Electromagnetic Reverberation Chambers

Appendix 3

Total Field and Total Power Variables

This appendix includes the calculations of the probability density functions and the moments of the total field and power variables. By total variables, we mean the fields or the powers measured by probes or antennas, which simultaneously collects the three E_x, E_y, E_z complex field projections.

A3.1. Total field variables

The total field variable taking E_t as a notation is given by the square root of the sum of six terms made up of all the square complex components of each E_{x y z}projection i.e.:

[A3.1]

The normalized variable of the total field is designated for the occasion by the lower case e_t notation. This variable comes from the extension of the definition introduced in section 3.2.3:

[A3.2]

We find in this formula the standard deviation σ_ν, which is attached to the complex components of E_{x y z}.

A3.2. χ² variable attached to the total field

Knowing that the E_{x y z} variables all follow the normal probability distribution,the square amplitude of the normalized total e_t field will be the χ² variable with six degrees of freedom:

[A3.3]

We can thus add to this variable, the pdf of χ², which is expressed by the notation conventions of ...