# Test #3 - Characteristic Currents

As it is completely useless and often also misleading to compare different pictures with current density plots, we proposed metric which should be equal to one for correctly calculated characteristic vector:

$$\chi_n = \displaystyle \max\limits_p \sqrt{\sum\limits_{q=-p}^{p} \Bigg| \int\limits_\varOmega \boldsymbol{\hat{J}}_n \left(\boldsymbol{r}\right) \cdot \boldsymbol{\hat{J}}_{pq}^\mathrm{TM/TE} \left(\boldsymbol{r}\right) \,\mathrm{d}S \Bigg|^2},$$

where all the current densities are normalized so that

$$\boldsymbol{\hat{J}} = \displaystyle\frac{\boldsymbol{J}}{\displaystyle\sqrt{\int\limits_\varOmega \boldsymbol{J} \left(\boldsymbol{r}\right)\cdot \boldsymbol{J} \left(\boldsymbol{r}\right) \,\mathrm{d}S}},$$

$\boldsymbol{\hat{J}}_n$ is numerically calculated characteristic mode, and $\boldsymbol{\hat{J}}_{pq}^\mathrm{TM/TE}$ is the analytically known characteristic mode (spherical harmonics).

#### Results:

Coefficient $\chi_n$ for spherical shell discretized into 500 triangles (750 RWG functions) at ka = 3/2:

Matlab script generating characteristic currents for TM and TE spherical modes is HERE.

For details see IEEE Trans. Antennas and Propagation paper.

/Edited 17. 07. 2017, MC/