Modeling Inductances of Wiring for a TES Array Read by FDM

Large Transition Edge Sensor (TES) arrays, required for the SAFARI imaging spectrometer on a planned SPICA space telescope, will be read out by Frequency Division Multiplexing (FDM). All the pixels are connected with densely packed and equally long superconducting wires. Inductive coupling between wire pairs forms critical performance issues. Mutual inductance is one of the origins of electronic crosstalk among pixels. We find that available literature is not complete in providing suitable calculation methods for the required modelling. In this paper, we describe a relatively fast inductance calculation method for long, arbitrary wires, which can be useful for analyzing crosstalk between pixels and can also be important for guiding wiring layout design. The mutual inductance between two wire loops is calculated using Neumann's formula by a double summation of analytical expressions implemented in Python. Self-inductance for a multi-segment wire can be calculated by the summation of self-inductance of each wire segment and the mutual inductance between all segments. Combining this method with other modelling techniques, we have simulated the inductances of an entire 160 pixel FDM test setup.