Compensation theorem for antennas

Compensation theorem: If the impedance Z of a branch carrying current I is changed by ΔZ, the changes in currents everywhere in the network are the same as those produced by a voltage source of value −I·ΔZ (opposing the original current) placed in series with the changed branch, with all other sources replaced by their internal impedances.

   Original           Changed         Compensation network
 --[ Z ]-- I       --[Z+ΔZ]-- I'      --[Z+ΔZ]--(−I·ΔZ)--
                                       gives ΔI = I' − I

So the new current is I' = I + ΔI, where ΔI is found from the compensation source alone.

Use in antenna systems:

• To find the change in antenna current and input impedance when a nearby object, parasitic element or ground changes the impedance of a branch.
• To find the effect of changing a load or tuning impedance at the antenna terminals without solving the whole system again.
• In arrays, to study how changing one element's impedance alters currents in the other (mutually coupled) elements.

The theorem holds for linear, bilateral networks, so it applies to antennas in a linear medium.