Well I can think of quite a few.
1. Testing battery discharge, if you have a project that runs on a constant current which most regulated devices will. You can test how long your batteries will last when drawing a certain current over their dropping voltage. Can't do that with resistors.
Just discharging a battery goes fine, but if you require dropping it to zero, yes, a resistor will get quite slow through the tail. Though not proportionally so, because the battery itself has an exponential decay rate, so the last 50% of voltage takes less than 50% of the time, even with much less than 50% of the current draw.
2. Testing power dissipation over a wide voltage range. If you want to test your supply to its limits and change the voltage but draw the same power, this will do it. Resistors won't.
Cough... that requires negative resistance, not constant current.
One that's programmable for positive or negative (or infinite in the middle) resistance would cover that nicely, of course.
4. Testing voltage ripple in a rectified power supply designed for a particular project. You can draw various currents and test it over a specified range of currents, in 2ma increments.
Are you expecting that the ripple will vary in an unnatural manner from zero to nominal?
Digitizing as many points as possible can be handy, and makes nice spreadsheets, but isn't always useful. This relates to the analytical relevance of information and sampling: unless the power supply design is shitty (weird operating modes at certain oddball currents), it should be sufficient to define its operation with just a few points and an interpolating curve. More points are redundant.
The box of high precision power resistors you would need to test 0-8A 0-24V at 50W I would hate to think how much space that would take up let alone the cost!
Precision?
1. If I need to know something that accurately, my power supply must be a pretty crappy (razor thin margins) design!
2. If I need to know something that accurately, I'll measure it directly (volts and amps, or measure the resistance at temperature), which is better than watching it through the offset, gain and nonlinearity of a test box's digital readouts.
To check the operating area of a 0-8A, 0-24V supply, I would use probably twice as many steps as suggested by the design (presumably this example is a stepped linear regulating supply?), and also let it sit for an extended period of time on the highest current tests to verify that it can handle that power continuously (hint: those cheap Mastek and myriad clones (e.g. 30V 5A) you find on eBay won't). If it's single range (200W square operating area instead), a grid of two or three voltages and currents will suffice to verify its operating range.
Load step is usually done with a moderate pre-load (10 or 50%) and the remainder switched; if the transient is well damped on both sides (i.e., for a load of R or 10*R), it's reasonable to expect it will tolerate a load of infinite R, and perhaps even negative R before going unstable. (The worst negative resistance a power supply should reasonably expect is dV/dI = incremental R = -V^2 / P, the constant power curve typical of switching supplies.) If the controller is well-behaved, the output impedance should be a well-defined RLC equivalent, which can be solved for based on transient response to find stability range.
Tim
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