A succinct way to diagonalize the translation matrix in three dimensions

Abstract

PM-HFET cold mixer is the good linearity of the i.f. output power with a rf power compression point of 11 dBm. More-Ž . over, moderate conversion losses 7 dB are obtained with no dc consumption. For the dual-gate mixer the main advantage Ž . is the high natural LO to rf isolation 30 dB . An interesting conversion gain is also shown, and the device avoids external LO to rf coupling.In this study, an exhaustive and accurate methodology is carried out. It is based on specific characterizations, in-house nonlinear modeling, circuit design using commercial harmonic balance software, complete measurement of the structures, and reverse engineering. The two topologies investigated are very attractive for the fabrication of mixers in millimeter waves. Because of the different advantages exhibited, the choice between the two devices will depend on the specifications and constraints of the envisaged application. ACKNOWLEDGMENT

Fast Multipole Method For 3-D Helmholtz Equation in Layered Media

“…Similar to the free space case, the multipole-expansion based FMM in this paper can not handle high frequency wave source interactions well as the number of terms in the MEs will increase in proportion to k * D [12] where k is the wave number and D is the size of the scatterer. To address this difficulty, plane waves expansions could be introduced to yield diagonal forms for the translation operators in the FMM to produce an O(N log N ) fast algorithm [30] [7]. Though, the plane wave expansion may suffer a low-frequency breakdown when interaction between sources within sub-wavelength distance is computed for large objects with small fine structures.…”

“…where S = (2n + 1)(2ν + 1)(2q + 1)/(4π). Although we have explicit formulas (4) and (7) for the separation matrices S mµ nν (b) and S mµ nν (b), they are too complicated to be used directly for practical computations. Fortunately, recurrence formulas are available for their computations (cf.…”

Analysis of microstrip-to-circular-waveguide transitions by a new spatial-images method

“…Consequently, larger systems of equations need to be solved. To overcome the extra computational effort, some authors have developed techniques to render sparse the associated IE matrices [20,21]. However, these methods are still in a preliminary stage for complex tridimensional problems that involve dielectric and conducting bodies.…”

Three-dimensional multilevel fast multipole algorithm from static to electrodynamic

“…static problems 6᎐7 and with O N log N computational w x complexity for dynamic problems 8᎐9 . A general way to diagonalize the translation matrix in three dimensions is w x developed in 10 .…”