Stable linear time-invariant systems can be made passive by a feedforward action. In this article, an analytical approach to obtain the matrix which allows to enforce passivity in the system is proposed. This matrix depends only on one parameter, namely alpha. The introduced method is based on the calculation of the characteristic polynomial of the Hamiltonian matrix associated to the Positive Real problem. This polynomial is then used to derive a finite set of values of the parameter alpha, in which the value assuring passivity enforcement with minimum dissipation can be selected. Numerical examples are reported.