| The "ballast" needs to provide a series impedance to the lamp circuit in order to drive the lamp at the designed current.
In order to eliminate as much power losses as possible, this impedance is a reactance. A reactance phase shifts the current from the voltage by 90deg.
If the ballast is an inductor, so a series choke (when OCV could be the same as the mains), or a HX (auto-)transformer, the current is lagging behind the voltage.
These ballasts are the simplest and cheapest, as the only part there is the inductor or the HX transformer (a transformer designed so it exhibits certain inductance in series with the output, usually accomplished by a magnetic shunt with an air gap between the primary and secondary). The drawback for the HX transformer is, the primary has to handle all the reactive power, leading to higher losses and/or need for heavier winding for the given power rating.
But the ballasting impedance could be a capacitor, so then the current phase is leading the voltage. With discharges there can not be the capacitor only, but it should have an inductor as well, the capacitor reactance is just larger, so once the inductor's one is subtracted, you get the desired ballasting impedance. This arrangement is more complex, so it is mainly used (in the 120V areas where voltage boost is required) with a transformer ballast, where the transformer is designed as a HX as well, providing the required series inductance. The lead reactive power of this ballasting style is then compensated by an air gap in the primary core section, so it does not reach the primary winding, reducing the load on it, so allowing lower losses or lighter ballast for the given power. It is this reason, why most "full power" single lamp magnetic ballasts are of this type. The drawback is the extra cost of the capacitor, but for the full power ballasts it is justified.
With just a series reactor (an inductor and capacitor in series) preheat ballasts (mainly the "230V" market) this is used only in multilamp ballasts.
Often with multi lamp ballasts (or in multilamp fixtures) a "lead-lag" arrangement: Some lamps are connected to branches arranged as "lag", other as "lead". The aim is to compensate the reactive power before it reaches the primary (on the 120V US ballasts) so it minimizes the losses and it makes the lamps 100/120Hz flicker off phase, so the overall light output exhibits less of it.
And it is the phase shift direction of the lamp current vs the mains voltage, what gives the name:
"lag ballast" using only inductive reactance,
"lead ballast" when using capacitive reactance
and "lead-lag" with multilamp ballasts when some branches use inductive and other capacitive reactance.
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