Study of Mode Coupling on Coaxial Resonators

A study of mode coupling phenomenon of coaxial resonators has been conducted with theories.Through establishing the source-free transmission line equation,boundary conditions of the coaxial resonators with a corrugated inner conductor are analyzed.In the end,calculations are performed in a wide range of corrugation parameters for the resonator of the Karisruhe Institute of Technology (KIT) relevant coaxial gyrotron.     

Study of Eigenmodes of Coaxial Resonators Using Coupled-Wave Theory

Based on the surface impedance theory (SIT) and the coupled-wave theory (CWT), this paper has established the second-order transmission line equation applicable to coaxial resonators with corrugated inner conductor. By utilizing the equation, the resonant frequency, Q factor and field profiles geometry of the eigenmodes of coaxial resonators can be calculated in view of the mode coupling, and the variables of the slot width and depth in the coupling coefficient can also be applied to calculate their impact on the resonant frequency and Q factor. The numerical results show that, the slot width and depth have significant impact on the resonant frequency, but their effect on Q factor is approximately negligible.     

Gold-Plated Micromachined Millimeter-Wave Resonators Based on Rectangular Coaxial Transmission Lines

Resonators based on microfabricated rectangular coaxial (recta-coax) transmission lines are presented. The resonators were fabricated using a multilayered nickel electroplating process that enables the fabrication of three-dimensional structures. As a method to improve performance, gold was plated on the resonators using an electroless process. A model for predicting the effect of the plating on a resonator quality (Q) factor is presented and verified by measurements. Measured resonators show that the plating can increase the Q factor of nickel resonators by over 50% at frequencies above 44 GHz. Utilizing gold plating, 50-Omega resonators are demonstrated at 44 and 60 GHz with unloaded Q factors of 213.1 and 242.3, respectively     

Fast evaluation of an integral occurring in digital filteringapplications

A fast evaluation procedure for the integral I_m,n,p=1/2πj∯_|z|=1H_m,n(z)H _m,n(z^-1)z^p-1dz for arbitrary nonnegative integer-valued m, n, and p, is presented, where H_m,n (z)=Σ_k=0^mb_m,kz^-k /Σ_l=0ⁿa_n,lz^-1,a _n,0≠0 is the transfer function of an arbitrary digital filter. Evaluation of this integral frequently appears in control, communication, and digital filtering. A notable result is the one-term recursion on p, for arbitrary but fixed nonnegative integers m and n. The computational complexity is analyzed, and two illustrative examples demonstrate some of the advantages of this approach     

Cold tests of open coaxial resonators in the range 9–17 GHz

A study of selective properties of coaxial open cylindrical resonators have been conducted experimentally and compared with theory. The resonator consists of an inner circular cylinder symmetrically located inside an outer weakly irregular open waveguide. Several fundamental TE modes were identified over the range 9 to 17 GHz through measurements of the resonant frequencies and the associated loaded quality factors. It has been verified that the structure and the number of resonant modes are both strongly dependent on the diameter of the coaxial insert. Such an electrodynamical system proves to be useful in guided wave applications requiring, for example, filters, frequency-tunable resonators and devices for analyzing the modal composition of a signal.     

Effects of Material and Dimension on TCF,Frequency, and Q of Radial Contour Mode AlN-on-Si MEMS Resonators

This paper investigates the effects of material and dimension parameters on the frequency splitting, frequency drift, and quality factor (Q) of aluminium nitride (AlN)-on-n-doped/pure silicon (Si) microelectromechanical systems (MEMS) disk resonators through analysis and simulation. These parameters include the crystallographic orientation, dopant, substrate thickness, and temperature. The resonators operate in the elliptical, higher order, and flexural modes. The simulation results show that i) the turnover points of the resonators exist at 55 °C, –50 °C, 40 °C, and –10 °C for n-doped silicon with the doping concentration of 2×1019 cm–3 and the Si thickness of 3.5 μm, and these points are shifted with the substrate thickness and mode variations; ii) compared with pure Si, the modal-frequency splitting for n-doped Si is higher and increases from 5% to 10% for all studied modes; iii) Q of the resonators depends on the temperature and dopant. Therefore, the turnover, modal-frequency splitting, and Q of the resonators depend on the thickness and material of the substrate and the temperature. This work offers an analysis and design platform for high-performance MEMS gyroscopes as well as oscillators in terms of the temperature compensation by n-doped Si.     

Ohmic selection in open coaxial resonators: An experimental study

A study of ohmic selective properties of open coaxial cylindrical resonators has been conducted experimentally and compared with theory. The resonator consists of an inner cylinder made of silicon carbide symmetrically located inside an outer cylindrical, tube shaped waveguide. Several fundamental TE modes were identified over the range 9 to 17 GHz through measurements of the resonant frequencies and the associated quality factors. Mode discrimination is achieved both by exploring selective ohmic effects and examining the electrodynamical properties of the coaxial cylindrical waveguide. The effectiveness of a silicon carbide coaxial insert in providing ohmic mode selection is demonstrated in that the totalQ factors of TE _mp modes with radial indexp≥2 become well below the quality factors for surface TE _m1 modes. It has been verified that both structure and number of resonant modes are strongly dependent on the diameter and the resistivity of the coaxial insert.     

高阻带微波带通滤波器的研制

为了提高通信设备的性能,研制了高阻带的微波滤波器。该滤波器由5个高Q值的同轴介电陶瓷谐振器构成的带通滤波器。谐振器之间通过介电基片上的电容相互耦合。在装入外壳前,调整好每个谐振器的谐振频率和耦合电容,之后就不需要再调整,外壳上也没有可调零件,从而保证滤波器结构稳定,性能可靠。用εr=74的介电陶瓷制作出滤波器的性能为f0=982 MHz,Δf=10.9 MHzI,L=3.8 dB,阻带在f0±30 MHz处大于69 dB,远阻带衰减优于70 dB。     

Nonlinear complex susceptibility of cresyl violet solution measuredwith a dynamic grating method

The absolute square of the complex nonlinear third-order susceptibility χ₃ was investigated by measuring the self-diffraction efficiency η of a transient laser-induced population grating. Cresyl violet in methanol was examined in the wavelength range of S₀ ground state absorption. For this dye, the real and imaginary parts of χ₃ were separated by additional determination of the nonlinear absorption. Both parts of χ₃ are plotted between 570 and 625 nm and their relation to each other was examined by using a Kramers-Kronig formula     

Precise measurements of the Q factor of dielectric resonators inthe transmission mode-accounting for noise, crosstalk, delay ofuncalibrated lines, coupling loss, and coupling reactance

Accurate measurements of the unloaded Q₀ factor of microwave resonators are necessary in many microwave applications. The most accurate values of Q₀ can be obtained by Q-circle fits from multifrequency S-parameter data. Practical measurement systems cause S-parameters of the resonators to be distorted from the circular ideal shape, rotated, and shifted from the origin resulting in errors in the Q-factor values. A novel Q-factor measurement method has been developed based on equations derived for resonators working in the transmission mode and fractional linear circle-fitting techniques. The transmission-mode Q-factor (TMQF) technique removes measurement effects of noise, noncalibrated measurement cables, connectors, coupling structures, crosstalk between the coupling loops, and impedance mismatch from the measurement data. The TMQF is especially useful in cryogenic measurements of high-temperature superconducting thin films and dielectrics since these measurements are typically done in the transmission mode and contain cables and connectors that are difficult to calibrate. The accuracy of the TMQF is better than 1% for practical measurement ranges and the method is applicable to a wide range of coupling. The range of Q factors measurable is from 10³ up to 10⁷     

Microwave Circuits for High-Efficiency Operation of Transferred Electron Oscillators

Compact circuits for obtaining high-efficiency operation of high-power transferred electron oscillators (TEOs) in L-band are described. One is a coaxial resonator and the other employs coupled TEM lines. The circuits are shown analytically and experimentally to be capable of matching a wide range of fundamental device impedances. Provisions for independently tuning the second-harmonic impedance over a wide range are included in both types of circuits. Pulsed conversion efficiencies up to 32 percent have been obtained TEOs mounted in the coaxial resonators and up to 27 percent with TEOs in the coupled TEM-line structures. The impedance at the second harmonic has been shown quantitatively to be extremely important in controlling device efficiency. By varying the second-harmonic tuning the device performance can be varied from high-efficiency operation to no output. Oscillators using these cavities were temperature stable over a wide range. The operating frequency of TEOs in the coaxial cavity and the coupled-TEM-line cavity varied less than 30 and 40 kHz//spl deg/C, respectively, over the range from - 54/spl deg/C to +125/spl deg/C.     

UHF double dielectric resonator filter with linearised tuning range

A UHF double dielectric resonator filter operating in the TE_01δ mode has been constructed with a high Q, wide (14%) and reasonably linear tuning range. This has been achieved by varying the gap between the resonators, and using the influence of the end wall on the movable resonator. The experimental device is readily scaleable to the cellular radio wave bands     

960 MHz同轴介质谐振器滤波器的研制

研制了用四个高Q值介质同轴谐振器构成的带通滤波器,谐振器之间的耦合通过陶瓷基片上的电容实现,讨论了影响谐振器插入损耗的主要因素。结果表明,该四级式低损耗介质同轴谐振器滤波器中心频率f0为960MHz,插入损耗小于3.0dB,能满足设计要求。     

Two-dimensional weight-constrained codes through enumeration bounds

For a rational α∈(0,1), let 𝒜_n×m,α be the set of binary n×m arrays in which each row has Hamming weight αm and each column has Hamming weight αn, where αm and αn are integers. (The special case of two-dimensional balanced arrays corresponds to α=1/2 and even values for n and m.) The redundancy of 𝒜_n×m,α is defined by ρ_n×m,α=nmH(α)-log₂|𝒜 _n×m,α| where H(x)=-xlog₂x-(1-x)log₂(1-x). Bounds on ρ_n×m,α are obtained in terms of the redundancies of the sets 𝒜_ℒ,α of all binary ℒ-vectors with Hamming weight αℒ, ℒ∈{n,m}. Specifically, it is shown that ρ_n×m,α⩽nρ_m,α+mρ _n,α where ρ_ℒ,α=ℒH(α)-log₂|𝒜 _ℒ,α| and that this bound is tight up to an additive term O(n+log m). A polynomial-time coding algorithm is presented that maps unconstrained input sequences into 𝒜_n×m,α at a rate H(α)-(ρ_m,α/m)     

Unloaded Q-Factor of Stepped-Impedance Resonators

The paper presents general expressions for the unloaded Q-factor of stepped-impedance resonators partially loaded with high-dielectric constant ceramics to realize miniaturized microwave bandpass filters. Some theoretical calculations for coaxial resonators are also presented in diagrams to show a correct design optimization of coaxial miniaturized filters. The formulas presented in this paper take into account the imaginary component of the characteristic impedance Z of the lines constituting the resonator; the results previously presented by other authors neglected such an imaginary component of Z. The relevant influence that this imaginary component has for the calculation of the correct unloaded Q of the resonator is pointed out by this paper through a comparison between correct calculations and calculations performed by neglecting the imaginary component of Z. Some experimental results are compared with theoretical calculations.     

Compact bandpass filters for 800-MHz band land mobile radio equipments

Compact bandpass filters for 800-MHz land mobile radio equipment has been developed using coaxial resonators with a high dielectric constant material of εr= 35. The use of dielectric material of high Q and a dielectric substrate for coupling capacitors made possible the construction of compact low-insertion-loss filters. The performance characteristics of these filters are described.     

Comparitive Study of Coaxial Bragg Resonators

A coaxial Bragg resonator can be performed in four kinds of structures: it is constructed by inserting a regular waveguide between two selective Bragg reflectors (being called the upstream reflector and downstream reflector, respectively), or it consists of only two Bragg reflectors without regular waveguide section between them, where connection of these two reflectors is smooth with phase difference Δ??=?0 or is step-changed with corrugation phase difference Δ? = +π or ?π, respectively. The present paper is devoted to a comparative study for the response of reflectivity and quality factor on frequency in these four kinds of coaxial Bragg resonators, including the influences of the location and corrugation-phase difference of the step-changed connection of the two reflectors. Results show that a coaxial Bragg resonator possesses most attractive properties when the corrugation-phase difference is Δ? = +π at the point of connection and the upstream reflector is longer than the downstream reflector.     

Application of inhomogeneous dielectric loading to coaxial resonators

A technique for improving the Q factor of air-filled coaxial resonators by inhomogeneous dielectric loading is reported.     

Backward Wave Oscillators With Coaxial Structures: Dispersion Relation and PIC Simulation

The dispersion relation of a corrugated—wall resonator with an inner coaxial structure has been analyzed as well as the effects of the corrugation period, amplitude and the radius of the coaxial structure on it. Furthermore, we got an output power of 2.1GW at frequency 11.09GHz in a non-uniform slow wave structure by using the PIC simulation software—MAGIC.     

New method for measuring transfer impedance and transfer admittanceof shields using a triaxial cell

Two performance parameters of a cable or connector shield are its surface transfer impedance Z_T and its surface transfer admittance Y_T. A new method for measuring these properties is presented. The use of two different terminations for the cable or conductor under test (CUT) allows one to determine both Z_T and Y_T. Through characterization of the inner and outer transmission lines of the triaxial cell, using time domain reflectrometry, Z_T and Y_T can be determined in amplitude as well as in phase. The phase is obtained by de-embedding the measured S-parameters up to the CUT. The de-embedding of the measurements also allows one to extend the frequency range up to 3 GHz. To illustrate this method a solid shield with a circular aperture and a coaxial cable with a braided shield have been measured and compared, respectively, with theoretical predictions and published results