Impedance Matching and Reradiation in LPTV Receiver Front-Ends: An Analysis Using Conversion Matrices

Linear periodically time-varying (LPTV) circuits are finding increased prominence in reconfigurable transceiver applications. Impedance matching of such circuits to the antenna impedance is essential for fully on-chip receiver topologies. However, deriving the S
₁₁
of an LPTV circuit is non-trivial in general. Moreover, reflections at harmonic offsets from input frequencies can also be expected due to the time-varying nature of the circuit. This paper utilizes the conversion matrix-based analysis technique to compute the S
₁₁
of a general LPTV circuit. Furthermore, it is shown that signal reradiation at harmonic shifts from input frequencies is also obtained as a natural consequence of this analysis. Examples related to mixer-first receivers, switched-capacitor receiver front-ends (with reset), and Filtering-by-Aliasing (FA)-based receivers are considered to verify the analysis. Design guidelines are provided to attain optimal S
₁₁
in a few such scenarios. Explicit analytical expressions are derived for reradiation in ideal N-path mixer-first receivers and FA-based receivers, while guidelines are provided for proper choice of conversion matrix expressions/sizes in case of numerical computation.