Average energy storage by a one-port and minimum energy synthesis

The average energy stored by the elements of a linear passive time-invariant one-port is examined. Except in special cases, the energy storage is not determined by the impedance function
Zo(p)
alone. However, it is shown that for a given
Zo(p)
there is a minimum energy storage for sinusoidal excitation. Further, this minimum energy can be achieved at all frequencies as a minimum energy synthesis.