498 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 57, NO. 3, MARCH2008 Performance Simulation of a Quadrupole Mass Filter Operating in the First and Third Stability Zones Thomas J. Hogan and Stephen Taylor Abstract—A method of computation that accurately simulates the performance of quadrupole mass filters (QMFs) is described. Behavior is described by determining the individual trajectories of a large number of ions (10 8 ) as they are injected into the QMF. The effects of the ratio of circular electrode radius r to electric field radius r0 on the performance characteristics have been investigated for zone 1 (a ≈ 0.237 and q ≈ 0.706) and zone 3 (a ≈ 3.16 and q ≈ 3.23) operation. We demonstrate that performance sensitivity to the r/r0 ratio is different for zone 3 than those previously reported for zone 1. The magnitude and variation of the “tail” in the mass spectral peak shapes that are apparent for zone 1 is much decreased for zone 3 and does not influence QMF resolution. Variation in ion trajectories and asso- ciated power-spatial frequency spectra when operated in zones 1 and 3 with varying r/r0 geometrical ratios are also presented. We demonstrate that these provide an alternative method in determin- ing an ideal value for r/r0. Index Terms—Mathieu stability regions, multipoles, power frequency spectrum, quadrupole mass filter (QMF), spatial frequencies. I. I NTRODUCTION Q UADRUPOLE mass analyzers separate ions according to their mass to charge (m/z) ratio and are a vital component of quadrupole mass spectrometers (QMSs) that provide the selective filtering that is necessary to separate the constituent components of the sample under analysis. Ion trap [1], [2], time of flight, and quadrupole mass filter (QMF) are all types of mass analyzers providing differing performance and operational characteristics. Attributes of the QMF have ensured that it has been deployed in a wide range of applications from modest residual gas analyzers to high-end mass spectrometers for molecular analysis. The characteristics that have ensured its widespread use include relatively simple mechanical con- struction, simple drive requirements, acceptable power con- sumption, and a linear mass scale. Modern process control and scientific instrument designers are under constant pressure to increase performance while simultaneously decreasing power consumption and physical size. The mechanical characteristics of the QMF make it suitable for miniaturization through the use of microengineered mechanical system (MEMS) techniques, providing a simultaneous reduction in operating voltage and Manuscript received January 11, 2007; revised June 21, 2007. The authors are with the Department of Electrical Engineering and Electronics, University of Liverpool, L69 3GJ Liverpool, U.K. (e-mail: t.j.hogan@liverpool.ac.uk; s.taylor@liverpool.ac.uk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2007.911632 Fig. 1. End view of the QMF that is constructed from hyperbolic-shaped electrodes with field radius r0 and case radius Rc. Fig. 2. End view of the QMF that is constructed from circular electrodes with electrode radius r, field radius r0, and case radius Rc. power budget. The use of these techniques may require more novel geometries to be developed. Previously reported exam- ples of miniature mass filters include [3]–[5]. For the QMS, ideal performance is obtained when the QMF is constructed from hyperbolic-shaped rods (Fig. 1) that are perfectly aligned. In practice, most commercial QMFs are man- ufactured from circular section electrodes (rods) for reasons of cost and ease of manufacture (Fig. 2), resulting in electric fields that deviate from the ideal. Stability zone 1 (a ≈ 0.23 and q ≈ 0.7) is the normal operating region for most commercial QMSs [6]. There are, however, advantages of mass spectral peak shape, decreased evidence of low-mass “tails,” and in- creased resolution to be gained from operation in the third 0018-9456/$25.00 © 2008 IEEE