Paschen's Law Breakdown Calculator

Paschen's Law Equation:

\[ V_b = \frac{B \cdot p \cdot d}{\ln(A \cdot p \cdot d) - \ln\left(\ln\left(1 + \frac{1}{\gamma}\right)\right)} \]

B Coefficient:

V/(Torr·cm)

Pressure (p):

Torr

Distance (d):

A Coefficient:

1/(Torr·cm)

Secondary Emission Coefficient (γ):

unitless

Breakdown Voltage (V_b):

Unit Converter ▲

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1. What is Paschen's Law?

Paschen's Law describes the breakdown voltage necessary to initiate an electric discharge (spark) between two electrodes in a gas as a function of pressure and gap distance. It's fundamental in high-voltage engineering and gas discharge physics.

2. How Does the Calculator Work?

The calculator uses Paschen's Law equation:

\[ V_b = \frac{B \cdot p \cdot d}{\ln(A \cdot p \cdot d) - \ln\left(\ln\left(1 + \frac{1}{\gamma}\right)\right)} \]

Where:

\( V_b \) — Breakdown voltage (V)
\( B \) — Material constant (V/(Torr·cm))
\( p \) — Pressure (Torr)
\( d \) — Distance between electrodes (cm)
\( A \) — Material constant (1/(Torr·cm))
\( \gamma \) — Secondary electron emission coefficient (unitless)

Explanation: The equation shows that breakdown voltage depends on the product of pressure and distance (p·d), with constants specific to the gas composition and electrode material.

3. Importance of Breakdown Voltage Calculation

Details: Understanding breakdown voltage is crucial for designing high-voltage equipment, insulation systems, and gas discharge devices like neon signs, plasma reactors, and spark gaps.

4. Using the Calculator

Tips: Enter all parameters in the specified units. Typical values for air: A ≈ 15 1/(Torr·cm), B ≈ 365 V/(Torr·cm), γ ≈ 0.01. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the Paschen minimum?
A: The minimum breakdown voltage occurs at a specific p·d product, below which breakdown voltage increases in both directions.

Q2: How does gas composition affect breakdown?
A: Different gases have different A and B constants. Electronegative gases like SF6 have higher breakdown voltages than air.

Q3: What are typical applications?
A: Used in designing circuit breakers, surge protectors, plasma devices, and high-voltage insulation systems.

Q4: Does temperature affect breakdown voltage?
A: Yes, indirectly through its effect on gas density (pressure). The law technically uses gas density rather than pressure.

Q5: What are limitations of Paschen's Law?
A: It assumes uniform electric fields and doesn't account for electrode surface effects, contamination, or time-varying fields.