  The Transition-Edge Sensor (TES) is an extremely sensitive device which is
used to measure the energy of individual X-ray photons. For astronomical
spectrometry applications, SRON develops a Frequency Domain Multiplexing (FDM)
read-out system for kilopixel arrays of such TESs. Each TES is voltage biased
at a specific frequency in the range 1 to 5 MHz. Isolation between the
individual pixels is obtained through very narrow-band (high-Q) lithographic LC
resonators. To prevent energy resolution degradation due to intermodulation
line noise, the bias frequencies are distributed on a regular grid. The
requirements on the accuracy of the LC resonance frequency are very high. The
deviation of the resonance frequencies due to production tolerances is
significant with respect to the bandwidth, and a controller is necessary to
compensate for the LC series impedance. We present two such controllers: a
simple orthogonal proportional-integrating (PI) controller and a more complex
impedance estimator. Both controllers operate in baseband and try to make the
TES current in-phase with the bias voltage, effectively operating as
phase-locked loops (PLL). They allow off-LC-resonance operation of the TES
pixels, while preserving TES thermal response and energy resolution. Extensive
experimental results -- published in a companion paper recently -- with the
proposed methods, show that these controllers allow the preservation of single
pixel energy resolution in multiplexed operation.

Instrumentation and Detectors;Instrumentation and Methods for Astrophysics;Systems and Control;Systems and Control