  We utilize an effective Hamiltonian formalism, within the Floquet scattering
framework, to design a class of driving-induced non-reciprocal components with
{\it minimal} complexity. In the high driving-frequency limit, where our scheme
is formally applicable, these designs demonstrate a leading order
non-reciprocal performance which is inverse proportional to the driving
frequency. Surprisingly, the optimal non-reciprocal behavior persists also in
the slow driving regime. Our approach highlights the importance of physical
loops in the design of these driven non-reciprocal components.
