We analyze the kinematic conditions under which the scattering of equivalent massive spin-1 vector bosons factorizes out of the complete process. In practice, we derive the conditions for the validity of the effective W approximation, proposed long ago but never established on a firm basis. We also present a parametric estimate of the corrections to the approximation and explicitly check its validity in two examples.

In this article, the authors conduct a study of bending effects of a paper‐based printed antenna in order to predict the behavior of an antenna placed inside a package with restricted dimensions. The study begins with a model of an electrical dipole consisting of two misaligned parts to evaluate qualitatively the effect of the angle between two parts and the proportion of their lengths on the radiation properties of the dipole. In order to validate the theoretical prediction, a wide‐band “mushroom‐shaped with two arms” monopole antenna structure printed on 0.104 mm thick paper is proposed. This antenna covers a very wide frequency range from 1.8 GHz to over 10 GHz, including two WLAN bands. Its radiation patterns are nearly omni‐directional at 2.45 and 5.5 GHz. The study of substrate bending effects shows that the matching properties of the antenna are maintained, but the antenna radiation patterns are rotated by an angle with respect to the case without bending. The results of our study can be used to predict the performance of an antenna when it is deformed in a telecommunication set‐top box with restricted dimensions.

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