74HC595 would work, but total current thru the IO pins needs to be limited to <= 70mA Absolute Max to avoid blowing the VCC or Gnd pins.So roughly 8mA per IO pin as mentioned above.
Normally, multi-digit 7-seg displays have common anodes and common cathodes and there is no choice but to multiplex. A 3-digit display would have 11 or 12 pins. Does your display have more? Like 27 pins for example?Also you say that the digits are 1.2" high but you need to drive them with 3.3V. Large digits often contain two or more LEDs in each segment, meaning 3.3V will not be enough to drive them. What is the forward voltage of the segments in your display?You also say you want to drive them with 10-20mA per segment. Is this to achieve high brightness, for outdoor use for example? If so, this will be difficult to achieve if you need to multiplex. Multiplexing lowers the average current and therefore brightness. Multiplexing by digit would result in a 1 in 3 duty cycle and would lower the average current and brightness to one third of your target. This can be compensated for by increasing the current and over-driving the display, but if you don't have data sheet, you don't know if that's safe to do without damaging the display.Also, even at 10mA per segment, you would need 210mA at 3.3V if not multiplexing. This is close to the limit of what the Nano's regulator can provide. Even large batteries will be quickly drained.So... please provide much more information, if you truly want our help. A link to the data sheet for the display, if you have it, or any codes printed on the display to allow a Google search. And details of the batteries to be used.
Nevermind.. a quick re-read showed me that I originally glazed over:"All to run on 3.3V from battery power"as I believe all MAX72xx chips require 5v..
"Power is planned to be from a 2-cell 18650 battery pack (rated 4400mAh)." So why not regulate that down to 5V with a switching regulator and use standard parts? Will make the design easier.
Can use MAX7219 then to do the multiplexing.
Or ten pins off the Arduino; use three to drive NPN transistors or N-channel MOSFETs to sink the common cathode from the 3 digits;
or if single segment multiplexing, then sink the current with an IO pin. Or save some pins by shifting the anode data into a MIC5891https://www.digikey.com/product-detail/en/microchip-technology/MIC5891YN/576-1310-ND/771779to provide the source current into the anodes, and multiplex across all 3 digits for a brighter output.Three transistors for sinking current, and use fewer pins overall. Clock, data, latch for the shift registers, and 3 pins to drive current sink transistors.
Regulate 3.6-4.2V down to 5V? Lost me there.
What about using three CD4511 chips? Vcc 3-18V, output 25mA per channel, Latching so only 7 pins required (4 for display and 3 latch pins).
I think CrossRoads is suggesting you connect the batteries in series to give 7.2~8.4V, then regulate that down to 5V. A linear regulator would waste much of your battery capacity. A DC-DC step-down convertor would only waste a little. Or connect the batteries in parallel and use a DC-DC step-up convertor to make 5V.I'd like to help with more suggestions, but a couple of my questions from post #16 have not been answered yet, around required brightness. That will help with the decision to multiplex or not.
Are 18650 size LiPo batteries made? I have only seen Li-ion. You don't have to charge them in series, you simply remove them and charge them in parallel in a dedicated charger.
And was the test 10 or 20mA per segment?Max7219 can source up to 30mA per segment when only 3 digits are scanned, so that will average 10mA, making a multiplexed display with one chip and no segment series resistors needed, just a couple of caps and one current setting resistor. This might be the simplest option, if 10mA per segment is bright enough.