circuit simulator, thereby greatly reducing the effort spent on subsequent electromagnetic simulations. To test the validity of the developed model, it is applied to a variety of situations involving a wide range of stack heights, dielectric constants, and transmission line geometry values. These situations cover most of the relevant broadband vertical transitions used in practical PCB and LTCC designs. Comparative analysis of the circuit model and electromagnetic simulations yields good agreement in all analyzed situations. Experimental assessment of the model is also provided for some of the transitions that were built and characterized in a back-to-back configuration.
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