“…The de-embedding technique is a simple one based on the shifts of the microstrip reference planes generated by the lengths of the coaxial connectors (SMA or K). The symmetric perturbations (same kind of male or female connectors at the input and output ports) caused by these shifts correspond to rotations of the immittance matrix unit amplitude eigenvalues through arbitrary phase angles [32,33]. The procedure to extract the connectors is as follows:…”
Section: The Measurements and The Connector De-embedding Proceduresmentioning
The simulation of nonlinear loaded high-speed microstrip interconnects by means of a convolution-based procedure is described when both, analytical and measured scattering parameters are used. Closed-form equations are employed to obtain the analytical scattering parameters. The influence of measured scattering parameters, when these are used instead the analytical ones, is investigated to know how the microstrip interconnect responses are affected. The convolution procedure is complemented by including the transmission line linear equation and the microwave circuit reflection theory.
“…The de-embedding technique is a simple one based on the shifts of the microstrip reference planes generated by the lengths of the coaxial connectors (SMA or K). The symmetric perturbations (same kind of male or female connectors at the input and output ports) caused by these shifts correspond to rotations of the immittance matrix unit amplitude eigenvalues through arbitrary phase angles [32,33]. The procedure to extract the connectors is as follows:…”
Section: The Measurements and The Connector De-embedding Proceduresmentioning
The simulation of nonlinear loaded high-speed microstrip interconnects by means of a convolution-based procedure is described when both, analytical and measured scattering parameters are used. Closed-form equations are employed to obtain the analytical scattering parameters. The influence of measured scattering parameters, when these are used instead the analytical ones, is investigated to know how the microstrip interconnect responses are affected. The convolution procedure is complemented by including the transmission line linear equation and the microwave circuit reflection theory.
“…e −jφ 1 e −jφ 1 0 0 0 e −jφ 1 e −jφ 2 e −jφ 3 0 0 0 e −jφ 1 e −jφ 3 e −jφ 2 e −jφ 1 e −jφ 1 e −jφ 1 0 0 0 e −jφ 1 e −jφ 2 e −jφ 3 0 0 0 e −jφ 1 e −jφ 3 e −jφ 2 0 0 0 where φ 1 is the reference phase, φ 2 = φ 1 +120 deg, and φ 3 = φ 1 −120 deg. Following the procedure of Jiménez [3], a distributed-element network was synthesized. The resulting network layout is shown in Fig.…”
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15-09-2006
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ABSTRACTA 6-port coupler has been implemented for use in an RN2 beam former at 60 GHz. The coupler was synthesized to provide the appropriate magnitude and phase division and then realized using micro-machined TEM transmission lines. At 60 GHz, all signal paths of the coupler have a measured insertion loss less than 1.14 dB and a phase error of less than 3.8 degrees. Abstract A 6-port coupler has been implemented for use in an RN 2 beam former at 60 GHz. The coupler was synthesized to provide the appropriate magnitude and phase division and then realized using micromachined TEM transmission lines. At 60 GHz, all signal paths of the coupler have a measured insertion loss less than 1.14 dB and a phase error of less than 3.8 degrees.
SUBJECT TERMS
“…A growing number of scientific papers and books on the electromagnetic problems where the authors used group theory is also a justification of our statement. This concerns, for example, scattering and inverse scattering problems (in particular, in target identification) [16]- [18], near-field measurements [19,20]), radar polarimetry [21], electromagnetic and geophysical remote sensing [22], problems of reflection of light in optics [23], waveguiding problems [9], analysis and synthesis of electrical networks [24,25], antennas and antenna arrays [10,26], nanoantennas [27], signal processing [28], problems of propagation of electromagnetic waves in complex media [9,14], Green's tensor calculations [29], for analysis of dielectric arrays [30], and others.…”
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic'' tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not contain a description of properties of electromagnetic fields and waves on the basis of group theory. We discuss in this paper from the didactic point of view, several types of symmetry and the corresponding groups and representations. The benefits of the use of grouptheoretical methods are a more deep physical understanding of the electromagnetic phenomena and a significant reduction of numerical calculations. These methods are general and exact.
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