Like a 7809 0r 7909 voltage regulator, the input of an LM317 adjustable regulator must be at least 2V higher than its output.
The protection circuit you found is used on a Lithium battery to prevent it from EXPLODING or CATCHING ON FIRE. An inverter circuit or a Ni-MH battery doesn't.
The article you found talks about a prevention circuit that prevents overcharging or over-discharging a Ni-MH battery to make it last longer.
You do not want a phone charger. You want a 9V battery charger that maybe you can buy or you can make one.
I don't think an EL inverter has a voltage regulator. The 9V alkaline battery is about 9.5V when brand new and its voltage quickly drops to 7.2V as it is used then slowly drops to 6V. The EL light will simply get a little dimmer that you might not notice.
A car battery is 14.4V when the car is first started then it drops quickly to 13.8V. When the engine stops the voltage slowly drops to 12.6V. A simple series resistor can reduce the voltage to 7V to 9V.
A "8.4V" Ni-MH rechargeable battery is about 9.8V when fully charged that quickly drops to 7.6V then it slowly drops to 7V when it should have its load disconnected.
Will I need any kind of protection circuit then? I know you said a good circuit would not need one but im a little fuzzy on what exactly the good charging circuit is. Is it the circuit where I go 9V charger to the battery with a voltage regulator, is that all it consists of ?
What stops the charger from over charging?
basically what im trying to do is take this inverter put in a rechargeable 9V and splice in a charging port into the existing battery wires then fill the battery compartment with potting so that nothing can get corroded from moisture. So I don't have to replace the battery I just charge the unit.
Forgive me if im frustrating you
If I do find a charger that charges a 9V then do I need to do anything at all to the inverter besides at a charging port? No protective circuit not any thing.
I think you are right just finding a charger with a 9v out put would be better than building it all inside the inverter. I just need to know what I need to put in the inverter now.
When you say it should have it load disconnected does that men if left on it could ruin the battery or cause issues?
Also ive seen where people have made circuits where they use capacitors and regulators in combination when the voltage is above 9V they store it in a capacitor and whe its below the capacitor helps out to equalize. Is that some thing that's hard to do and would it work in my application?
Thanks a lot this is really helpful.