This is a similar circuit to the above and provides a 4 LED bar graph indicating the voltage of a common 3.6 volt Lithium - Ion recharable cell phone battery. The reference voltage is provided by a TL431 programmable voltage source which is set to 3.9 volts where the TL431 connects to the 1K resistor. The lower reference for the LED at pin 14 is set with the 5K adjustable resistor.
The programmed voltage of the TL431 is worked out with a voltage divider (10K 5.6K). The adjustment terminal or junction of the two resistors is always 2.5 volts. So, if we use a 10K resistor from the adjustment terminal to ground, the resistor current will be 2.5/10000 = 250uA. This same current flows through the upper resistor (5.6K) and produces a voltage drop of .00025 * 5600 = 1.4 volts. So the shunt regulated output voltage at the cathode of the TL431 will be 2.5 + 1.4, or 3.9 volts.
Working out the LED voltages, there are three 390 ohm resistors in series with another adjustable (5K) resistor at the bottom. Assuming the bottom resistor is set to 2K ohms, the total resistance is 390+390+390+2000 = 3170 ohms. So, the resistor current is the reference voltage (3.9) divided by the total resistance, or about 3.9/ (390 + 390 + 390 + 2000) equals 1.23 mA. This gives us about .00123*2000= 2.46 volts for the bottom LED, and about .00123*390 = .48 volts for each step above the bottom. So, the LEDs should light at steps of 2.46, 2.94, 3.42, and 3.9. A fully charged cell phone battery is about 4.2 volts. You can adjust the 5.6K resistor to set the top voltage higher or lower, and adjust the lower 5K resistor to set the bottom LED for the lowest voltage. But you do need a 6 to 12 volt or greater battery to power the circuit.