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In this paper, various architectures of three-dimensional compact microwave balanced to unbalanced (balun) transformers for Bluetooth/WiFi antenna applications are successfully designed and optimized using the design of experiments (DOE) approach. Two different multilayer topologies, one microstrip and one stripline, are investigated on low temperature co-fired ceramic (LTCC) substrate. The design goals for both baluns are perfectly balanced outputs from 2 to 3 GHz and a resonant frequency of exactly 2.4 GHz. It is demonstrated, using only eight simulations, that perfectly balanced outputs are not possible under the given conditions in the case of the microstrip balun. Nevertheless, the stripline balun can be optimized due to its almost symmetrical structure, and both simulations and measurement results verify the conclusions. The DOE method is very simple to implement and gives a clear understanding of the system behavior at the beginning of the design process, reducing the amount of work required for achieving the design goals by orders of magnitude compared to the widely used trial-and-error approach. The matching and unique measurement issues regarding the calibration, placement of probes and the de-embedding of the microstrip to coplanar waveguide transitions are discussed in detail for the optimized stripline balun. This technique can be easily applied to the fast and efficient optimization of complicated radiation structures, such as reconfigurable or multilayer multiband antenna arrays.