Calculator
Flashlamp pulse forming network (PFN)
Design the LC network that drives the flashlamp of a solid-state laser, simulate the current pulse with the real lamp law and check its limits: explosion energy, life, current density and wall loading. Also for IGBT electronic PFNs.
Network
- Capacitor C
- 183 µF
- Inductance L
- 54.7 µH
- Voltage Vo
- 468 V
- Impedance Zo = √(L/C)
- 547 mΩ
- Damping α
- 0.80
- Lamp Ko
- 12.8 Ω·A½
- Stored energy
- 20 J
Simulated pulse
- Peak current
- 424 A
- Time to peak
- 129 µs
- Width at 1/3 of peak
- 254 µs
- Width at 10 %
- 315 µs
- Energy into the lamp
- 20 J
Lamp limits
- Peak current density
- 2.16 kA/cm²
- Explosion energy Ex
- 615 J
- Fraction of Ex
- 3.25 %
- Estimated life
- over 10⁶ shots
Warnings
No warnings: the design is within the catalog limits.
- Beyond 10⁶ shots, life is set by the electrodes and deposits, not by the explosion formula.
How to use it
- Enter the lamp data: gas, arc length, bore and fill pressure. If the manufacturer gives Ko or Ke, enter them and they replace the calculated ones.
- Pick a mode. Design: enter energy, pulse duration and damping, and get C, L and voltage. Simulate: enter the C, L and voltage you already have and see the pulse. Multi-section network: for a nearly square pulse. Electronic PFN: a capacitor bank switched by an IGBT.
- Check the current plot, the lamp limits and the warnings. With the repetition rate you also get the wall loading and the cooling it needs.
The method
- The lamp follows the Goncz law, V = Ko·√i, with Ko = 1.28·(P/P0)^0.2·l/d (P0 = 450 torr for xenon and 805 for krypton). It holds above about 500 A/cm².
- The design is Markiewicz and Emmett (1966): C = (2·E·α⁴·T²/Ko⁴)^⅓, L = T²/C and Vo = √(2E/C), with T = √(LC) and total duration 3·T. With α = 0.8 the pulse is critically damped.
- The current does not come from an approximate formula: the circuit is simulated with the nonlinear lamp equation. That shows the real peak, the width at 1/3 of peak and whether the current reverses.
- Explosion energy is Ex = Ke·√T, with Ke = Q·l·d (Q = 24,600 for bores up to 8 mm, l and d in cm), and life is estimated as (E/Ex)^-8.5 shots.
- Wall loading is the average power over the inner arc area: up to 15 W/cm² convection is enough, up to 30 W/cm² forced air, and above that liquid.
- Multi-section network: an artificial line of n LC sections gives a nearly square pulse of duration τ = 2·√(L·C). At constant current the lamp acts as a resistance V/I; the classic theory matches the network impedance to it. Since the lamp dynamic resistance is half its static one, in the simulation an impedance of 0.75·V/I keeps the current from reversing at the end, and a first inductor 1.6 times larger lowers the ripple from ±8 % to ±2 %. Both factors can be changed.
Model limits
It does not include triggering or arc expansion, so for pulses shorter than about 100 µs the calculated capacitor is usually larger than needed. The explosion-based life holds in the high-energy regime; beyond 10⁶ shots the electrodes set the life. These are starting design figures: the final pulse is tuned by measuring the current.
Sources
- J. P. Markiewicz and J. L. Emmett, "Design of flashlamp driving circuits", IEEE J. Quantum Electron. QE-2, 1966.
- Excelitas Technologies (formerly EG&G and PerkinElmer), High-Power Water-Cooled Flashlamps: PFN design, explosion, life and cooling.
- Verre & Quartz (VQF), flashlamp catalog: peak current and explosion energy.
- Analog Modules, 8800V application note: IGBT electronic PFN.
- G. N. Glasoe and J. V. Lebacqz, Pulse Generators, MIT Radiation Laboratory Series, 1948: multi-section networks.
- W. Koechner, Solid-State Laser Engineering, Springer: pump sources for solid-state lasers.