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A new concept called the dynamic coarse model is proposed and is applied to the optimization design of low-temperature co-fired ceramic (LTCC) multilayer RF circuits with the aggressive space mapping (ASM) technique. The dynamic coarse model is a combination of an evolutionary equivalent-circuit model and an efficient quasi-static numerical electromagnetic (EM) model-partial-element equivalent-circuit model. Namely, there are two forms of coarse models jointly in use: the coarse schematic model and the coarse EM model. The coarse schematic model evolutionarily incorporates parasitic effects that can be extracted from its accompanying coarse EM model. This process can greatly facilitate the original ASM process by easily determining a "high-quality" optimized coarse model. Two LTCC frequency-selective passive modules, i.e., a bandpass filter and a diplexer, are designed using the proposed scheme and ASM. No nonuniqueness in parameter extraction is encountered. Good convergence performance is achieved for the designs of both modules.