This article presents the development of an analytic model of variation of power or energy in function of the band width of the IEEE 802.15.4a UWB channel. This analytic model characterizes the fade depth of the channel UWB IEEE 802.15.4a, also shows that the power in the frequency domain of the UWB channel follows a Gamma statistical distribution. The overall results are obtained by simulation in Matlab, validated by Kolmogorov-Smirnov test and calculating the mean square error. Finally the theoretical results are compared with measurement campaigns done by other authors.