Derivation of a stochastic distribution for the radiated energy of unintentional emitters for large frequency bands

Within the last decades, the threat of fast transient electromagnetic pulses is rising, especially since new technologies of sources with higher mobility are available. Therefore, it is important to determine the threshold levels for the breakdown of electronic systems and its subsystems and components. For the determination of these threshold levels, time consuming measurements are necessary leading to an unreasonable expense. Hence, stochastic approaches to describe the coupling characteristics of signals into systems need to be developed. In earlier works, a distribution for the directivity of unintentional emitters has been derived. However, the directivity is only defined for single frequencies (continuous wave signals). This paper introduces the normalized energy in frequency domain for large frequency bands. A stochastic distribution to describe this normalized energy is derived. It is analytically shown that the energy is gamma distributed. Furthermore, the approach is validated by simulations and measurements.