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              <p>In this article, we systematically reviewed the theory of designing multiband filters based on frequency transformation methods and the design methods based on planar circuits. Firstly, we reviewed the general methods of designing filters based on planar circuits and introduced the concept of designing multiband filters using frequency transformation methods. Secondly, we discussed the mathematical expression of frequency transformation method in depth and provided rigorous mathematical proofs. Furthermore, we presented the topology and design circuit examples of filters based on lumped parameters and coupling matrix synthesis. Finally, we compared the advantages and disadvantages of frequency transformation method and summarized the entire article.</p>
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