Synthesis of Networks: Direct Coupling Matrix Synthesis Methods

This chapter examines the coupling matrix representation of microwave filter circuits. It presents two methods for the direct synthesis of the coupling matrix for a network with given transfer and reflection characteristics: first for the N X N matrix and second for the N + 2 matrix. Although the N + 2 matrix is more flexible than the N X N matrix and is little easier to synthesize, it is informative to explore the principles behind the N X N matrix synthesis technique. An alternative method for the synthesis of a coupling matrix is by using the folded lattice array. The method synthesizes fully canonical matrices of even or odd degree, realizing asymmetric or symmetric characteristics. The method takes advantage of a property of the folded lattice array that all components, frequency‐varying susceptances, frequency‐invariant reactances (FIRs), and coupling inverters are equal‐valued about the plane of symmetry that bisects the network.