The simulation and design of an on-chip superconducting millimetre filter-bank spectrometer

Superconducting on-chip filter-banks provide a scalable, space saving solution to create imaging spectrometers at millimetre and sub-millimetre wavelengths. We present an easy to realise, lithographed superconducting filter design with a high tolerance to fabrication error. Using a capacitively coupled $\lambda/2$ microstrip resonator to define a narrow ($\lambda/\Delta\lambda = 300$) spectral pass band, the filtered output of a given spectrometer channel directly connects to a Lumped Element Kinetic Inductance Detector (LEKID). We show the tolerance analysis of our design, demonstrating $
Comment: 8 pages, 5 figures. Pre-print for proceedings for the Journal of Low Temperature Physics, 19th Low Temperature Detectors Conference (LTD19)