Free Resources — Mass Spectrometry Community

Engineering Tools
for Mass Spec Research

Interactive calculators and reference tools built for researchers and engineers working with quadrupole mass filters, RF ion guides, and ion mobility systems. All calculations run locally in your browser — no signup required.

Resolving Power · Coax Cable Reference · Quadrupole Calculator · Mathieu Stability Diagram · RF Resonant Circuit · Ion Kinetic Energy · K₀ / CCS Converter · Ion Funnel Calculator · FET Rise Time · Resolving Power · Coax Cable Reference · Quadrupole Calculator · Mathieu Stability Diagram · RF Resonant Circuit · Ion Kinetic Energy · K₀ / CCS Converter · Ion Funnel Calculator ·
Calculators & Reference Tools

Quadrupole & RF Calculators

Practical design tools for the mass spectrometry community. Compute RF and DC operating voltages, visualize Mathieu stability regions, and plan mass scan parameters for quadrupole mass filters driven by GAA RF systems.

RF & Quadrupole
Quadrupole Mass Filter — RF / DC Calculator
Calculate RF amplitude (V₀), DC voltage (U), and Mathieu parameters for a quadrupole mass filter. The stability diagram is computed via RK4 numerical integration of the Mathieu equation — the same physics used in commercial instruments.
RK4 Integration Mathieu Equation First Stability Region
millimetres
Hz — e.g. 1000000 for 1 MHz
Daltons (unified atomic mass units)
Daltons — peak passband width (e.g. 1.0 = unit resolution)
Operating point: stable
RF amplitude V₀
Volts (0-to-peak)
DC voltage U
Volts
V₀ peak-to-peak
Volts (p-p)
Mathieu q
Mathieu a
a/q ratio
Passband width ΔM
Daltons (Mathieu diagram)
Estimated resolution R = M/ΔM
at target m/z
⚠ Mathieu limit vs. real instrument performance. This calculator shows the theoretical minimum passband set by the Mathieu stability diagram — the best resolution any ideal quadrupole could achieve at a given a/q. In practice, the achievable ΔM is always larger (worse) due to:
  • Quad length / RF cycles — resolution scales with the number of RF cycles an ion experiences in the field. Short quads or low frequencies reduce this count and limit resolution.
  • Ion axial energy — faster ions spend less time in the field and see fewer RF cycles. Lower ion energy improves resolution but reduces transmission and may increase space-charge effects.
  • Fringing fields — entrance and exit field distortions broaden peaks, particularly at low m/z where the passband is wide.
  • Rod geometry — mechanical tolerances and rod roundness affect the purity of the quadrupole field and set a practical resolution floor.
The Mathieu passband is a useful lower bound and correctly predicts how resolution scales with a/q and m/z — but your instrument's practical minimum ΔM must be determined empirically by tuning with a calibration standard such as Agilent Tune Mix.

Mathieu stability diagram — computed via RK4 integration of the Mathieu equation
Computing…

m/z sweep — RF and DC voltages across mass range

Required a/q & DC voltage vs. m/z — for fixed target ΔM

For a fixed ΔM target, the required a/q decreases as m/z increases — meaning the scan line slope must change during a scan to maintain constant peak width in Da. A fixed-slope scan line through the origin gives constant R = M/ΔM but varying ΔM in Da. To hold ΔM constant across the mass range an AMU offset (non-zero intercept) is required — which is why real instruments need gain/offset calibration.

Driving a quadrupole with GAACE hardware? The MIPS RF Quad module and standalone RF Generator are designed to operate at the voltages this calculator produces. For custom frequency or voltage ranges, contact us — we configure systems to your exact geometry.
RF Circuit Design
RF Resonant Circuit — LC, Coil & Reactance Calculators
Four linked tools for designing the LC tank circuits used in quadrupole RF drivers, ion guides, and RF traps. Solve for any LC parameter, design your coil geometry using Wheeler's formula, look up wire gauge specifications, and calculate the RF currents and voltage stress at resonance. All tools are interconnected — changing the coil design automatically updates the frequency and current calculations.
Wheeler Formula LC Resonance AWG Reference Reactance & Current
1 — LC Resonant Frequency Solve any unknown
f = 1 / (2π√LC)  ·  select which parameter to calculate
MHz
µH
pF
Resonant frequency
MHz
Angular frequency ω
Mrad/s
Period T
µs
2 — Air-Core Coil Inductance Wheeler's Formula
L(µH) = r²·N² / (9r + 10ℓ)   [r and ℓ in inches] — single-layer air-core coil
mm (outside diameter)
mm
total turns
Inductance L
µH
Required TPI
turns / inch (close-wound)
Pitch per turn
mm / turn
3 — Reactance & RF Currents at Resonance X = ωL = 1/ωC
At resonance XL = XC. Circulating current I = V / XL. Capacitor stress VC = I · XC.
MHz
µH
V (0-to-peak)
typical 20–200 for mass spec RF
Ω — measure with DMM
Reactance XL = XC
Ω
Circulating current I
A (0-to-peak)
Resistive power loss P
W
Capacitor voltage VC
V (0-p) — check rating!
Resonant capacitance
pF
Driver voltage needed
V (0-p) into tank
4 — Wire Gauge Reference Table AWG · TPI · resistance
Turns per inch assumes close-wound (no gap). For spaced winding, actual TPI will be lower. Coil calculator required TPI: — best-fit gauge highlighted below.
AWG Bare dia. (mm) Insul. dia. (mm) TPI close-wound Resist. (Ω/m) Max I (A) Notes
* Max current ratings are conservative guidelines for chassis wiring. At RF frequencies skin effect increases effective resistance — use heavier gauge or silver-plated wire for high-Q coils.
Using GAACE RF hardware? The RF Generator and RF Mega heads are designed to drive resonant loads in the range these calculators produce. For help matching a coil to your specific quadrupole geometry or load capacitance, contact us.
Ion Optics
Ion Kinetic Energy Calculator
Calculate ion velocity, accelerating voltage, or kinetic energy from mass and charge state. Also computes center-of-mass collision energy for CID experiments — the energy that actually goes into bond breaking when an ion hits a neutral gas molecule.
KE = z·e·V = ½mv² CID collision energy Solve any unknown
Select what to calculate
Daltons (Da / u)
integer (1, 2, 3 …)
Volts
m/s
KE = z·e·V = ½·m·v²
v = √(2·z·e·V / m)
Velocity
m/s
Kinetic energy
eV
Velocity (mm/µs)
mm/µs — useful for TOF
v/c (relativistic check)
fraction of speed of light

Center-of-mass collision energy (CID)
ECM = Elab × Mgas / (Mgas + Mion) — the fraction of lab-frame energy available for bond breaking.
Da — overrides dropdown if "Custom" selected
ECM collision energy
eV
Elab (ion KE)
eV
ECM / Elab ratio
efficiency of energy transfer
Switched Ion Optics
Capacitive Load Power Calculator
Every time a switched voltage is applied to a capacitive load — an electrode, ion gate, or detector — charge must flow to change the voltage. At high switching rates this constitutes a continuous power draw even though no DC current flows through the load. This calculator quantifies load power, peak current, energy per cycle, and driver thermal stress for square wave, sinusoidal, and trapezoidal waveforms. Essential for selecting FET switches, sizing power supplies, and understanding why high-frequency switching of large electrode arrays demands surprisingly large power budgets.
P = C·ΔV²·f Square / Sine / Trap FET switch sizing Multi-channel arrays
Square wave
Voltage switches abruptly between two levels. Each transition moves Q = C·ΔV in a short rise time, producing a large current spike. Power scales linearly with frequency. Ion gates, Bradbury-Nielsen gates, deflectors, trap switching.
Sinusoidal
Current leads voltage by 90° — the load is purely reactive. Power delivered continuously rather than in spikes. FAIMS asymmetric waveforms, RF ion guide drive monitoring, AC-coupled electrode systems.
Trapezoidal
Square wave with finite, controllable rise/fall times and adjustable duty cycle. More realistic for real driver outputs. Peak current set by ΔV/trise. TWAVE electrodes, SLIM switching arrays, shaped pulse ejection.
Ion gate / deflector10–100 pF, 100–500 V, 1–100 kHz. Peak currents of 0.1–5 A are common.
TWAVE electrode arrayMany electrodes in parallel multiply total C. Use channel count to see full supply burden.
SLIM deviceHundreds of electrodes × tens of pF. Total load can reach nF at MHz rates.
FAIMS waveformAsymmetric high-voltage sine at 1–5 MHz. Sinusoidal mode gives the correct estimate.
FET switch selectionIpk sets minimum FET ID rating. Ron×Ipk² determines device heating.
Supply sizingTotal supply current (all channels, with efficiency) sets minimum supply current rating.
Waveform type
P = C · ΔV² · f   |   Ipk = C · ΔV / trise   |   Ecycle = C · ΔV²
Load parameters
pF — measure with LCR meter or estimate from geometry
V — full swing (square/trap) or 0-to-peak amplitude (sine)
Hz — switching rate or drive frequency
ns
Driver parameters
Ω — FET RDS(on) or output impedance
V — DC rail voltage
% — typical FET driver 80–95%
multiply for electrode arrays — TWAVE, SLIM, ion funnels
Results — per channel & total
Load power P
W per channel
Total load power
W (all channels)
Supply current
A from supply
Peak current Ipk
A into cap during rise
Energy per cycle
nJ
Driver dissipation
W in Ron
Charge per cycle Q
nC
Avg charge current
A average
Calculating…

Waveform preview — voltage and current vs time (one cycle)
Waveform preview.
Power vs frequency — log scale · red dot = current operating point
Power vs frequency.
Switching ion optics with GAACE hardware? The FET switch, TWAVE driver, and FAIMS electronics in the MIPS platform are designed to drive the capacitive loads this calculator describes. For help matching a driver to your electrode geometry and switching requirements, contact us.
Vacuum Science
Vacuum Pressure Unit Converter
Convert between all common vacuum pressure units used in mass spectrometry and vacuum technology: Pascal, millibar, Torr, mTorr, atm, psi, and more. Enter a value in any field and all others update instantly.
Torr · mTorr Pascal · mbar atm · psi μbar · μHg
Common mass spec ranges: Foreline / rough vacuum 1–10 Torr  ·  Ion source 10⁻³–10⁻⁵ Torr  ·  Analyser region <10⁻⁵ Torr  ·  Ion trap / ORBITRAP <10⁻⁸ Torr
Vacuum Science
Vacuum Orifice Flow & Gas Load Calculator
Calculate molecular-flow conductance, throughput (gas load), and required pumping speed for a circular orifice or short tube between two vacuum regions. Essential for sizing differential pumping stages and predicting pressure in each stage of a mass spectrometer.
Molecular Flow Conductance Throughput Pump Speed
Orifice conductance (molecular flow): C = 3.638 · A · √(T/M)  [L/s]  ·  Throughput: Q = C · ΔP  ·  Required pumping speed: S = Q / P₂
millimetres
Torr
Torr (must be < P₁ by ≥ 2×)
Kelvin (293 K = 20 °C)
Flow regime: molecular
Results
Orifice area
mm²
Conductance C
L/s
ΔP
Torr
Throughput Q
Torr·L/s
Required pump speed
L/s (at P₂)
Mean free path @ P₁
mm
Designing differential pumping stages? GAACE builds custom MIPS-based control systems for multi-stage instruments. Contact us to discuss your vacuum architecture.
Vacuum Science
Mean Free Path & Collision Frequency Calculator
Calculate the mean free path λ, molecular collision frequency, and molecular number density for a gas at a given pressure and temperature. Includes Knudsen number estimation for a characteristic length — tells you which flow regime your system operates in.
Mean Free Path Knudsen Number Collision Freq. Number Density
λ = kBT / (√2 · π · d² · P)  ·  Z = √2 · π · d² · n · v̄  ·  Kn = λ / L
Torr
Kelvin
mm — tube ID, gap, or cell size
Mean free path λ
Number density n
molecules/cm³
Mean speed v̄
m/s
Collision freq. Z
collisions/s
Knudsen number Kn
λ / L
Flow regime
Mean free path vs. pressure — Air at 293 K
Pressure (Torr) Pressure (Pa) Mean free path Regime (L=10 mm)
Ion Mobility
K₀ / CCS Ion Mobility Converter
Convert between drift time, reduced mobility (K₀), and collision cross section (CCS, Ω) for drift tube ion mobility spectrometry. Supports He, N₂, Ar, and CO₂ buffer gases. Uses the Mason-Schamp equation — the standard relationship used in IMS, SLIM, and travelling-wave mobility experiments.
Mason-Schamp Drift Tube IMS He · N₂ · Ar · CO₂ K₀ ↔ CCS
Conversion mode Select what you want to calculate
Buffer gas
Gas molar mass
28.01
g mol⁻¹
Kinetic diameter
3.64
Typical K₀ range
~2.0–2.5
cm² V⁻¹ s⁻¹
Loschmidt N₀
2.687
×10¹⁹ cm⁻³ (STP)
ms
m
V m⁻¹
Da
K (300 = 27 °C)
Torr

CCS Ω
Ų
Reduced mobility K₀
cm² V⁻¹ s⁻¹
Drift time td
ms
Actual mobility K
cm² V⁻¹ s⁻¹
Drift voltage Vdrift
V (E × L)
Reduced field E/N
Td (townsend)
K → K₀ factor
P·T₀ / (P₀·T)
CCS comparison across buffer gases Same ion, all four gases

Given the K₀ computed above, this table shows the equivalent CCS in each buffer gas at your T and P. CCS values are gas-specific and are not directly interchangeable — a CCS measured in He is not the same physical quantity as CCS in N₂.

GasMolar mass (g/mol)Reduced mass μ (Da)CCS Ω (Ų)K₀ (cm² V⁻¹ s⁻¹)Drift time (ms)
Enter values above to populate table
Physics reference Mason-Schamp equation
K₀ = (3/16) × (ze / N₀) × (2π / μkBT)¹˲ × (1 / Ω)  —  Mason-Schamp
K = K₀ × (P₀/P) × (T/T₀)  —  actual mobility at operating conditions
td = L / (K × E)  —  drift time from mobility and field
Low-field limit valid when E/N < ~5 Td  ·  T₀ = 273.15 K  ·  P₀ = 760 Torr
Constants
e = 1.602×10⁻¹⁹ C  ·  kB = 1.381×10⁻²³ J K⁻¹
N₀ = 2.687×10¹⁹ cm⁻³ (Loschmidt, STP)
u = 1.661×10⁻²⁷ kg/Da  ·  z = 1 (singly charged)
Limitations
Valid in low-field limit (E/N < ~5 Td)
Assumes singly charged ions (z = 1)
Not directly applicable to TWIMS (needs calibration)
CCS values are gas-specific: He ≠ N₂ CCS
Building a drift tube IMS or SLIM system with GAACE hardware? The MIPS platform provides the DC bias, RF drive, and TWAVE control needed for drift tube and SLIM ion mobility experiments. The MFT and SLIM Reverser modules are specifically designed for serpentine SLIM paths. Contact us to discuss your IMS configuration.
Mass Analysis
Resolving Power Calculator — Quadrupole & TOF
Calculate mass resolving power R = m/Δm for quadrupole mass filters and time-of-flight analyzers. The quadrupole mode derives RF cycle count from rod geometry, frequency, and ion kinetic energy, then compares measured R against both a practical empirical benchmark and the Dawson theoretical limit. The TOF mode builds a full time-domain noise budget — detector bandwidth, timing jitter, ion energy spread, extraction pulse width, and collision broadening from residual gas — added in quadrature to give achievable R. Includes reflectron mode, optimum accelerating voltage finder, and bottleneck identification.
Quadrupole Time-of-Flight Dawson Limit Noise Budget Reflectron
Measured peak
Da
Da
Instrument geometry
mm
MHz
eV
derived
m/s
Resolving Power
R = m / Δm
Peak FWHM
Da (measured)
Classification
Cycle count out of range — check geometry and energy inputs.
Resolution benchmark
The Dawson limit assumes a perfect quadrupole field, monoenergetic ions, zero space charge, and no fringe fields. Real instruments fall many orders of magnitude short of this ceiling.
Practical resolution limit
Practical min Δm (Da)
Practical max R
Efficiency vs. benchmark
Empirical: Rmax ≈ 75 × N  ·  Well-built research quadrupoles (5,000–10,000 R at ~100 cycles)
Efficiency vs. practical limit
0%50%100% (benchmark)
Effect of changing geometry
Max R at 2× rod length
Max R at ½ KE
Max R at 2× frequency
v = √(2·KE·e / m). N = (L / v) × f. Practical limit: Rmax ≈ 75 × N — empirical, calibrated to well-built research quadrupoles achieving 5,000–10,000 R at ~100 cycles. Unit resolution (Δm ≈ 1 Da) corresponds to R ≈ m/z. Dawson limit: Δmmin ≈ 0.1 × m / N² — mathematical ceiling for an ideal quadrupole, unachievable due to field imperfections, fringe fields, and ion energy spread.

Driving a quadrupole with GAACE hardware? The MIPS RF Quad module and standalone RF Generator are designed to operate across the voltage and frequency range this calculator produces. Contact us to discuss your geometry.
Ion & instrument
Da
V
m
Detection system
MHz
ns
Ion beam (optional)
eV
ns
Vacuum
Torr
Configuration
derived
derived
Reflectron mode: energy spread cancelled (first order). Effective path length doubled.
Theoretical R
BW limit only
Achievable R
all contributions
Total Δt (FWHM)
ns
Collision prob.
% ions scatter
Classification
Bottleneck
dominant limit
Time-domain contributions (quadrature sum)
Bandwidth
Jitter
Energy spread
Pulse width
Collisions
BW (0.35/BW) Jitter (×2.355) Energy (t·ΔE/2V) Pulse Collisions
Optimum accelerating voltage
Optimum voltage (V)
Max R at optimum V
Flight time at opt. V
Balances bandwidth/jitter (worse at low V) against collision broadening (worse at low V for slow ions). Found by numerical search 200–30,000 V.
Path length & voltage scaling
R at 2× path length
R at 4× path length
R at 2× voltage
t = L × √(m/2eV). Δt² = Δt²BW + Δt²jitter + Δt²energy + Δt²pulse + Δt²collision. Collision broadening: Δtcoll = 2.355 × t × √(L/λ) × (mgas/mion) × √(kT/KE). Mean free path λ = kT/(P·σ), σ = 2×10⁻¹⁹ m². Collision probability = 1 − exp(−L/λ). Reflectron cancels energy spread (first order) and doubles effective path length. Lower accelerating voltage slows ions — longer flight time improves R until collision broadening takes over, creating a resolution optimum at intermediate voltage.
Reference
Coaxial Cable Reference — Parameters & Applications
Key electrical parameters for coaxial cables commonly used in mass spectrometry and ion optics research — impedance, velocity factor, capacitance, dielectric type, voltage rating, and attenuation. Includes application notes specific to RF drive lines, electrometer signals, vacuum feedthroughs, high-voltage pulsers, and trigger routing. Filter by impedance or sort any column.
50 Ω 75 Ω 93 Ω RF & Signal Vacuum Compatible
Filter by impedance
Click column headers to sort
Cable Impedance Vel. Factor Cap. pF/ft Cap. pF/m Dielectric Max V (RMS) Atten. dB/100ft @ 10 MHz Research Applications
Capacitance matters in ion optics. Every picofarad on a high-voltage electrode or electrometer input costs energy to charge and slows signal edges. For electrometer signal cables, minimize length and use low-capacitance types (LMR-200, LMR-400, RG-62). For RF drive lines to ion funnels and quadrupoles, the cable capacitance adds directly to the load seen by the RF generator — use PTFE-dielectric types (RG-316, RG-142) near heated regions or vacuum boundaries. PTFE (Teflon) dielectric cables are preferred for vacuum feedthroughs due to low outgassing. Velocity factor affects electrical length and matters for matched-length trigger or timing lines. Attenuation values are at 10 MHz; attenuation increases approximately as √f — a cable with 1.0 dB/100ft at 10 MHz will show ~3.2 dB/100ft at 100 MHz.
Coming Soon

More Tools In Development

Additional calculators are being developed for the mass spectrometry community. Check back regularly or contact us to request a specific tool.

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Ion Trap Parameter Calculator
Calculate trapping RF amplitude, secular frequency, and pseudopotential well depth for a Paul trap from r₀, z₀, and drive frequency.
Ion Traps
FET Pulser Rise Time Calculator
Estimate rise and fall times from load capacitance and drive resistance. Directly applicable to GAACE FET switch and pulser products (10–15 ns typical).
Electronics
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