WestFw and IanB, We might just be facing a wording, semantics problem here, and your knowledge about electronics is immense, but I am very certain you are mistaken here with what you both are saying, maybe sometimes if only by your way of explanation
I hope with 10000 words or less I can clarify the situation. I don't want constant current v. current limiting to become a "What came first, the chicken or the egg?" argument!
A constant voltage source comes first and sets the nominal, non-current limited output voltage, and the current limiting or constant current circuit stage then monitors the current being drawn out of the constant voltage source and adj's voltage output down to achieve the constant current mode of operation. We can say that the constant current stage feeds back to control the constant voltage stage to make this happen.
You might notice, in my circuit that the constant current sensing and control is the in of the constant voltage output stage, but that it feeds back to control the LM317 voltage output to achieve constant current operation.
IanB states also in reply,"That's contrary to every other piece of advice out there in electron land." is also mistaken in the same way as WestFw.
You might notice, for example, in my circuit (which is in fact a commonly seen implementation of many other circuits published) that the constant current sensing and control is in the constant voltage output stage, but that it feeds back to control the LM317 voltage output to achieve constant current operation.
If you try to do it the opposite way, the constant voltage stage will never work to provide a constant current because it is always trying (at the output of your supply) to provide a constant voltage.
i repeat, The constant voltage stage most be controlled by the constant current stage but part of its circuit senses the current in the constant voltage output state, and there is usually some way of feeding back or controlling the constant voltage stage to correct the current to the desired set value.
So, is it a just a problem of semantics, that we are both trying to say the overall method of operation is to use a part of the whole circuit that to sense the output current used by the load to and control the constant voltage output stage circuit to achieve voltage compliance to maintain the output current of a power supply?
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Microbug: your question, "OK, I've had a look around - would the first design here work?"
The answer is yes, it would, but it is not a very good circuit.
This circuit would have bad transient response, and this causes sudden load changes (such as happens when you first connect your power supply to a circuit and a high current is drawn) to cause your power supply to overshoot the correct output voltage and the excess voltage could be enough to damage your test circuit you are working with.
The bottom line is that the LM317 is a very poor choice to be somehow "jerry-rigged" to create a switching power supply. The datasheet shows how it can be done, but that is misleading. The datasheet writer is just trying to sell you on the idea to use this part, to sell you their part, so they present this schematic to try to get you to use their part in an awkward way.
I think the idea of trying my circuit is better because it is simpler, it is a linear not a switching power supply, and their exists some range of linear constant current control.
Good transient response is an important characteristic of a power supply in that it allows the power supply to act well with sudden load changes.
IanB: We are getting into a weird battle of semantics here, but as you say it, you are wrong because you are misleading Microbug in telling him that:
"A practically realizable constant voltage supply does not exist."
"A practically realizable constant current supply does not exist."
They do exist and are being sold and used everyday. You are correct to say there is no such thing as a "constant voltage" or a "constant current" supply if you think such a thing can work perfect in any imaginable load condition.
Every constant voltage or constant current supply has its limitations set by the ratings of a supply parts, the maximum current that is available to be delivered safely and without overheating, there is always a limit to the maximum perfection of output regulation that can be achieved, etc.
But when you use the word "practical" here, it is misleading, "practical circuits" do exist, and can be quite tiny and work well. Ideal or theoretical circuits often do not.
If you used the work "Ideal" or "theoretical" (instead of "practical", when you try to give the meaning that a perfect power supply, operating perfect in every possible load condition does not exist), then you could have explained the problem of "theoretical" versus "real world" practical better.
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IanB: in another reply you are incorrect and confusing when you say "In reality there is no difference between these two concepts." in trying to clarify if there is really any difference between constant current and constant voltage supplies.
A constant current supply, within its range of voltage compliance, which is the limits of its constant current operation, delivers a constant current that is set by a control.
A constant current supply has many applications, for instance, it is a circuit device and tool that allows such allows smooth voltage ramp generation with a capacitor, it can also set the limit of current delivered by a power supply, and a constant current power supply is often required for battery charging methods that safely charge batteries.
A current limited supply may smoothly or abruptly switch to a current limited condition of operation, and the current limit may not be adjustable by the user, but just be set and limit the output flow of current to a safe value that would not damage the power power supply. Current limiting is a way of talking about how a power supply protects itself, rather than the circuit it is attached to. which may not be designed to be constant, just limit the current to a safe value to protect the supply or the circuit it is attached to.
An example where current limiting is used but a constant current is not delivered is when "Foldback Current Limiting" is used. In this case the current is first limited to a higher value, then as the load is increased, the power supply voltage drops with a fast-sloped characteristic limiting curve to limit current at a lower level prevent damage to the circuit involved and to the power supply supplying the current. Any 555 timer, 7805 or LM317 regulator have current limiting, but the actual current is neither constant and varies with temperature nor is the current limit user adjustable.
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Finally, I would point out the hype advice you find in some datasheets, they often try to get you to use as many of the devices shown as possible in a given application so as to maximize sales of the device. In many cases, the optimal circuit solution to a circuit application or problem shows only one the answer, "just use more and more of these excellent xxx devices to do it"
Not all application notes or datasheets do this, and studying them is probably one of the most important ways to learn about electronics, but remember this, the purpose of a datasheet is meant to be just about the part it is describing, it is not being intellectually honest helping you in finding better ways to solve your circuit problem.
I wish to thank everyone for their replies, and please excuse me for letting bold print get out of control somewhere.
I also am very grateful for your replies that give me food for thought (even while I am having lunch) and a giving me a chance to clarify things in electron land. Because I have only my lunch hour to reply, I might have created a poorly edited words-in-excess reply that attempts to say what I really wanted to say here.