I want to power a Uno board with the lowest possible voltage external supply to minimize the power dissipated in the regulator and avoid as much heat generation as possible.
I'm just guessing that something between 6V and 7V would be the limit, but getting as close as I can to the absolute minimum would make me feel better.
[Aside: If the board's powered through USB, is the 5V regulator bypassed? I don't intend to use rely on that right now, but I am curious about it.]
You can power it with 5V applied to the power header. regulator is not used at all then.
Or use a wallwart and power it via the USB connector, same as if a PC was powering it. No regulator involvement then as you surmised.
Dropout of the 5volt regulator is about 1volt at the ~50mA draw of an Uno.
The micro/chips on an Uno should work reliably from 3.8volt.
So in theory, 4.8volt on V-in is enough to keep things going.
But at that voltage you have no regulation, no headroom, no 5volt on Aref.
6volt on V-in gives a stable 5volt rail, but still no headroom.
At 6.6volt on V-in the USB backflow protection mosfet activates.
The regulator has now enough headroom (1.6volt) to properly do it's job.
I would say a voltage of 7-7.5volt is ideal for V-in.
At that voltage everything works within specs, and you can draw some current from the 5volt pin without overheating the regulator quickly.
Max total current draw (all pins) at 7volt on V-in is about (1/(7-5)) - 0.05 = 450mA, assuming 1watt max dissipation.
The DC socket has a reverse protection diode with a 0.7volt drop in series.
Calculate accordingly if you want to use that input.
Powering the Uno via the USB socket (with 500mA polyfuse) bypasses the 5volt regulator.
Powering the Uno with 5volt directly on the 5volt pin also bypasses the regulator.
Leo..
Thanks to both of you. If I can't find a decent (cheap) 7V supply, maybe I'll reconsider pumping 5V in through the USB port.
[I thought I'd posted my query to the "Project Guidance" forum, since I saw a number of other questions involving power supplies there. Did I somehow end up here, or did management decide that this was a better place for me to be and moved by post? I've been writing software for Arduino boards for a while, but this is the first time I used the forum, so I wouldn't be surprised if I wandered into the wrong neighborhood]
“maybe I'll reconsider pumping 5V in through the USB port.”
OR
As Crossroads says:
“You can power it with 5V applied to the power header”
larryd:
“You can power it with 5V applied to the power header”
My understanding is that this can damage the board if it is plugged into USB at the same time - which is why I favor powering via the USB port if you are using external 5v.
Or you can ‘make it a rule’ disconnect the power header connector when the USB cable is plugged in.
A piece of tape over the USB connector or power header warns me.
For a Pro Mini I cut off the power pin on the FTDI male header.
BertHy:
I'm just guessing that something between 6V and 7V would be the limit, but getting as close as I can to the absolute minimum would make me feel better.
Why guess ?
Look at the regulator on your UNO, it will very likely have a part number on it, maybe something like 'AMS1117'.
Then use a handy Internet search tool (Google for instance) to find the data sheet with a search like;
'datasheet AMS1117'
Then look in the datasheet and it will likley have a chart which tells you the dropout voltage for the current you are interested in.
There is no guarantee that each and every varient of the UNO uses the exact same regulator and as you did not say at what current you wanted to know the dropout voltage, only you can answer the question really.
DrAzzy:
My understanding is that this can damage the board if it is plugged into USB at the same time - which is why I favour powering via the USB port if you are using external 5v.
Which is completely wrong! 
Powering via the 5 V pin is the preferred way of powering it - the board runs on 5 V, the 5 V pin is the most direct connection to the main 5 V supply rail which feeds all chips and therefore the most appropriate way to power it.
There is no risk of damage to the Arduino as there is no mechanism to cause damage. (You might perhaps "blow" the self-resetting polyfuse.)
There is a concern that powering via 5 V while connected to the USB port of a laptop may "back-feed" its USB port and thereby cause damage. This is an interesting notional concern and while I cannot deny it, it is also the case that the vast majority of powered USB hubs connect the 5 V terminals of the input as well as all outputs directly to the 5 V power supply of the hub and therefore represent exactly the same or greater risk to the laptop. It seems to me that if this were a significant risk, it ought to be well-publicised as there are surely far more powered USB hubs in use than Arduino UNOs.