Preheat time: Obviously if you use higher current, the preheat time would be shorter, only with too high current you only might run into troubles with overheating them. Preheat current of 2*Inom leading to 1sec is typical "choice" in lot of many programed-start ballasts as quite good compromise (with simple current mode preheat) for user convenience and lamp life with the assumption of manufacturing tolerances. The goal is to heat up electrodes to temperature, where (the "literature say") filament resistance is 4times the resistance in their cold state, closer you reach, longer the cyclic life. This ultimate goal you might reach by (as best) some feedback system: - Or some active one (theoretically would work as best, but never seen it in real life), where the controller monitor the filament resistance and go to the "ignition" mode when it reach the ultimate "4*Rcold" value - Passive one - supply the filament by the voltage source, so the heating power is reduced automatically by the increasing filament resistance by itself. This method is used in all "infinite start cycles" rated ballasts and CFL's i've seen. The supply for the filament originate from auxiliary "secondaries" on the ballasting choke. The disadvantage is, then the filament can not anymore serve as EOL protection, so the circuity need an active EOL protection, but this is usually of no extra cost, as the programmed start functionality require quite complex controller anyway, so the protection could be build-in easilly. By the way this voltage mode heating is the "concept of choice" even in most US 60Hz RS magnetic ballasts, where it allow to operate electrodes on the correct temperature regardless of the real arc current, so allow the ballast factor to go virtually from zero to about 1.5 (arc current is split into two parts, each flow trough one side of the filament, so no part is overloaded) without
RS circuits "2-stage" starting: This behavior is undesired consequence of the required margin for reliable starting at worse conditions (cold, humidity, thin krypton tubes,...) - the OCV is set quite high. It is so high, as at normal temperatures and dry environment the tube start in cold-cathode glow-discharge even before filaments heat up. The "golden" combination would be, then the discharge does not ignite till the filament reach required temperature. So the lamp would start with some delay at once to full power. The consequence of this behavior is shorter cycle life.
Other reason (mainly on capacitive ballasted "HPF" types) would be the temporary lamp rectification: Each electrode is a bit different, so reach the emission temperature in different time (mainly the real temperature emission border differ here - depend on actual wear,...), so the lamp ignite for current in one direction. This charge the ballasting capacitor by DC offset, what increase the voltage of the "other" polarity, so forces some current even in cold-cathode mode. The result is, then the lamp is (upon power ON) at first dark (no discharge yet at all), then glow dimly (rectification mode; the AC voltage component is high, so the current trough the ballast is low, so low brightness) and then go to full power (both electrodes are hot enough)
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