monitor a dual supply, help

I've made myself a nice +/- 1.5v-15v supply where the positive and negative are both adjustable
im planning on having an arduino get the voltage/current stats from it and display to an lcd, but how could I monitor the negative voltage? Im probably gonna have a separate supply for the arduino for when the supply is in its lower limits, but what would be the simplest way to measure both?
my first thought was a diode bridge for the negative but then ill lose some volts
I was thinking tieing the negative rail to the arduino ground and using a properly sized resistor divider to the supplies ground, which would appear positive to the arduino
then a larger divider to the positive rail and just subtract the negative to get that positive rail, but id like to keep the arduino ground at the supplies ground for just in cases sake
is there a better way? I know an op amp can be set as a differential amplifier, so could I somehow have an inverting differential amp in a less than 1:1 ratio? (If it exists)

You want to do a 2-stage transposition.

First you need to scale the supplies for sensing so that they are +/- 2.5v.

Then you need to add 2.5v to the result.

That way you get 0-5V with "0v" being actually at 2.5v, -15v being 0v, and 15v being 5v.

The scaling you can do with a simple potential divider. Adding the offset voltage is a little more tricky, but a simple op-amp should do the trick.

So a simple 1/3 divider would work (maybe higher for safety) , how would I add the offset with an opamp? And I guess that op amp would need to be dual supply or a rail to rail one?

I'd go 1:4 for safety. And yes, a rail-to-rail I/O op-amp is best, though it doesn't need to be.

Just create a basic inverting buffer and apply 50% of Vcc (through a potential divider) to the non-inverting input. The op-amp will raise the output to +/- 2.5v.

This will, of course, invert the output, so you will have to subtract your reading from 1023 to get the real reading.

No need for op amps unless you want 10-bit resolution on the negative supply. Tie the Arduino ground to common ground. To monitor positive voltage up to +15v you just need a 2:1 potential divider to ground, feeding an analogue input. To monitor the negative supply, use a 3:1 potential divider between the negative supply being monitored and the +5v Arduino supply, feeding another analogue input. The analogue reading for this one will vary from 768 when the monitored supply is at 0v, down to 0 when the monitored supply is at -15v.

If you do that I'd be inclined to protect the ADC pins with a couple of zener diodes to both stop any large voltages killing the chip, and also to remove any negative voltages from the ADC inputs.

majenko:
If you do that I'd be inclined to protect the ADC pins with a couple of zener diodes to both stop any large voltages killing the chip, and also to remove any negative voltages from the ADC inputs.

No need for that, if you use large enough values for the resistors in the potential divider (e.g. 100K for the resistors between the pins and the supplied being monitored) then the internal protection diodes will do the rest. Also I suggest a capacitor (10nF to 100nF) between each pin and ground to prevent the high relatively source resistance affecting the readings when you switch between pins.

That voltage divider does sound easier, is it much riskier than the opamp?
And for the op amp circuit the inverting input would get fed after a voltage divider to bring it to<-5v right?

Neither solution is risky.

For the 3:1 voltage divider, you need to get the ratio of the resistor values accurate if you are going to achieve accurate readings of 768 at 0v and 0 at -15v. Alternatively, see what readings you actually get for these values and then calibrate the software. The resolution with which you measure the negative supply with this approach is 15/768 = 20mV, compared with 15/1024 = 15mV for the positive supply, because you are only using 3/4 of the range of the ADC.

If you want to use an op amp to monitor negative supply, then I would use an LM358 or similar whose common mode input voltage includes the negative supply to the op amp. Power it from +5v and ground. Connect the non-inverting input to ground. Connect the inverting input through 100K to the negative supply being monitored, and through 33k to the op amp output. Then the output will range from 0 to 5v as the input ranges from 0 to -15v, and you can feed the output directly into an analog input pin.

And the op amp will allow me to get the better resolution right?

Yes, with the resistor values in the ratio 3:1 it will give you the full resolution, just like the simple 2:1 voltage divider on the +ve supply does.