Abstract:
In this paper, the general mathematical theory of linear
passive one-ports and the class of positive real functions are briefly
reviewed as background material. Then a time domain method for
synthesis of a finite lumped RC system is given, which involves
breaking down the given system into n subsystems. Finally, it is
shown that one method of separation of a finite number of exponentials
from a given completely monotonic curve over a finite interval is
related to the above mentioned method of time domain synthesis.
Here the given curve is treated as the impulse response of a finite
lumped RC system. It is shown that the parameters being sought
are related to the eigenvalues of the system matrix and the first
components of the orthonormal eigenvectors corresponding to those
eigenvalues, and it is proved that the system matrix has distinct
positive eigenvalues.
