COMBINERS & COUPLERS Power Combiners , Impedance Transformers and Directional Couplers : Part III

Microwave hybrids The branch-line couplers or hybrids were firstly described more than six decades ago; however, the problem of their exact synthesis remained a puzzle for a number of years [53]. Initially, the branch-line hybrid was analyzed as a four-arm symmetrical network based on a superposition of the results obtained in the even and odd modes [54]. By writing the even and odd mode matrices together, the characteristic impedances of the branch lines and coupling into different ports can be obtained. A general synthesis procedure which can be applied to any structure of a multibranch hybrid, based on an invariance of the Richard’s variable S = jtanθ to the transformation of S → 1/S apart from a 180° phase change, had become available a decade later [55]. As a result, with highly precise computer-design techniques available for branchline hybrids, it became possible to generate any coupling value in the useful 0 to 15 dB coupling range. Waveguide designs which have been used in large complex feeds for phase-array radars, are compact, highly predictable in amplitude and phase characteristics, and handle very high power. Coaxial, microstrip or stripline implementations of branch-line hybrids provide simple planar structures of moderate bandwidth capability, up to about 2/3 of an octave. For a fully matched case with standard 50Ω source and load impedances, when the characteristic impedances of its transverse branches are 50 Ω and the characteristic impedances of its longitudinal main lines are the microstrip branch-line hybrid shown in Fig. 30 represents a 3-dB directional coupler, for which power in arm 1 divides evenly between arms 2 and 3 with the phase shift of 90°. No power is delivered to arm 4, because the signal flowing through different paths (lengths of λ/4 and 3λ/4) have the same amplitude and opposite phases at this port. The branch-line hybrid does not depend on the load mismatch level for equal reflected coefficients from the outputs when all reflected power is dissipated in the 50-Ω ballast resistor. However, in practice, due to the quarterwavelength transmission-line requirement, the bandwidth of such a single-stage quadrature branch-line hybrid is limited to 10-20%. Figure 31 shows the calculated frequency bandwidth characteristics of a single-section branch-line hybrid matched at the center bandwidth frequency with the load impedance ZL = Z0 = 50 Ω, where C12 is the insertion loss calculated as the ratio of powers at the input 50 2 35 4 / . = Ω This multi-part article on coupler and combiner structures continues with an examination of microwave hybrids using various topologies