  We study the magnetic excitations of the trimeric magnetic compounds
A$_3$Cu$_3$(PO$_4$)$_4$ (A = Ca, Sr, Pb). The spectra are analyzed in terms of
the Heisenberg model and a generic spin Hamiltonian that accounts for the
changes in valence electrons distribution along the bonds among magnetic ions.
The analytical results obtained in the framework of both Hamiltonians are
compared to each other and to the available experimental measurements. The
results based on our model show better agreement with the experimental data
than those obtained with the aid of the Heisenberg model. For all trimers, our
analysis reveals the existence of one thin energy band referring to the
flatness of observed excitation peaks.
