The Vacuum Impedance and Unit Systems

In the electromagnetic theory, the vacuum impedance Z0 is a universal constant, which is as important as the velocity of light c0 in vacuum. Unfortunately, however, its significance is not appreciated so well and sometimes the presence itself is ignored. It is partly because in the Gaussian system of units, which has widely been used for long time, Z0 is a dimensionless constant and of unit magnitude. In this paper, we clarify that Z0 is a fundamental parameter in electromagnetism and plays major roles in the following scenes: reorganizing the structure of the electromagnetic formula in reference to the relativity; renormalizing the quantities toward natural unit systems starting from the SI unit system; and defining the magnitudes of electromagnetic units