Transformer coupling and its modelling for the flux-ramp modulation of rf-SQUIDs.

Microwave frequency domain multiplexing is a suitable technique to read out a large number of detector channels using only a few connecting lines. In the HOLMES experiment this is based on inductively coupled rf-SQUIDs (Superconducting QUantum Interference Devices) fed by TES (Transition Edge Sensors). Biasing of the whole rf-SQUID chain is provided with a single transmission line by means of the recently introduced flux-ramp modulation technique, a sawtooth signal which allows signal reconstruction while operating the rf-SQUIDs in open loop condition. Due to the crucial role of the sawtooth signal, it is very important that it does not suffer from ground loop disturbances and EMI. Introducing a transformer between the biasing source and the SQUIDs is very effective in suppressing disturbances. The sawtooth signal has slow and fast components, and the period can vary between a few kHz up to MHz depending on the TES signal and SQUID characteristics. A transformer able to face such a broad range of conditions must have very stringent characteristics and needs to be custom designed. Our solution exploits standard commercial, and inexpensive, transformers for LAN networks used in a suitable combination. A model that allows to take care of the low as well as of the high frequency operating range has been developed.