Analytical model for the signal-to-noise-ratio of drift tube ion mobility spectrometers

While the resolving power of drift tube ion mobility spectrometers has been studied and modelled in detail over the past decades, no comparable model exists for the signal-to-noise-ratio. In this work, we develop an analytical model for the signal-to-noise-ratio of a drift tube ion mobility spectrometer based on the same experimental parameters used for modelling the resolving power. The resulting holistic model agrees well with experimental results and allows simultaneously optimizing both resolving power and signal-to-noise-ratio. Especially, it reveals several unexpected relationships between experimental parameters. First, even though reduced initial ion packet widths result in fewer injected ions and reduced amplifier widths result in more noise, the resulting shift of the optimum operating point when reducing both simultaneously leads to a constant signal-to-noise-ratio. Second, there is no dependence of the signal-to-noise-ratio at the optimum operating point on the drift length, as again the resulting shift of the optimum operating point causes all effects to compensate each other.