Mac Mini Power Supply

"I have always found switchmode supplies to be VERY noisy and mechanical sounding."

I don't question your findings but I hope you realize that this voltage (is it 18V?) goes inside of Mac Mini thru internal switching regulators to deliver voltages for micro and rest of digital circuitry.

Linear powers supply is also a switcher operating at 120Hz. It takes current from mains in very narrow current spikes of big amplitude. Width of the spikes depends on the load.

Switchers got bad rap from cheap computer power supplies but realized properly are not only very quiet but also line and load regulated (class D is switching mode supply). High switching frequency is not audible and easy to filter out. For that reason Jeff Rowland uses switchers in Capri preamp.

Mintzar - I don't know of a single switching mode power supply that operates in audible band. The lowest I know to operate is about 50kHz - non audible. Modern switching power supplies are switching at zero voltage/zero current while linear power supply switches at max voltage.

As I understand it you need about 6A for this supply while LM338 is rated only 5A (continuous). Linear regulators are noisy, require huge transformers are most often unregulated. They are also not as easy to design as it seems. Older regulators like LM338 are sensitive to output capacitors' ESR - might start oscillating when ESR is too high but also oscillate when it is too low.

"Ideally you would want the switching frequency to be so fast that it would be impossible to tell when it turned off and back on." - Only for efficiency sake. Fast switching brings more noise pollution.

As for designing with LM338 - I did it over 20 years ago and would not do it again. LM338 is really old stuff. I requires almost 3V input output differential making it total of 8.5V drop across regulator if you provide for +10/-20% line variation (3V +18.5Vx0.3). This means 8.5V x 6A = 51W (big heatsink). In addition LM338 has very poor ripple rejection equal 0dB (none) at 100kHz. You can do much better with modern regulators. Transformer is also a problem because 110 W supply requires almost twice rating because of the nature of load. Current spikes from bridge/capacitors have much higher RMS value than average value heating copper (windings) while high frequency content is heating the core. If you need to deliver 110W with 50W lost in regulator I would pick at least 250W transformer.