  This paper addresses the analysis and design of non-reciprocal filters based
on time modulated resonators. We analytically show that time modulating a
resonator leads to a set of harmonic resonators composed of the unmodulated
lumped elements plus a frequency invariant element that accounts for
differences in the resonant frequencies. We then demonstrate that harmonic
resonators of different order are coupled through non-reciprocal admittance
inverters whereas harmonic resonators of the same order couple with the
admittance inverter coming from the unmodulated filter network. This coupling
topology provides useful insights to understand and quickly design
non-reciprocal filters and permits their characterization using an
asynchronously tuned coupled resonators network together with the coupling
matrix formalism. Two designed filters, of orders three and four, are
experimentally demonstrated using quarter wavelength resonators implemented in
microstrip technology and terminated by a varactor on one side. The varactors
are biased using coplanar waveguides integrated in the ground plane of the
device. Measured results are found to be in good agreement with numerical
results, validating the proposed theory.
