Trying to better understand voltage and current sources

Question

I feel like I am going a little crazy here because the more and more I read about these things the less I understand them.

So I understand that an ideal voltage source has no output impedance, no extra resistance in series between itself and the load, ensuring that nothing else will drop the voltage along the way, meaning the load will get the exact voltage listed.

An ideal current source has infinite output impedance, infinite resistance in parallel between itself and the load, ensuring that the load will get every bit of current as listed (no current will get diverted elsewhere).

I understand that these "ideal" sources are ideal and don't exist in practice. In reality there is always some resistance. What I don't understand is why then are are able to switch between them, or how we can talk about insensitivity to load changes when Ohm's Law says V = IR, if I have a voltage source, is that not fixed? And then if I add a bigger resistor, doesn't that mean less current must flow in turn? Or for a current source, if I change the resistor, am I not then changing the voltage? And since I am able to change the other variable, why are we then able to swap between them? (by swap/switch I mean replacing voltage with current sources and vice versa)

None of it makes any sense to me because I rarely see examples with numbers to illustrate what's going on and how I am supposed to think about these things. Can anyone please give a few examples showing these "ideal" forms, why they are unrealistic, why we are somehow able to switch between them, and what a "real" example might look like?

Answer 1

I understand that these "ideal" sources are ideal and don't exist in practice.

They do to a point. Voltage regulators maintain constant output voltage up to some maximum current.

In reality there is always some resistance.

No. The voltage regulator will maintain the voltage across a range of current draw. Since \$ \frac {dV}{dI} = 0 \$ over that range of current then its output impedance is zero.

What I don't understand is why then are are able to switch between them, ...

Switch between what?

... or how we can talk about insensitivity to load changes when Ohm's Law says V = IR, if I have a voltage source, is that not fixed?

Yes. So if I connect a 1k load across a 5 V supply I draw 5 mA. If I connect a 100 Ω load across the same supply I draw 50 mA. The voltage remains at 5 V. It is ideal up to the designed current limit of the PSU.

And then if I add a bigger resistor, doesn't that mean less current must flow in turn?

For a constant voltage supply, yes.

Or for a current source, if I change the resistor, am I not then changing the voltage?

Yes, of course.

Figure 1. A random bench PSU image.

• I have a bench power supply with an adjustable current limit on it. If I set the current limit to 20 mA and the voltage limit to 30 V and switch it on, the voltage will rise to 30 V in an attempt to push 20 mA between the terminals. It can't. The air's resistance is too high.
• If I now connect a red LED between the terminals the current will rise to 20 mA and the voltage will fall to about 2 V.
• If I now connect 12 red LEDs in series to the terminals the current will still be 20 mA and the voltage will rise to about 24 V.

The power supply is operating as an ideal current source for loads between 0 Ω and 30 V / 20 mA = 1.5 kΩ. Since the current remains constant over that voltage range we get \$ R = \frac {dV}{dI} = \frac {dV} 0 = \infty \$.

And since I am able to change the other variable, why are we then able to swap between them?

Again, it's not clear what you are asking here.

Can anyone please give a few examples showing these "ideal" forms, why they are unrealistic, why we are somehow able to switch between them, and what a "real" example might look like?

They're not unrealistic over a certain range of operating conditions. I'm still not clear what you're switching between. I've given an example.

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By "switching" I refer to when people say you can transform a voltage source into some equivalent current source and vice versa.

For a fixed resistance you can supply a load with constant voltage or constant current. If the resistance can change then you need to choose one or the other depending on what you want to happen.

In most applications you can't switch a CV supply for a CC one or vice versa. Most circuitry is designed to work on a constant voltage. The national grid (even though it's AC) is designed on this basis. Cars, buses, airplanes, phones, computers and most "electronics" are designed to work on a particular voltage. The most common exception is LED lighting where constant current supplies are used due to the shape of the LED's IV curve.

Answer 2

An ideal voltage source will output any current required to keep the voltage at its terminal at the nominal value. Its characteristic in the V-I plane is a vertical line passing for the ideal (nominal value). The internal (series) resistance Rs of an ideal voltage source is zero.
An ideal current source will output any voltage required to keep the current through it at the nominal value. Its characteristic in the V-I plane is an horizontal line passing for the ideal (nominal value). The internal (parallel) resistance Rp of an ideal current source is infinite.

When the internal resistance of the source is finite (Rs>0 in the case of the voltage source, and Rp<infinity in the case of the current source) the source will not be able to supply the same ideal nominal value for every possible value of the load because part of the voltage will drop on the nonzero series resistance or part of the current will flow through the finite parallel resistance.
The V-I characteristic, with a simple linear internal resistance added, are slanted lines corresponding to Vout = Videal - Rs Iload in one case and Iout = Iideal - Vload/Rp in the other.

We can see what happens when we connect a resistive load to a nonideal source: the characteristic of the resistive load in the V-I plan is a line going through the origin, expressing the V = R I constitutive equation and the working point is the intersection with the source characteristic:

We can see that in the case of the voltage source the voltage is a little less then the ideal value (which still appears as the open circuit voltage), while in the case of the current source the current is a little less then the ideal value (which still appears as the short circuit current).

If, when changing the load resistance, the quantity that remains approximately constant is the voltage, you call the source a voltage source. Conversely, if it's the current that does not vary much, that's called a current source.

In general, a generator can have a behaviour not easily classified as constant current or constant voltage. Even in the case of generators with a linear internal resistance you can end up in this situation

where you can use both the Thevenin or Norton equivalent circuit to characterize the source. In this sense you can treat this generator equally as a voltage or current source.
If you think about it, all the nonideal generators above can be considered of this kind: it's just a matter of adjusting the scale on the V and I axis. It is customary, though to use the Thevenin equivalent circuit for a source that outputs a more or less constant voltage and a Norton equivalent circuit for a source that outputs a more or less constant current. As long as they are not ideal, you can pass from one to another without having to deal with infinities and singularities.

Real sources in the real world have a different, usually nonlinear, characteristic but in the region where they are 'compliant' the behave roughly as either a reasonable ideal voltage source or a reasonably ideal current source. In order to do that, they use active accessory circuits with feedback so they are not describable as the simple neat circuits of basic circuit theory.