Depends on the design, the load, the duration, and the amplitudes, etc.

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A linear power supply usually consist of a transformer, rectifier, filter (usually just large electrolytic capacitors), an then a linear regulating circuit.

The linear regulating circuit regulates with a minimum input-to-output voltage requirement. This minimum voltage might be from 0.8 to perhaps 2.5 Volts (For the perfectionists I'm going to ignore smaller LDO regulators that might go down to <0.2V). When there is insufficient AC line voltage, the output voltage will begin to drop. If the power supply is still supplying plenty of current, you also will begin to see some ripple voltage appear riding on the DC output at 2x the line AC frequency.

Example 24 VDC supply where the voltage on the electrolytic filter is only 22 volts, and the regulator section requires a minimum of 2 Volts more than the output setting, the output will be 20 VDC with some AC ripple.

For AC voltage spikes, the output will probably change much less than 100 mV. That is, of course, as long as the voltage spike doesn't exceed the voltage ratings of the rectifier, filter capacitors, or the maximum input voltage of the regulator.

I don't know what the typical circuits are in an inductive angle encoder. Sounds like it's mostly analog. That means op-amps. Op-amps have their own PSRR spec (power supply rejection ratio) that is typically up to 60 db. This means the opamps can keep doing what they are supposed to do even when there is noise or voltage varation of the power to them. That is as long as the opamp output voltage doesn't get too close to the power rails (opamps also have minimum difference between power and output requirement as well).

Thanks!

Brownouts and power spikes can severely affect linear power supplies, especially those that provide 24 V to an inductive angle encoder. When a brownout occurs, the voltage delivered to the Amp-Loss-Sensor will be too low for the sensor to detect, resulting in inaccurate readings. In addition, fluctuations in voltage may cause damage to both the linear power supply and the device it's supplying electricity to. Power spikes are even more dangerous because they can overheat or melt electronics if a linear power supply is not correctly handled.

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We can only guess unless you tell use the model (link to specs and your brown-out levels and qualification test results. You cannot guess without testing them.

For spikes I'd regard a linear supply as quite robust, but for brownout a switchmode power supply will provide an advantage.