Chebyshev-Response Branch-Line Couplers with Enhanced Bandwidth and Arbitrary Coupling Level

A new approach to the synthesis of broadband branch-line couplers with arbitrary coupling level was investigated in this paper. It was shown that the operational bandwidth of a classic branch-line coupler can be increased by utilizing N-section impedance transformers added to each of the coupler’s ports. Furthermore, the obtained response can be approximated by the Chebyshev polynomial. Moreover, it was proven that for such couplers a range of coupling coefficient values can be obtained by the modification of classic branch-line topology. The analysis of the electrical parameters of the proposed branch-line couplers was comprehensively investigated. To verify the correctness of the proposed design procedures, 3-dB, and 6-dB broadband branch-line couplers operating at the center frequency of 2 GHz having return losses greater than 20 dB were designed, fabricated, and measured.

Spectral analysis of the spin-boson Hamiltonian with two bosons for arbitrary coupling and bounded dispersion relation

We study the spectrum of the spin-boson Hamiltonian with two bosons for arbitrary coupling [Formula: see text] in the case when the dispersion relation is a bounded function. We derive an explicit description of the essential spectrum which consists of the so-called two- and three-particle branches that can be separated by a gap if the coupling is sufficiently large. It turns out, that depending on the location of the coupling constant and the energy level of the atom (w.r.t. certain constants depending on the maximal and the minimal values of the boson energy) as well as the validity or the violation of the infrared regularity type conditions, the essential spectrum is either a single finite interval or a disjoint union of at most six finite intervals. The corresponding critical values of the coupling constant are determined explicitly and the asymptotic lengths of the possible gaps are given when [Formula: see text] approaches to the respective critical value. Under minimal smoothness and regularity conditions on the boson dispersion relation and the coupling function, we show that discrete eigenvalues can never accumulate at the edges of the two-particle branch. Moreover, we show the absence of the discrete eigenvalue accumulation at the edges of the three-particle branch in the infrared regular case.