New tools for theoretical comparison of rectangular and sine wave operation of ion traps, guides and mass filters

The first completely digital quadrupole mass filter was recently introduced. There is now a need to understand and demonstrate the benefits of digital operation and compare them to the commercial standards. Our work to date has demonstrated that sine and square wave operation are very similar because of their similar stability diagrams and because they use a direct current (DC) potential between the electrode pairs to narrow and limit the mass range. In contrast, rectangular wave-operated digital mass filters and ion traps narrow and limit the stable mass range with the waveform duty cycle without the need for a DC potential. To understand and compare the differences between rectangular and sinusoidal modes of operation, our group has developed new spreadsheet tools that permit calculation of the m/z versus frequency space stability diagrams with the application of a DC potential between the electrode sets for rectangular and sine waveforms, and plots of the pseudopotential well depth against the entire range of stable m/zs for rectangular and sine waveforms. Our spreadsheets were used to make comparisons between fixed-frequency variable-voltage and fixed-voltage variable-frequency modes of operation. They provide a comprehensive companion tool for operating in the laboratory frame and are tunable to the instrument. This manuscript introduces these tools as it compares sine and rectangular wave modes of operation and provides a basis for understanding the advantages and disadvantages of digital operation relative to conventional technology.