Electromagnetic modeling of tunability of Barium Strontium Titanate and Magnesium Borate composites

A complete tunability electromagnetic simulation model for the Ba$_{0.6}$Sr$_{0.4}$TiO$_3$ (BST), with 𝜀𝑟 ≈ 2000, and Mg$_2$B$_2$O$_6$ (MBO), with 𝜀𝑟 ≈ 7, composites is proposed here. The model is based on electrostatics, to simulate the effects of bias fields distribution in the composite varactor at the unbiased state to create the biased state for all volumetric mixture compositions. A bulk-ceramic varactor approach is chosen for the fabricated varactors. Varactors are fabricated with different volume compositions of BST and MBO, ranging from 10 to 100 vol-% of BST. Simulated results of the varactor model are then verified with the measured results of the varactor. The simulated and measured tunability shows considerable discrepancy at room temperature, which leads to Curie temperature 𝑇$_𝐶$ investigation of the fabricated varactors. It has been observed that a shift in 𝑇$_𝐶$ is directly proportional to the discrepancies in the simulated and measured tunability. After incorporating the 𝑇$_𝐶$ shifts in the model, the results show close proximity between measured and 𝑇$_𝐶$ -shifted simulated tunabilities with differences being reduced from around 32% to 2% for 80 vol-% BST varactor.