Equivalence between stepped-impedance ring and T-shaped cascaded transmission line network

Two new equivalences in transmission line (TL) networks are proposed. The first one is found between a shunt fed stepped-impedance ring and a T-shaped TL network with a short-circuited series stub. Both the networks are composed of TL segments with the same electrical length. By using the Y and the ABCD matrices, an equivalent condition can be obtained, which is independent in frequency. Meeting the condition, the two networks with different topologies could generate exactly the same response. As the counterpart of the first one, the second equivalence is found between a series fed ring and a T-shaped network with an open-circuited shunt stub. The two equivalences are useful in circuit modelling and analysis; and provide extra design flexibility in circuit implementations.