the cap was in series with the lamp.... it was an oil cap... i think 13.5 MFD?? so i guess that means its CWA?
Yes, it is CWA.
and cant run without a cap? why does a ballast f the same construction function so different? is it the amount of windings? or the core type? or something else?
Technically they even both are a high leakage transformers, it is just their parameters what makes them different.
To explain, I will start with more general things that you likely know already, just to remind of the important things there.
Now what is a transformer: A device, where one coil (primary) generates a magnetic field, which (precisely its changes) induce a voltage into that coil (so keeps the current precisely just such, the induced voltage matches the input minus losses), as well as another coil. The power is then extracted from the other coil. The magnetic force generated by the secondary then subtracts from the one generated by the primary, so to keep the flux (the part, which dictates all the voltages) constant (corresponding to the primary voltage and turns). As the flux is the same in both windings, the voltages are forced to match each other all the times, just corresponding to the number of turns.
In case of an autotransformer either the secondary voltage is stacked on top of the input primary (step up), or the primary is extracted as a difference between the input and output secondary (step down).
The high leak transformer is a transformer, which magnetic circuit is on purpose designed so, part of the flux enforced by one coil gets diverted from passing the other, so the voltages may differ. That diversion is made by a magnetic shunt placed between the primary and secondary, which forms a path for the flux part, which correspond to the voltage difference (per unit turn). When the secondary is not loaded, the easiest path for the flux is through both windings, so the no load voltages match the turns. But once some current is drawn from the secondary, the path via the shunt becomes "more attractive" for at least part of the flux, so the secondary voltage becomes different.
Electrically you may imagine that as an extra inductor in series with any winding of a standard transformer. It is even physically correct: When you short the secondary and connect a voltage source to the primary, it forces corresponding flux through it. But the shorted primary does not allow any flux there (the induced current will fight against so no voltage is induced there, hence no flux), so all the primary flux has to pass the way through the magnetic shunt. So with that you have a coil, with some magnetic reluctance in the path of its magnetic flux, so in other words you got an inductor. And that is the inductor you see in the output impedance of the high leakage transformer. That implies, the bypass shunt should be magnetically designed so, it is able to pass the flux needed to be diverted, so all the voltage drop across that virtual inductor.
The high leakage transformer is a basic form of what is sometimes called "integrated magnetic" device: More electromagnetic functions integrated into one common device (the voltage transformation, plus the series inductor in case of a high leakage transformer; there were way more complex systems used mainly in the industry automation). The motivation to use this integrates approach is the fact, than majority of the losses are inside of the coils, so the aim is to make as much of required functionality with as minimum coils as needed - so in our case instead of three windings with separate components (primary and secondary of a transformer, plus the series inductor) we suffice with just two coils, yet still have the same functions there, so we saved almost 1/3 of the losses plus 1/3 of the copper cost; so with the same budget we may make the two remaining coils beefier and so save further losses there when going to integrated approach instead of two separate devices.
Now what is different between HX vs CWA ballasts is the way, how the leakage inductance is used, so how the shunt is designed. So next I will describe it around the leakage inductance as a separate component fed with high enough voltage (OCV), so no voltage transforming function is there:
In "HX" ballast this leakage inductance is the main ballasting impedance in the lamp circuit. So it should be exact and it should never saturate, as that will increase the circuit current with very little control and that we don't want for a lamp ballast (saturation reduces the inductance, so lowers the impedance, hence the higher current). So the magnetic shunt has sufficient cross section with a margin, typically nearly the same as the core in the primary, so it retain sufficient margin towards saturation during normal operation.
The CWA is a bit more complex: There a capacitor is connected in series with the leakage inductance. Because their impedances are 180deg phase shifted from each other, they effectively subtract from each other. ormally they are designed so, the capacitive reactance is the higher one, so part of it remains after the subtraction and forms the ballasting impedance.
Now why to make it so complex: The reason lies in the fact the ballasting impedance is an inductive reactance subtracted from the capacitive one. So when the inductance reduces, less is getting subtracted, so higher the resulting impedance, so lower the lamp current.
And now comes the main magic: As written above, when saturated, the inductance gets reduced. And the saturation happens, when the current is too high. So if you put all together, you get quite simple, yet effective current stabilizing arrangement: Once the current is becoming too high, the inductive part saturates, less is subtracted from the capacitive reactance, so the total ballasting impedance increases, so prevents the current from increasing further. Normally the ballast is designed so, the shunt is driven slightly into saturation, so it leaves some room for the system to vary the ballasting impedance in both ways from the nominal, so in that way so it allows to accommodate quite wide input voltage tolerance and still keep the lamp pretty current constant. And with a constant lamp arc voltage (that was the case for an unsaturated vapor running MV's) a constant current means constant power, even with the mains fluctuating, hence the name "Constant wattage" (although when the load is what varies, it is the current and not power, what is constant with these). Although all CWA's for the same lamp have to have the same resulting ballasting impedance (asuming teh same currents and OCV), they may differ on how big percentage of the capacitive reactance it is. In order to get 120Ohm (that is about what needed for a 175W MV with 220V OCV), you may work as 220-120 (using 12uF/330VAC cap), as well as e.g. 300-170 (using 9uF/450VAC cap) or any other. These then differ in the capacitance they need and its rating, as well as in the losses (later will have higher losses, as the secondary has to be designed for higher voltage), but they differ in the supply range they are able to cover (the usable regulation ratio is the same percentage wise for the inductance, so the same ratio will give larger range for the later). And it is important to note, this regulation principle does not cover only the supply fluctuations, but it is able to cover certain manufacturing tolerances as well.
To make the CWA ballast magnetic complete, there is another air gap in the primary section of the magnetic circuit. The reason is, the overall capacitive nature of the lamp circuit needs some inductive component parallel to the input to make the overall input power factor near unity. The gap in in the primary core does just that. So in fact in a CWA magnetic we have not two, but already three components integrated in one unit with just two coils: The saturating inductor for the current stabilization, the transforemr to change the voltage (120V to the ~220V OCV) and the power factor compensation inductor.
As you see, the main difference between CWA vs HX magnetics is with HX the shunt (the leakage inductance) never saturates so the inductance is important in that unsaturated state, the CWA normally operates in slight saturation. So when you use CWA magnetic as just a HX ballast, the current may be way off and even no one is able to say how much (in that respect the manufacturing tolerances may be very high).
Some ballasts were designed intentionally to protect the magnetic and lamp against a capacitor failure (mainly short circuit), so the current is then way smaller than it is supposed to be.
Others are designed to minimize the losses (see the losses vs regulation range trade off above), so the inductance will be rather low, so it will lead to overcurrent and saturation if connected without the cap.
The only clue is the rated capacitor value: When it is below ~10uF (assume 175W lamp rating and 220V OCV), the current without the cap will be lower than nominal so safe against accidental capacitor short, with ballasts designed for above 10uF (the same lamp and OCV) the current will be higher than normal. When the OCV is higher (ballast rated for probe MH's as well), the corresponding border shifts towards lower capacitances...
