May be possible, but with a challenge because the cores of transformers and ballasts are designed to have different properties
The magnetic effects in the core behave in a similar way to electrical Voltage, Current and Resistance
In electricity :
Ohms law : I = V / R
Current density : J = I / Area
In magnetics :
Magnetomotive Force [IN] - The magnetic force introduced by the coil. This force equals to the current in the coil I times the number of turns N. For example, a coil of 1000 turns of 10mA and of 10 turns of 1A would make the same force. The MMF in magnetics is like voltage in electricity
Magnetic Reluctance [R] - The resistance of the path in which the magnetic field goes to the magnetic field. For example, in "EI" (common for transformers) or "Ei" (common core for lighting ballasts), the path goes through the center leg and one side leg in a closed loop. Steel is good magnetic conductror and have low reluctance, air is poor magnetic conductor and have high reluctance. The Reluctance in magnetics is like resistance in electricity
Magnetic flux [ϕ] - Think of it as how many magnetic field lines are going through the core. The Flux in magnetics is like current in electricity
Magnetic field [B] - Think of it as how many magnetic field lines are going through a unit cross section (like 1 mm^2). The Field in magnetics is like current density in electricity
Ohms law : ϕ = IN / R
Field : B = ϕ / Area
The MMF provides a link from the electrical world to the magnetic world : The current in the coil and the number of turns determine the MMF
The link back is the inductance [L] : L = N^2 / R
And there is a design limitation :
In electricity wires have limited ampacity. That is, J is limited to some maximum value, and if we cross it the wire overheats
In magnetics the Steel in the core have limited capacity for magnetic field. It simply won't contain more than specific magnetic field. If we try to push more, the Steel gets saturated - which means that it loses its magnetic properties
We are limited in size (unless we want a small lamp ballast the size of a welding transformer), so the core cross section area is limited
Which means the 1st design constraint : B = limited Area = limited B * Area = ϕ = limited ϕ = IN / R = limited
The Steel used in the core is electrically conductive. Every layer of Steel (in a cross section) acts as a turn of coil made of Steel, which is shorted. As the ballast or transformer works, this turn will act as an unintentional secondary coil, on which voltage will appear and current will flow. Ths current - Eddy currents - is up to no good and it creates losses, heating the core. The core is broken down to isolated thin plates to break the large current paths, but a small path in each plate remains
The 2nd step to minimize the Eddy currents is to lower the voltage in every such "1 turn secondary coil" :
In transformers, V [pri] / V [sec] = N turns [pri] / N turns [sec]
V [pri] is the voltage of the actual coil, determined by the application (ballast drop voltage according to the lamp requirements, or full 120V or 230V in case of transformer)
V [sec] we want as low as possible
N turns [sec] is 1
so : We want N turns [pri] to be as high as possible, to lower the voltage applied to Eddy current loops
But finally, there are only so much turns that will fit in a ballast or transformer of the size we want (and the more turns and thinner the wire is, the higher is its resistance so electrical losses. So we have to find the best compromise between Eddy current and coil resistance losses)
Now imagine a ballast (choke) and a transformer connected to the input voltage without anything on the output (i.e. a choke too, as the secondary coil is not connected)
With a ballast : When the choke is connected in series with a lamp, we want the lamp's working current to go through. It is significant current, so to allow it, the inductance of the ballast must not be too high. Inductance of lighting ballasts is in the range of like 0.1H for some HID chokes (high current) up to 2H for small PL chokes (low current)
With a transformer : Ideally when it is only connected to input power, but nothing is on the output, we dont want it to draw any current. It does, but it is designed to draw as little current as possible, so the inductance is designed to be very high
Choke :
N = want it moderate L = N^2 / R = want it low so : R = want it high enough (not close to 0)
Transformer :
N = want it moderate L = N^2 / R = want it high so : R = want it low (close to 0)
And here we get it - The core for ballasts have high R, for transformers have low R. It may well be possible to make a working non optimal ballast with low R or transformer with high R, but you have to know the parameters of the core you work with and see if it is do-able
What is the actual structural difference ?
In most ballasts, the E plates and I plates are made so, when the ballast is assembled there is an air gap between the E's center leg and the I's. This is done either by using short I's and not pushing them all the way in (most modern European ballasts), Shorter center leg on the E (in some "transformer shaped" ballasts), or indentation in the I (some Fluorescent ballasts). The air gap introduces high reluctance in the magnetic path
In most transformers, the E plates and I plates are all in the same direction. They are made so, when the transformer is assembled thy fit exactly, minimizing air gaps. In most transformers each plate set is inserted from alternating directions, so there is no "crack" between the block of E's and I's, to distribute that small remaining gap so to reduce its effects as a gap
You may try a different approach, atleast when the ballast is close enough to what the lamp needs :
Get a ballast which is suitable for the current rating, but not for its induction value
Make an autotransformer (with transformer low R core) to change the supply voltage, so the ballast on hand becomes the correct ballast for the lamp at your custom supply voltage
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