It has been recently demonstrated that superconducting transition edgesensors (TESs) behave as weak-links due to longitudinally inducedsuperconductivity from the leads with higher Tc. In this work we study theimplication of this behaviour for TES-based bolometers and microcalorimeterunder ac bias. The TESs are read-out at frequencies between 1 and 5 MHz by aFrequency Domain Multiplexer based on a linearised two-stage SQUID amplifierand high- Q lithographically made superconducting LC resonators. In particular,we focus on SRON TiAu TES bolometers with a measured dark Noise EquivalentPower (NEP) of $3.2 \cdot 10^{-19} W/Hz^{1/2}$ developed for the shortwavelength band for the instrument SAFARI on the SPICA telescope.
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