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I need to drive 13 20ma (constant) loads with a single microcontroller with only 5 available pins. My first thought was to just use a mcp23017 or some 74hc595's but after reading the datasheets it appears they both have low max current into vcc (125/70 respectively) so that won't work directly. I have a bunch of uln2003 chips so I was thinking of using those with the port a expander to drive the loads but it feels heavy for what I'm doing. Am I missing something simple here?

The mcp23017 says it has max 150ma into vcc and 125 out vdd, could I do something clever like source 7 of the loads and sink 6 of them through one mcp23017?

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The 150mA/120mA are absolute maximum numbers and you should not get anywhere near those levels if you want reliability. The output voltage is only guaranteed at 3mA source/8mA sink.

If the relatively high output voltage of the UL2003A Darlington outputs (maybe 0.7V typically @20mA) is not a problem for you, that's probably your best choice to buffer the expander outputs. Very cheap and robust part and 7 outputs in one small package.

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You could use the port expander to drive discrete transistors (2n2222 would handle those loads no problem), in turn driving your load. This is often done in consumer and industrial products where the financial or space expense of an overkill IC is not acceptable.

In my experience, digital IC outputs rarely drive anything but high-impedance digital lines, and something like a ULN or transistor is used at the end of the chain to drive the load.

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Nothing stops you to do that. The maximum power is not at least 1/4 reached and everything is in the specs limits. Don't worry about the "absolute maximum" you're nowhere near. The chip should work in parameters. The I/O is stated as 25ma capability you're barely at the half.

You can also look at this chip or similar.

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