Electrical Breakdown Calculator

DC Inputs

Gas / Dielectric

Pressure Torr

Gap Distance cm

Applied Voltage V

Your system voltage — used to compute safety margin

Paschen law (L&L Eq. 14.3.9):
V₂ = B·pd / [ln(A·pd) − ln(ln(1 + 1/γ))]
Townsend coefficients (L&L Table 14.1):
α/p = A·exp(−Bp/E)
Breakdown when α sustains avalanche: secondary electrons (γ_se) maintain discharge.

RF / Microwave Inputs

Gas / Dielectric

Pressure Torr

Gap Distance cm

Electrode spacing or waveguide gap

Frequency MHz

RF: 1–100 MHz | Microwave: 1000+ MHz

Peak Voltage V (peak)

Peak voltage across the gap

Effective field method (L&L Eq. 18.1.41):
E_eff = ν_m·E₀ / [√2·√(ω²+ν_m²)]
Maps the oscillating field to a DC-equivalent for Townsend ionization analysis. RF breakdown voltage scales as √(1 + (ω/ν_m)²) above the DC Paschen value.

Paschen Curves (log–log scale)

Townsend Coefficients (L&L Table 14.1)

Gas	A (cm⁻¹·Torr⁻¹)	B (V·cm⁻¹·Torr⁻¹)	γ_se	E_iz (eV)	Source

Full source list:
A, B coefficients: Lieberman & Lichtenberg, Principles of Plasma Discharges and Materials Processing, 2nd ed., Wiley (2005), Table 14.1. Fits to experimental data from Petrovič & Marić (2004). CO₂ from Meek & Craggs, Electrical Breakdown of Gases, Oxford (1953) and Raizer (1991) Ch. 2. SF₆ from Rabie et al., J. Phys. D: Appl. Phys. 46, 334004 (2013).
γ_se values: Representative values from Raizer, Gas Discharge Physics, Springer (1991) and von Engel, Ionized Gases, Oxford (1965). Actual γ_se depends strongly on cathode material — see L&L Tables 14.2a/b.
E_iz (ionization energies): NIST Atomic Spectra Database.
ν_m (RF tab): Estimated from momentum-transfer cross-sections via LXCat (Phelps & Morgan databases) and the NRL Plasma Formulary.

Liquid Dielectric Inputs

Fluid A

Fluid B

Blend 50% A · 50% B

Volume fraction of Fluid A (drag to blend)

Applied Voltage V

Peak or DC voltage across the gap

Gap Distance mm

Electrode spacing in millimeters

Liquid breakdown model:
Liquids do not follow Paschen's law. Breakdown initiates via streamer propagation and depends on pulse duration, electrode geometry, impurities, and temperature.
Mixed-fluid ε_r and E_bd use linear volume-fraction interpolation — a practical engineering approximation.
E_applied = V / d

Nature of the data

DC breakdown voltages are computed from the Paschen equation (Lieberman & Lichtenberg Eq. 14.3.9) using Townsend ionization coefficients from Table 14.1. These are classical, well-established models appropriate for uniform-field DC gaps in the pressure-distance range where Paschen's law holds (roughly 0.1–100 Torr·cm).

Townsend coefficient accuracy

The A and B coefficients are curve-fit parameters valid over a limited E/p range. For most common gases the fits are accurate to within ~10–20% in the Paschen minimum region. SF₆ values are from Rabie et al. (2013) and may deviate at high E/p due to attachment and detachment processes not captured by the simple Townsend model.

Secondary electron emission (γ_se)

The γ_se values used are representative gas-phase estimates. Actual secondary emission depends heavily on cathode material, surface condition, and contamination. See L&L Tables 14.2a/b for cathode-material-specific data. Errors in γ_se shift the calculated Paschen minimum but have smaller impact on breakdown voltage at higher pd.

RF / Microwave limitations

RF breakdown predictions use the effective-field mapping (L&L Eq. 18.1.41), which converts the oscillating field to a DC-equivalent using the estimated collision frequency ν_m. This approach is valid in the intermediate-to-collisional regime. Additional phenomena not modeled include:

Multipactor discharge (important in vacuum at <50 mTorr)
Electron diffusion losses at low pressure and high frequency
Non-uniform field effects in cavity resonators
Stochastic heating at very high frequencies

For rigorous microwave breakdown analysis consult MacDonald (1966) and Raizer (1991) Ch. 13.

Intended use

This calculator is for educational and preliminary engineering estimation. Results should not be used as the sole basis for high-voltage system design, safety margins in energized equipment, or critical research measurements without verification against experimental data or detailed simulation.

No warranty

Abeyant Maker makes no warranty regarding the accuracy or fitness for purpose of any calculated values. Users assume full responsibility for any engineering decisions based on these results.