1kohm resistors setup as a voltage divider to make a ground (+2.25v, 0v, -2.25v)
Ok, so this is called "0V voltage source of 500 ohms output resistance".
I connect the negative voltage to pin 11 and the positive voltage to pin 4.
I always tie GND directly and Vcc via a small resistor. LM324 should not pull more than several mA so tying it your way shortens its operating life
Use 22R resistor for 0.2A short circuit current to tie Vcc instead.
R1 is 1kohm and RF is 1kohm. So shouldn't this mean that if the non-inverting input is fed 0.5v, then the output should be 1v? AV = 1k / 1k + 1. So AV is 2?
No, it is not. You have tied R1=1k to a 0V reference with 500R. So that means a reference voltage is tied to inverting node via 1k5 resistance.
The problem is when I feed 0.5v into the non-inverting pin, I get 0.65v on the output. Is there something that I am missing?
Voltage source always has its output resistance/impedance.
Recent discussion about that. It may be 1R, may be 1M but it is always there. If you add 1k to 1R then that is a minor issue but not in your case. Just use R1=500R to get what you want. Or use 2k divider and tie that to input directly, as in summing amp configuration.
I am using the center tap of the 1k voltage divider as the ground reference. I know there is a limitation to the output, would my output not even be able to reach 1v and it is just being clipped off?
The output ranges from Vcc-1.5V (+0.75V in here) down to almost GND (-2.25V in here) with low load. You won't reach 1V on the output.