Electronic – Not getting 2.5A or 2 A DC current

The point of the current limiter is that, if the current is higher than desired, it will reduce voltage, which with most Ohmic loads will reduce the current draw.

This uses the fact that voltage drop == resistance times current, and the regulator reduces voltage if it sees a voltage on the reference pin that is greater than the reference (1.2V? something like that)

Does this mean that the voltage out from the current limiter is at least 1.2V less than the input? Yes, it does!

However, if you have a microcontroller, and don't need "immediate" feedback (your uC response time is OK) then you can simply sample the voltage drop across a current sense resistor (something small like 0.1 Ohms) to estimate current, and drive any variable resistor, like a regular power transistor, using an analog output from your uC (or a filtered PWM.)

You probably want another solution, like an existing programmable potentiometer in the feedback loop of an opamp, for example. Use a current sense resistor that's small (0.1 Ohms?) and program the amplification of the voltage drop using an opamp. When amplification is 10x, then you get to 1.2 volts at 1.2 amps; when the amplification is 100x, then you get to 1.2 volts at 120 mA.

Is it be correct to say that the CSR = ESR + external resistor = 1.3 + 0.5 = 1.8 ohms?

According to a footnote in the datasheet, "CSR(compensation series resistance) refers to the total series resistance, including the equivalent series resistance (ESR) of the capacitor, any series resistance added externally, and PWB trace resistance to C_O."

In most cases, the trace resistance will be small enough that you can ignore it, and your formula would be correct enough.

Now I would much rather use a ceramic cap, which from what I've read, has an ESR in the milliohms.

Remember that a ceramic cap in the 10 - 15 uF range is going to be fairly large, which can cause reliability issues (due to mismatched CTE between the cap and board).

It looks like a CSR of 0.1 to 2 ohms would be sufficient.

Notice, comparing figs 28 and 29, that the required CSR changes depending on the capacitor value.

And your capacitor value will change depending on voltage and temperature. But 1-3 Ohms total resistance seems to be okay for any capacitance value.

If I use a ceramic cap instead of the tantalum, and if I add an external resistance of say 1 ohm would this yield proper operation?

Based on the above, this should work. Be sure that your capacitor will have 10 uF or so minimum value over all operating conditions.