Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a confocal elliptical waveguide filled with multi-layered homogeneous isotropic me...Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a confocal elliptical waveguide filled with multi-layered homogeneous isotropic media is derived; then the eigenequation for it is given. When an elliptical waveguide becomes a circular waveguide, the electromagnetic fields and the eigenequation of the circular waveguide can be obtained from the eigenequation of the elliptical waveguide using the asymptotic formulae of Mathieu and modified Mathieu functions for a large radial coordinate in the elliptical coordinate system, and the eigenequation of a circular waveguide filled with multilayered dielectrics can be treated as a special case of an elliptical waveguide. In addition, some numerical examples are presented to analyze the propagating characteristics influenced by the permittivity, permeability of dielectrics filled in the elliptical waveguide, etc. The results show that changing the permittivity or permeability of the dielectrics filled in the waveguide and the major semiaxis value of the i-th layer can change the propagating characteristics of an elliptical waveguide.展开更多
We design and fabricate two types of superconducting niobium coplanar waveguide microwave resonators with different coupling capacitors on high purity Si substrates.Their microwave transmissions are measured at 20 mK....We design and fabricate two types of superconducting niobium coplanar waveguide microwave resonators with different coupling capacitors on high purity Si substrates.Their microwave transmissions are measured at 20 mK.It is found that these two types of resonators possess significantly different loaded quality factors;one is 5.6×10^(3) and the other is 4.0×10^(4).The measured data are fitted well by classical ABCD matrix approach and consequently the coupling capacitances are determined.It is found that the transmission peak deviates from the standard Lorentizian with a frequency broadening.展开更多
A dual-tone technique is used to produce multi-samples in optimising calibration of six-port junction. More accurate results are achieved by using the least-square method and excluding those samples which may cause bi...A dual-tone technique is used to produce multi-samples in optimising calibration of six-port junction. More accurate results are achieved by using the least-square method and excluding those samples which may cause bigger errors. A 0.80 -1.10 GHz microwave integrated circuit （MIC） six-port reflectometer is constructed. Nine test samples are used in the measurement. With Engen＇s calibration procedure, the difference between the HP8510 and the six-port reflectrometer is in the order of 0.20 dB/1.5° for most cases, above 0.50 dB/5.0° at boundary frequency. With the optimised method, the difference is less than 0. 10 dB/1.0° for most cases, and the biggest error is 0.42 dB/2.1° for boundary frequencies.展开更多
文摘Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a confocal elliptical waveguide filled with multi-layered homogeneous isotropic media is derived; then the eigenequation for it is given. When an elliptical waveguide becomes a circular waveguide, the electromagnetic fields and the eigenequation of the circular waveguide can be obtained from the eigenequation of the elliptical waveguide using the asymptotic formulae of Mathieu and modified Mathieu functions for a large radial coordinate in the elliptical coordinate system, and the eigenequation of a circular waveguide filled with multilayered dielectrics can be treated as a special case of an elliptical waveguide. In addition, some numerical examples are presented to analyze the propagating characteristics influenced by the permittivity, permeability of dielectrics filled in the elliptical waveguide, etc. The results show that changing the permittivity or permeability of the dielectrics filled in the waveguide and the major semiaxis value of the i-th layer can change the propagating characteristics of an elliptical waveguide.
基金Supported by the National Natural Science Foundation of China under Grant No 11174373the National Basic Research Program of China under Grant No 2010CB923104.
文摘We design and fabricate two types of superconducting niobium coplanar waveguide microwave resonators with different coupling capacitors on high purity Si substrates.Their microwave transmissions are measured at 20 mK.It is found that these two types of resonators possess significantly different loaded quality factors;one is 5.6×10^(3) and the other is 4.0×10^(4).The measured data are fitted well by classical ABCD matrix approach and consequently the coupling capacitances are determined.It is found that the transmission peak deviates from the standard Lorentizian with a frequency broadening.
基金The National Natural Science Foundation of China (No.60441006)
文摘A dual-tone technique is used to produce multi-samples in optimising calibration of six-port junction. More accurate results are achieved by using the least-square method and excluding those samples which may cause bigger errors. A 0.80 -1.10 GHz microwave integrated circuit （MIC） six-port reflectometer is constructed. Nine test samples are used in the measurement. With Engen＇s calibration procedure, the difference between the HP8510 and the six-port reflectrometer is in the order of 0.20 dB/1.5° for most cases, above 0.50 dB/5.0° at boundary frequency. With the optimised method, the difference is less than 0. 10 dB/1.0° for most cases, and the biggest error is 0.42 dB/2.1° for boundary frequencies.
