  We report on the development and demonstration of a MHz frequency domain
multiplexing (FDM) technology to read out arrays of cryogenic transition edge
sensor (TES) X-ray microcalorimeters. In our FDM scheme, TESs are AC-biased at
different resonant frequencies in the low MHz range through an array of
high-$Q$ LC resonators. The current signals of all TESs are summed at
superconducting quantum interference devices (SQUIDs). We have demonstrated
multiplexing for a readout of 31 pixels using room temperature electronics,
high-$Q$ LC filters and TES arrays developed at SRON, and SQUID arrays from
VTT. We repeated this on a second setup with 37 pixels. The summed X-ray
spectral resolutions $@$ 5.9 keV are $\Delta E_{\rm 31 pix ~MUX}=2.14\pm0.03$
eV and $\Delta E_{\rm 37 pix ~MUX}=2.23\pm0.03$ eV. The demonstrated results
are comparable with other multiplexing approaches. There is potential to
further improve the spectral resolution and to increase the number of
multiplexed TESs, and to open up applications for TES X-ray microcalorimeters.
