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This paper presents an effective formulation tailored for electromagnetic-technology computer-aided design coupled simulations for extremely-high-frequency ranges and beyond (>;50 GHz). A transformation of variables is exploited from the starting A-V formulation to the E-V formulation, combined with adopting the gauge condition as the equation for scalar potential. The transformation significantly reduces the cross-coupling between electric and magnetic systems at high frequencies, providing therefore much better convergence for iterative solution. The validation of such transformations is ensured through a careful analysis of redundancy in the coupled system and material properties. Employment of the advanced matrix permutation technique further alleviates the extra computational cost introduced by the variable transformation. Numerical experiments confirm the accuracy and efficiency of the proposed E-V formulation.