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Why is sense the resistor swapped with the load resistor here constant current source using lm317

and how does this circuit work? From my understanding of circuit output (node at LED anode) will be at constant 1.25V, and it will change with load I = 1.25/R(load). What am I missing?

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up vote 2 down vote accepted

The principle behind this circuit is that the LM317 will work to make the voltage on the ADJ pin always be Vref (1.25V) less than the voltage on OUT pin. Therefore it acts as a current limiter. The sense resistor is sized to choose what current it is limited to.

For the voltage on ADJ to be 1.25V less than OUT, the following must be true:
$$V_{out} - I*R = 1.25$$ where I is the current through the resistor and R is the 1.25 Ohm resistor. Rearranging and solving for Vout,
$$V_{out} = 1.25*(1+I).$$

Let's take the two extreme cases as examples and look at the current in the circuit.

Case 1
The circuit is open exactly as shown in the graphic. In this case, the only load on the circuit is the LED and accompanying resistor. Starting from the OUT pin and assuming the Vf of the LED is 1.2V:

$$V_{out}-1.25*I-1.2V-100*I=0$$ $$I = 0.5mA$$ $$V_{out} = 1.25*(1+0.5mA) = 1.250625V$$

Case 2
The output nodes are shorted together. In this case, we can ignore the LED and its resistor because its current will be negligible. The voltage across the resistor is regulated by the LM317 to be 1.25V less than the OUT pin. Since the output is shorted, it will try to pull as much current as it can. Using Ohm's Law:
$$1.25V = I * (1.25 Ohm)$$ $$I = 1.25V/(1.25 Ohm) = 1A$$ $$Vout = 1.25 * (1+1A) = 2.5V$$ In other words, the LM317 will regulate the voltage on the OUT pin to keep the current to exactly 1A if the circuit is trying to pull more than 1A.

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The LM317 attempts to hold the voltage between the OUT and ADJ pins at 1.25V. With a resistance of 1.25ohm, this means that it will need to output 1A. A very tiny amount of this current will go back into the ADJ pin, and the rest will pass through the load regardless of the actual resistance of the load.

If the load's impedance decreases or increases then the LM317 will output a lower or higher voltage at OUT to compensate, such that the voltage between the OUT and ADJ pins is always at 1.25V.

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