Matching of fundamental modes at a junction of a cylinder and atruncated cone; application to the calculation of some radiation impedances

The problem of the junction between a cylinder and a truncated cone atfrequencies below the first cutoff of the cylinder is investigated, inparticular for the case of acute angles. An analytical model of the matchingof a cylinder and a truncated cone is derived for the general case of a coneof finite length having a known terminal impedance. When the cone isinfinite and the angle is right, the problem is similar to the classicalproblem of a tube radiating in an infinite baffle. The model is based on ageneral formulation of the junction of several waveguides at low frequencies(when only the fundamental mode propagates in each guide), and on theassumption that at high frequencies, the radiation impedance of the cylinderis equal to its characteristic impedance. The model has the form of anequivalent circuit, and involves several parameters related to the geometry(the areas of the surfaces defining the matching cavity and the volume ofthis cavity). In addition, the model requires one supplementary parameteronly, i.e., the zero frequency value of the added mass (or lengthcorrection), which has to be determined numerically (the Finite ElementMethod is used). Analytical and numerical results agree very well at low andmoderate frequencies, up to the cutoff of the first higher-order mode. Forthe radiation into an infinite flange, the results improve upon those in arecent publication that were obtained by optimization. The case of obtuseangles is more complicated and is briefly discussed. Finally for the case ofinfinite cones, the reflection coefficient is compared to that obtained inprevious studies.