  Simple route of engineering topological phases for any desired value of
winding and Chern numbers is found in the Su-Schrieffer-Heeger (SSH) model by
adding a further neighbor hopping term of varying distances. It is known that
the standard SSH model yields a single topological phase with winding number,
$\nu=1$. In this study it is shown that how one can generate topological phases
with any values of winding numbers, for examples, $\nu=\pm 1,\pm 2,\pm
3,\cdots,$ in the presence of a single further neighbor term which preserves
inversion, particle-hole and chiral symmetries. Quench dynamics of the
topological and trivial phases are studied in the presence of a specific
nonlinear term. Another version of SSH model with additional modulating nearest
neighbor and next-nearest-neighbor hopping parameters was introduced before
which exhibit a single topological phase characterized by Chern number,
$\mathcal C=\pm 1$. Standard form of inversion, particle-hole and chiral
symmetries are broken in this model. Here this model has been studied in the
presence of several types of parametrization among which, for a special case
the system is found to yield a series of phases with Chern numbers, $\mathcal
C=\pm 1,\pm 2,\pm 3,\cdots.$ In another parametrization, multiple crossings
within the edge states energy lines are found in both trivial and topological
phases. Topological phase diagrams are drawn for every case. Emergence of
spurious topological phases is also reported.
