A general method for extending a lossy network to a lossless network using the matrix decomposition

In the paper, we discuss a method to extend an arbitrary reciprocal lossy network, which may be a passive device or a passive network cascaded by a series of passive devices, to a reciprocal lossless matrix. Meanwhile, we analytically proved that the scattering matrix of the extended lossless network has the smallest order, in another word, this method can calculate the least essential ports to be extended. Hence, the method build a bridge between the lossy network and the lossless network. Furthermore, the desired lossy network can be extracted from the well-designed lossless network which can be synthesized based on mature lossless methods.