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In this paper, a general synthesis method is proposed for the design of multi-frequency impedance transformers (MFITs) for arbitrary frequency-dependent complex loads (FDCLs) by adopting the concept of multi-frequency inverters (MFIs). An MFI, which is placed between two susceptance blocks, is constructed with a transmission line and two-side multi-frequency susceptances (MFSs), whose values at multiple frequencies are independently specified. By merging neighboring susceptances, we get a very simple Pi-shaped topology of MFITs, which in theory has no limitation on the number of matching frequencies. The MFS blocks are realized with one or more parallel shunt stubs, providing needed susceptance values at several specified frequencies. A genetic algorithm is used in extracting the circuit parameters of the parallel stubs. Several dual-, triple-, and quad-frequency impedance transformers for FDCLs are designed for illustrating the design methods. Experiment and simulation results are compared with good agreement, validating the feasibility of the theory. The designed impedance transformers are concise in circuit and compact in dimensions.