I'm building a homebrew PIC programmer, and want to support devices with varying Vpp voltages, so I'm using the DAC output of a PIC16F1825. But the PIC is supplied with a +5V Vdd, so that's the maximum output of the DAC. I can use an opamp to increase that voltage with an available +12V rail using the following circuit (DAC buffer opamp stage not shown):
What has me mystified is how to determine the voltage gain in this circuit apart from trial and error with R1 and R2 values. Ideally, in this case, I'd like a gain of about 2.5 with signals referenced to ground (the real ground, not a virtual one as is typical in single supply AC amplifiers).
For normal dual-supply AC amps, I have a formula of 1+(R2/R1), but that doesn't seem to be valid here.
So my question is: is there a formula to determine the gain produced with a given R1 and R2 or, conversely, to determine R1 and R2 to produce a given gain?
(I could probably accomplish this with a simple transistor, but since I need the DAC buffer anyway, I have a spare opamp available)