Radio Transmission Formulae

Abstract

A radio transmission formula is derived by summing the fields due to an infinite number of reflected waves. The problem is rigorously solved for two parallel infinitely conducting planes, and an approximate solution is obtained for two concentric conducting spheres of finite conductivity. The results thus obtained are found to be in accord with those obtained by G. N. Watson in 1919 by the use of spherical and zonal harmonics. The method here employed approximates much more closely to the point of view adopted by recent workers in the radio field and adapts itself more readily to a study of gradually varying boundaries. A modification in the coefficient of the exponential term in the Austin long wave radio transmission formula which alters it from $(\frac{120\ensuremath{\pi}\mathrm{lI}}{\ensuremath{\lambda}\ensuremath{\rho}}){(\frac{\ensuremath{\theta}}{sin\ensuremath{\theta})})}^{\frac{1}{2}}\mathrm{exp}[\ensuremath{-}\frac{0.0015\ensuremath{\rho}}{{\ensuremath{\lambda}}^{\frac{1}{2}}}]$ to $(\frac{120\ensuremath{\pi}\mathrm{lI}}{\ensuremath{\lambda}}){(\frac{3\ensuremath{\pi}\ensuremath{\theta}}{8phsin\ensuremath{\theta}})}^{\frac{1}{2}}\mathrm{exp}[\ensuremath{-}\frac{0.0015\ensuremath{\rho}}{{\ensuremath{\lambda}}^{\frac{1}{2}}}]$ is suggested by the analysis and a theoretical justification for the ${\ensuremath{\lambda}}^{\ensuremath{-}\frac{1}{2}}$ in the exponent for the case of long wave transmission is emphasized. The results obtained by the application of the modified formula to the long wave transmission data obtained by Guierre is discussed and an improvement in the agreement found.