You can never have enough power supplies!
A fun project is to start with a L200 voltage regulator.
It's a bit like the standard voltage regulators (Like 7805, LM317, etc), but it has a few extra pins for current sensing.
With a single resistor you can set a maximum output current.
Then you can extend this project in a few ways.
One way is to add an opamp to amplify the voltage over the current shunt resistor, and feed the amplified voltage back to the regulator.
This wil result (with a potmeter) in a power supply with an adjustable current limit.
Another way to extend this power supply is to add a charge pump to generate a small negative voltage, and use that to power the "GND" pin of the L200. Then you can regulate the output voltage all the way to 0.
But even with circuits as simple as this, you should have an oscilloscope to check for oscillations and other anomalities.
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Another (famous) and fun circuit to build is a reference voltage with an opamp, a zener diode and 3 resistors.
LM358 is a cheap opamp that can be used from a single supply voltage (input and output work to close to 0V).
The circuit should work as follows:
The voltage over a zener diode usually is not very stable. It depends on the current through the zener.
However, if you have a stable voltage, with a series connection of a zener and a resistor, then the zener current will be constant, and thererefore also the voltage over the zener.
The opamp is then used to amplify the zener voltage (1.5 to 4 or so times), to a higher DC voltage, and the zener + series resistor are powered from the stable output voltage of the opamp.
If you do not have a zener diode, you can also use a LED, The voltage over a LED depends on the color of the LED. Most are between 1.5V and 2.1V. White Leds (which are almost always blue leds, coated with fosfor to make the other colors) can go upto around 3V.
You can use it as a puzzle, and design the circuit from my description, or you can find it on the 'net.
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Opamps are used for almost any analog circuit.
Get yourself a copy of "opamps for everyone" aka slod006b
A very simple and still educational is to use an opamp with FET inputs, such as the TL072 (also very cheap, buy a bag full)
With opamps, traditionally a distinction is made between "single power supply" opamps, and "dual power supply" opamps.
But this is mostly bollocks. There simply is no way in which an opamp can magically sense where "GND" is.
"GND" is usually some arbitrarily chosen reference.
Opamps which are considered "dual power supply" usually do not work when the inputs or output are close to either voltage rail. They often need 1 to 2V headroom.
One of the simplest circuits with an opamp is a buffer.
Use a somewhat higher power supply voltage ( between 15V and 32V) for the TL072.
Then connect the output to the inverting input.
Connect the non-inverting input to a capacitor, and the other side of the capacitor to your "GND" reference (usually the lowest voltage rail).
put a bit of charge on the capacitor, by touching the positive voltage rail with one hand, and the connection between the capactior and opamp with your other hand.
Measure the output voltage of the opamp.
If you stop touching the capacitor, the output voltage should be fairly stable. It can take hours to discharge a capacitor through a high impedance input of an opamp.
Experiment with different capacitors.
Some have internal leakage, others don't.
From the rate the output voltage of the opamp changes, you can calculate the current through the capacitor.
Do that, and compare it with the datasheet of your opamp.