In this work, the parametric quadrupole resonance caused by the phase modulation of waveform potential is studied. Based on analytical and numerical description of the ion motion in the quadrupole mass filter with the phase modulation, a stability island is found with good ion optical properties such as high ion transmission efficiency (16%), high mass resolution (peak width measured at 10% of peak height, R 0.1 = 6000), the required separation time (100-150 radio frequency [RF] cycles), and good peak shape of trapezoid form. Furthermore, the analysis of the frequency spectrum of the applied potential and the quadrupole mass filter (QMF) acceptance are also presented; a resonance frequency is found from this spectrum. Finally, a suitable stability X-islands with relative modulation frequency, ν = 2 AE β, β = 1 P ,10 ≤ P ≤ 40 , is established and studied in detail. Here, β is the imaginary part of the characteristic exponent of stable solutions to the Mathieu equation. K E Y W O R D S acceptance, disturbance of the working parameters, parametric resonance, phase modulation, resolution, spectrum of the phase modulated RF potential, X stability island 1 | INTRODUCTION Parametric resonance is the phenomenon of oscillation amplitude increase, occurring when system's parameter changes periodically. 1,2 Ion motion in the quadrupole electric fields can be described by the Mathieu equation 3 : d 2 u dξ 2 + a−2qcos2ξ ð Þ u = 0, ð1Þ where u = x or u = y are transverse dimensionless coordinates, a and q are the Mathieu parameters, and ξ is the dimensionless time. In Equation 1, if one parameter, such as a, q or frequency changes harmonically, for some frequencies, it will lead to parametric resonance. 4 Another way to obtain parametric resonance is to use a small auxiliary quadrupole potential. 5-10 As a result, the area of the first stability diagram is divided by instability bands, which form stability islands. The stability diagram of the first stability region is the area on the plane of a, q parameters where ion displacement always remains finite. The upper island has attracted the attention of researchers first, 4-6 because other islands can cross the scan line a = 2λq. The upper island is located near the working tip of the first stability region of the Mathieu equation. The instability bands follow the iso-β lines on stability diagram. The parameter β characterizes the nature of ion motion in the stable region and determines the spectral composition of the ion oscillation 3 :