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I'm trying to build the following circuit

Except mine is a 24V ~20A (500W) motor, so I need to swap the components. I'm currently looking into transistors and I've stopped on the 2N6284 (NPN) transistor, which is rated at 100V 20A. This basically means it's good to up to 2000W (right?), but it says the maximum power dissipation is 160W. Now this makes no sense so I'm guessing it's how much of the 2000W going through it will be lost as heat? I've looked all over the data sheet and there are a lot of things I don't understand on top of which is this diagram that suggests that temperature increases as power dissipation decreases? Isn't the relationship supposed to go the other way around, the more power lost as heat the higher the temperature?

If any of my assumptions is correct then how can I calculate how much power will be lost running my 500W motor at 24 volts?

First, the power burnt up in a component is equal to the voltage drop of that component times the current going through it. The transistor has a $V_CE$ of 3V when the collector current is 20A, so that works out to 60W.

Second, the power derating curve works by telling you the dissipation you can allow for a given case temperature. You read across until you find your design case temperature, then up to find the allowable dissipation (or, usually, the other way -- in your case you'd start at 60W, then read across to find that you should design for a case temperature of around 135 degrees C).

Third, you'll need heat sinking to keep the case temperature down -- that thing won't dissipate 60W by itself.

Fourth (and beyond what you were asking), you need a base current of 200mA to maintain that 3V $V_CE$, and that's pushing into a base at a voltage of 4V. You are not going to do that with a microprocessor GPIO pin.

Use a MOSFET instead of a NPN, You'll be dissipating a lot less power that way. Using "Rdson" also makes calculating power loss easier. You may also want to consider adding a gate driver at that size of device.

Never get a MOSFET rated for X amps when you think you will need X amps. Your part is rated for 20A if you can keep the part cool enough. There is often not a way to actually provide that much cooling. Use the current rating for things like inrush current (not motor starting current).

Calculate your power dissipation first, try to keep it low to limit your cooling requirements, and then use that information as a specification to find the part you need.

First thing to understand is that power dissipation and power handling are related, but they’re not the same thing.

Power handling is a basic rating for how much current and voltage a device can sustain. It’s a basic measure of the capacity of a switch.

Power dissipation is the measure of power loss in the switch - in this case, a transistor. This is due to the I-R drop from collector to emitter. This is proportional to collector current and the collector-to-emitter voltage, Vce, at that current. For example, if Vce is 3V at 20A the loss will be 60W.

Side note: I’m going to suggest that you will use a higher voltage than 5V for the motor - losing 3/5ths of the power in the switch doesn’t seem like a good trade off. Last time I worked on something with a 2N6284 in it was for a servomotor that ran on 30V.

What the derating graph is telling you is the safe limit of dissipation at a given case temperature. As the temperature increases, the safe operation limit goes down. With the 20A current and dissipation of 60W from the example, the graph tells you that you need to keep the case temperature below 125 deg. C. Practically, that’s a very large heatsink and possibly a fan, too.

The benefit of using a FET is that they don’t have the Vce drop. Instead, they have on resistance, Rds (on), which can be very, very low for a big FET. They too will have dissipation from the I-R drop but it’s considerably less than for the transistor. Nevertheless they also have safe operation limits and require derating for elevated temperature.

A tip: you can combine devices in parallel to boost the power handling capacity.