How can I build a practical 100uA current source from a 2.5V voltage source?
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Without knowing too much about the load I can suggest an option that may be able to trigger some ideas for you. If you can find a low power Rail-Rail op-amp that can operate from the 2.5V source then you can build a decent 100uA Source. Use the 2.5V supply to create a low voltage reference via either an LDO linear reference or a zener based one. I suggest using one around a value of 1V. Connect the reference to the non-inverting input of the op-amp. On the output of the op-amp you can drive the base of a BJT. On the emitter of the BJT there is a resistor connected to ground. The voltage node at the emitter and resistor (R) gets routed back to the negative terminal of the op-amp. The 100uA source is created by taking Vref/R (ex: Ref = 1.25V, R = 12500 ohms, yields Iload = 100uA). So you can tie your load between the 2.5V source and the collector of the BJT. This works because the op-amp will always try to drive the BJT such that the voltage into both the inverting and non-interting inputs have the same voltage.
The above suggestion doesnt give you a ground reference for your load which may or maynot be good for your application. If you need an Isource that provides you a ground connection then I can offer up a suggestion which uses a PNP transitor and a P-Channel MOSFET.
Current output current shunt monitors also can make good current sources. A differential measurement over a shunt resistor produces a corresponding current output that can be adjusted by adjusting the voltage drop over the shunt resistor. TI's INA138 would be a good example although this has a minimum 2.7V supply.
Developing current sources or voltage references I recommend taking a look into this book:
"Current Sources and Voltage References: A Design Reference for Electronics Engineers" - Linden T. Harrison
One of my favourite at all