Approximate formulas for frequency dependence of microstrip parameters

Some commonly used formulas for the frequency dependence of microstrip parameters have a number of shortcomings such as limited range of validity and faulty asymptotic behaviour. Therefore it is recommended to use the planar waveguide model with a recently published dispersion formula and a modified formula for the effective width.     

Approximate formulas for step discontinuities in circular waveguides

The authors discuss approximate formulas to determine the normalised impedance for a discontinuity between two concentric circular waveguides. These formulas are used for the computation of step transformers. Experimental results validate these approximations.<>     

Noise-figure expressions for crossed-field amplifiers

Noise-figure expressions for crossed-field amplifiers are presented in a compact and unified form by making use of normal-mode amplitudes. Expressions are given for space-charge-wave amplifiers and cyclotron-wave amplifiers, and are applicable for both forward- and backward-wave amplifiers when the power gain appropriate to each amplifier is used.     

Approximate optical gain formulas for 1.55-μm strainedquaternary quantum-well lasers

We have used an efficient analytical model to calculate the optical gain of the strained quantum-well laser of InGaAsP-InP material system. Based on the anisotropic effective mass theory, empirical formulas delineating the relations between optical gain, emission wavelength, well width and material compositions are obtained for 1.55-μm In_1-xGa_xAs_yP_1-y quaternary strained quantum-well lasers. Results show a logarithmic relation between the peak optical gain and carrier concentration for all possible material compositions of the quaternary system. We show that the logarithmic relation can be derived algebraically     

Approximate formulas for the far field and gain of open-ended rectangular waveguide

Approximate formulas are derived for the far field and gain of standard, open-ended, rectangular waveguide probes operating within their recommended usable bandwidth. (Such probes are commonly used in making near-field antenna measurements.) The derivation assumes first-order azimuthal dependence for the fields, and anE-plan pattern given by the traditional Stratton-Chu integration of the transverse electric (TE_{10}) mode. TheH-plane pattern is estimated by two different methods. The first method uses a purelyE-field integration across the end of the waveguide. The second, more accurate method approximates the fringe currents at the shorter edges of the guide by isotropically radiating line sources. The amplitude of the line sources is determined by equating the total power radiated into free space to the net input power to the waveguide. Comparisons with measurements indicate that forX-band and larger waveguide probes, both methods predict on-axis gain to about 0.2 dB accuracy. The second method predicts far-field power patterns to about 2 dB accuracy in the region90degoff boresight and with rapidly increasing accuracy toward boresight.     

Coupled-mode equations for crossed-field beam tubes

The coupled-mode equations or a thin beam in a crossed-field electron ube are given for the general case of a noncentered beam.     

Noise-figure calculations for crossed-field forward-wave amplifiers

The problem of finding an adequate model for derivation of noise-figure expressions for crossed-field forward-wave amplifiers is investigated. The modified Llewellyn-Peterson equations are used for the portion of the beam near the cathode. Four waves, two cyclotron waves and two space-charge waves, are used for the space connecting the gun and interaction region. Noise-figures are found by considering five waves in the interaction region. The results are very close to those found when only the space-charge waves are considered in the development of the equations for both drift and interaction regions. A matrix, like the space-charge-wave matrix for O-type beams, giving the transformation of beam fluctuations along a drifting, crossed-field stream including the effects of four waves is presented. Expressions for fluctuations of transverse velocity and beam center of gravity are derived to account for all the excitation quantities which are believed to be important in crossed-field amplifiers. The transformation of fluctuations of beam position, or center of gravity, along an accelerating stream is derived. Calculated values of noise figures are far in excess of experimental values. The reasons for the discrepancies are discussed.     

Approximate formulas for the thermal resistance of IMPATT diodes compared with computer calculations

Two analytical formulas, which allow the thermal resistance to be calculated approximately for layered heat sinks with finite radii, are presented. They are shown to agree closely with finite-difference computer solutions of the steady-state heat equation for typical diode structures. The approximations allow rapid calculations without recourse to a computer.     

Approximate SIR and BER formulas for DS-CDMA based on radiationpattern characteristics of adaptive antennas

Approximate formulas are presented for the signal to interference gain and the bit error rate when radiation pattern characteristics such as the beamwidth and average sidelobe level are considered for adaptive antennas in DS-CDMA. These formulas can be used to produce results easily for a range of ideal or effective values and hence provide a fast and simple way to evaluate the performance of an adaptive antenna in a DS-CDMA system     

Coupled-mode analysis for nonuniform crossed-field drift beams

Coupled-mode theory is used to describe the propagation of waves on a nonuniform crossed-field beam in a drift region. The nonuniformity considered in this paper is due to potential variation along the beam. Numercial solutions are obtained for the normal-mode amplitudes for two types of potential variation, namely, linear and exponential. It is shown that the coupling between the modes, which is due to the potential variation, can be used to reduce the noise figure of crossed-field amplifiers.     

A design method for crossed-field electron guns

A design method for crossed-field guns based on a space-charge-flow solution in crossed fields is given. By using the method of analytic continuation in the complex plane, it is shown that it is possible to find the exact form of the electrodes required The design results in a gun similar to the French "short gun" with the great advantage that the current emitted from the gun and the current density at the cathode can be predicted. It is also shown that by making certain approximations to the exact space-charge-flow solution, a new type of gun can be designed, a "long gun" which can have extremely high convergence. The theory for this latter gun is extremely simple and the electrode shapes can be given entirely in analytic form.     

Pump-free crossed-field free-electron laser

Starting from basic concepts, we propose a new kind of free-electron laser (FEL): the pump-free crossed-field FEL in which the condition E_o+V_o×B_o=0 is not satisfied, and the electron orbit without radition fields and undulator or wiggler fields is not straight line (in planar configuration) or cycloid (in magnetron-like configuration). This paper presents a fluid dynamical analysis of the pump-free crossed-field FEL, in which the space charge effect is not taken into consideration. FEL instability is found near resonance \(\omega _{ \pm 1} - k\dot z_a = 0\) . While no FEL instability is found near resonance \(\omega _q - k\dot z_a \pm \sqrt {1 - \beta \mathop z\limits^2 a^\omega o} = 0\)      

Broad-band injected-beam crossed-field amplifiers

The design and operation of injected-beam-crossed-field amplifiers, which provide efficient amplification over octave frequency bands with grid control in compact PM Focused format, are described. Dielectric supported meander lines, which are used to provide the low-dispersion and high-interaction impedance required to achieve octave bandwidth, are detailed. Relationships between space charge, gain factor, beam impedance, circuit loss, and circuit dimensions are derived for design optimization. An electron gun with a negative grid, which provides noise suppression, as well as a nonintercepting current control electrode, is shown to be effective in controlling the beam current continuously from zero to full operating value. Operating characteristics of production CFA's, providing 1 kW of average power in pulsed and CW operation and up to 5-kW peak pulsed power, are presented to illustrate the inherent multimode performance which can be achieved with low-voltage grid control.     

Accurate closed-form formulas for the electromagnetic parameters of squared coaxial lines

This article presents a set of accurate closed-form formulas for the electromagnetic parameters (inductance (L), capacitance (C) and characteristic impedance (Z_c)) for squared coaxial lines with circular and square inner conductor. The analytical expressions, deduced from rigorous analysis by the finite element method (FEM), method of moments (MoM) and curves fitting techniques, can be easily implemented in CAD simulation tools, to design components for wireless communication. This study presents accurate and suitable general expressions for all squared coaxial lines with a wide range of outer to inner conductors ratio between 1.2 and 10. As an application, we present the design of 60 GHz branch line couplers.     

A crossed-field multisegment depressed collector for beam-type tubes

The velocity-dependent action of crossed electric and magnetic fields can be used to sort the electrons of the spent beam of a klystron or traveling-wave tube into two or more velocity classes, and to collect each class of electrons at a potential appropriate to its velocity. Secondary electrons produced at the collection surfaces do not return to the interaction space of the tube because of the nonreciprocal action of the crossed fields. An experimental tube permitted two-segment operation with 20 per cent of the beam power dissipated in the collector at small signals. Velocity sorting that permitted operation near this percentage of beam power over a considerable range of RF signal levels was observed. The major limitation was found to be migration of secondary electrons within the collector region from low-potential to high-potential electrodes, and this process prevented the depression of the collector power below 20 per cent of the beam power.     

Simple sensitivity formulas in terms of immittance parameters

Simple formulas are derived for computing the sensitivities of a network function with respect to its network elements for a lumped/distributed active network. These formulas are in terms of immittance parameters of an augmented network. It is shown that these formulas may be used directly for the computation of higher-order sensitivities.     

弱导非线性自聚焦光纤无量纲模式参量的变分公式

用变分法导出了弱导近似下非线性自聚焦光纤线偏振模的无量纲在量和传播常数的解析式，结果由归一化频率，光功率和临界自降焦功率给出。