Paschen's law
From HvWiki
Paschen's law describes how the breakdown voltage of a spark gap depends on electrode separation and the pressure of the surrounding gas. It states that the voltage required to spark a specific gas is constant if the pressure times separation is. Thus if you halve the pressure and double the separation the breakdown voltage is supposed to be the same. In reality this relationship breaks down completely at low pressures and very short distances.
Breakdown voltage in a gas:
- V is the breakdown voltage in volts
- p is the pressure in atmospheres
- d is the gap distance in meters
The constants a and b depend upon the composition of the gas. For air at standard atmospheric pressure, a = 43.66 and b = 12.8.
Paschen curves
Useful graphs that show breakdown voltages for a given pressure and separation product are called Paschen Curves. Each gas has its own curve. Properly these should have the product on the x axis but it is usually more practical to assume normal atmospheric pressure and give separations on the x axis. Paschen's Law can be used to convert graphs with different axes.
General properties of breakdown voltages
Different gases have different breakdown voltages. Each gas has a minimum sparking voltage. Anything less than this cannot cause a spark no matter how close the electrodes are. The shape of the electrodes also affects the breakdown voltage.
Rules of thumb
Most people use simplistic rules of thumb to estimate spark gap breakdown voltages. Maybe the simplest, and one that isn't particularly accurate, is 1 kV/mm for air at normal atmospheric pressure.
