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Frequency domain multiplexing (FDM) is an attractive option for the readout of imaging arrays of microcalorimeters. The most straightforward implementation of FDM is based on alternating voltage (AC) biasing of the individual microcalorimeters. It is clear that for future applications the performance in terms of energy resolution and count rate capability is crucial. We discuss the consequences of AC bias for the performance of a microcalorimeter, and make a direct experimental comparison between the performance of a TES based microcalorimeter AC and DC bias. Modeling, as well as experiments, show that the performance of the device is is very similar in terms of energy resolution and pulse shapes (100 μs effective time constant). The measured energy resolution at 5.89 keV photon energy is 6.3 eV for AC bias at 46 kHz and 5.5 eV for DC bias.