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Using the Kubo-Greenwood formalism the resistivity anisotropy for electrondoped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, hole doped (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$and isovalently doped Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ in their antiferromagneticstate has been calculated in order to clarify the origin of this importantphenomenon. The results show good agreement with experiment for all caseswithout considering impurity states extending over several unit cells ortemperature induced spin fluctuations. From this it is concluded that theresistivity anisotropy at low temperatures is primarily caused by an in-planeanisotropic magnetoresistance. Accounting for the band dispersion with respectto $k_z$ is however mandatory to explain the results, showing the importance ofthe three-dimensional character of the electronic structure for the ironpnictides. Furthermore, it is shown that the counterintuitive sign of theresistivity anisotropy is no fundamental property but just a peculiarity of theanisotropic band structure.

In-plane anisotropic magnetoresistance in antiferromagnetic  Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ and  Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$