The quadrupole consists of four parallel metal rods. Each opposing rod pair is connected together electrically, and a radio frequency (RF) voltage with a DC offset voltage is applied between one pair of rods and the other. Ions travel down the quadrupole between the rods. Only ions of a certain mass-to-charge ratio will reach the detector for a given ratio of voltages: other ions have unstable trajectories and will collide with the rods. This permits selection of an ion with a particular m/z or allows the operator to scan for a range of m/z-values by continuously varying the applied voltage. Mathematically this can be modeled with the help of the Mathieu differential equation.
Ideally, the rods are hyperbolic. Cylindrical rods with a specific ratio of rod diameter-to-spacing provide an easier-to-manufacture adequate approximation to hyperbolas. Small variations in the ratio have large effects on resolution and peak shape. Different manufacturers choose slightly different ratios to fine-tune operating characteristics in context of anticipated application requirements. In recent decades some manufacturers have produced quadrupole mass spectrometers with true hyperbolic rods.
These mass spectrometers excel at applications where particular ions of interest are being studied because they can stay tuned on a single ion for extended periods of time. One place where this is useful is in liquid chromatography-mass spectrometry or gas chromatography-mass spectrometry where they serve as exceptionally high specificity detectors. Quadrupole instruments are often reasonably priced and make good multi-purpose instruments. The single quadrupole mass spectrometer with electron impact ionizer is used as a standalone analyser in residual gas analyzers, real time gas analyzers, plasma diagnostics and SIMS surface analysis systems.