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I have made a circuit diagram for a DC power source and is working on building it. However, the voltage and amperage right after the transformer is about 34V, with an amperage spike of about 80A. The amperage then consistently spikes up to about 38A afterwards. Bad power factor to be sure but I'm not at the point where I can build a controller to correct that and our grid should be robust enough to handle a 33V DC power supply.

I'm guessing the initial 80 amp spike is due to turning on the supply, but when building the power supply, do I need to get a power transformer that is rated for 80A or more? Or would a transformer rated at ~38A suffice?

The LM314 is a small regulator, typically up to 1.5 amps. So where is all this current going? I would suggest it is a modelling phenomenon, like charging the smoothing caps from a transformer with zero ohms windings. Try limiting the current with a suitable resistor, about an ohm, added to the model. In real life a transformer of a couple of amps should be adequate for an LM314. You can use average current for power transformers, their thermal characteristics are so slow they won't get hot and melt windings during a half cycle of mains, be it 50Hz (uk) or 60Hz (world).

Looking a bit closer at the circuit, the BR1 symbol represents a bridge rectifier but does not permit setting of all parameters. By using it straight into a 2000 microfarad capacitor you will certainly get high modelled currents, though these won't appear in a real circuit. As I said, try modelling an ohm or two in series between BR1 and C5.

It definitely reduced the max amperage to about 23A after the transformer, but now I'm curious, how can I get more accurate simulations? Are there other tools I should be using?

I understand the best way to learn is to actually build it but I don't want to buy parts on a design that may not even work.

Perhaps you might permit a little more ripple on C5 by reducing its value? Of course you would have to increase the input voltage. Another way of spreading the current pulse is to have a series inductor like this https://www.eleccircuit.com/wp-content/uploads/2009/11/amplifier-power-supply-using-high-current-transformer.jpg. Sorry I can't supply a value, my best guess is about 1H with a dc current rating equal to your supply output. I would also suggest you use the LM314 with an external pass transistor, as shown in the data sheet, to supply sufficient output current. Power supplies get a bit 'difficult' when you want more than 1A. I would suggest adding protection, at least current limiting and possibly 'fold-back'.

If you can't get that link, try: https://www.eleccircuit.com/amplifier-power-supply-using-high-current-transformer/

...and I said LM314, should've said LM317.

Awesome, thanks for the input!