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Any transfer function, in order to be physically realizable as a lossless coupling network terminated in a single resistance, must have an even or odd polynomial as its numerator. Such a function, representing a transfer admittance, a transfer voltage ratio, or a transfer impedance, can be realized by the method of this paper as a lossless lattice network terminated in resistance and possessing no mutual inductance. If the numerator of the transfer admittance or voltage ratio is even and the numerator of the transfer impedance is odd, these lattices can always be reduced to unbalanced networks. No ideal transformers are needed in the final network; only one real transformer is required, where a real transformer is defined as one that has a coupling coefficient smaller than one and finite magnetizing inductance.