Matching a nonuniform MTL with only passive elements is not always possible

This paper presents for the first time a theoretical proof that at certain frequencies it may be impossible to match a nonuniform multiconductor transmission line by terminating it with a multiport load network of only passive partial admittances. The analytical proof is based on a detailed modal analysis of the chain connection of two unequal uniform lossless line sections, each one made of two parallel wires above ground. We show that, when the propagation modes of the resulting nonuniform MTL are about to resonate, the matching load network of partial admittances will require the presence of one negative resistor.