Microwave cavity resonators. Some perturbation effects and their applications

Lagrange's equation is utilized to show the analogy of a lossless microwave cavity resonator with the conventional LC network. A brief discussion on the resonant frequencies of a microwave cavity resonator and the two degenerate companion modes H01 and E11 appearing in a cavity is given. The first order perturbation theory of a small deformation of the wall of a cavity is discussed. The effects of perturbation, such as the change in the resonant frequency and the Q of a cavity, the change in the electromagnetic field configurations and hence mixing of modes are also discussed. An expression for the coupling coefficient between the two degenerate modes H01 and E11 is derived with the help of the field equations. Results indicate that in the absence of perturbation the above two degenerate modes can co-exist without losing their individual identities. Several applications of the perturbation theory, such as the measurement of the dielectric properties of matter, study of ferromagnetic resonance, etc., are described.

The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems

Use of some new planes such as the R-x, R2-x (where R represents in the n-dimensional phase space, the radius vector from the origin to any point on the trajectory described by the system) is suggested for analysis of nonlinear systems of any kind. The stability conditions in these planes are given. For easy understanding of the method, the transformation from the phase plane to the R-x, R2-x planes is brought out for second-order systems. In general, while these planes serve as useful as the phase plane, they have proved to be simpler in determining quickly the general behavior of certain classes of second-order nonlinear systems. A chart and a simple formula are suggested to evaluate time easily from the R-x and R2-x trajectories, respectively. A means of solving higher-order nonlinear systems is also illustrated. Finally, a comparative study of the trajectories near singular points on the phase plane and on the new planes is made.

Some aids in the design of microstrip components II: Nomograms

Nomograms have been developed for coupled microstrips. With the help of these, it is possible to design various microstrip components. The design of a multiplexer using the directional filter is described and experimental results are given. Nomograms relating the even and odd mode impedances of coupled microstrip lines to the width to height rate and spacing to height ratio have been developed using the relations formulated by Schwarzmann. A multiplexer using directional filters is designed to operate with three channels at frequencies of 3÷3, 3÷4 and 3÷5 GHz and bandwidths of 10 MHz in each channel. Experimental results are given. The design specifications are satisfied reasonably well.

Some adsorption-nucleation-based models for electrochemical phase formation

A new class of models which are based on adsorption, nucleation growth and their coupling is discussed. In particular, the potentiostatic response of a model that involves nucleative phase growth via direct incorporation and adsorptive discharge of metal ions on the free area is analysed for both instantaneous and progressive nucleation. This model is able to predict certain experimental features in the potentiostatic transient, like the initial fall, shoulder or maximum (as well as minimum) which have not been predicted by models analysed hitherto.Limiting behaviour for short and long times as well as a description of the above-mentioned features in terms of model parameters are given.A special case of the above model, viz. a reversible adsorption–nucleation model, wherein the adsorption is very fast, is shown to give rise to transients which can be distinguished from the pure nucleation-growth transients only by its parametric dependence, but not by the form.

Some characteristics of tropical lightning

An integrated and generalized account of the characteristics of lightning flashes observed in the tropics is presented, along with features of tropical lightning which differ from flashes at other latitudes. Several years of lightning recordings were made at two locations in India by using the electromagnetic radiation of the flash in a suitable radio band. The distances of thunder audibility, the number of thunders/hr, the peak flash rate, the flash duration, the time interval between flashes, the duration of flashing activity of a cloud, the number of cells in the lifetime of the cloud, etc. were all found to follow log-normal distributions. Fewer cells were observed to occur in temperate regions, and thunder was found to be associated with ground flashes only.