Sat Jan 24, 2015 6:09 pm
It is a closed loop unity-gain AMPLIFIER, with an offset. I am uncertain about the true schematic values because the Adafruit schematic shows both resistors as 10k, but the GitHub schematic has the bias resistor, R2, as 10K, and the load resistor, R3, as 47k. I believe that the GitHub values are more correct since they will produce an offset that sets the drain of Q3, the DMG2305UX PFET, 43mV below the source when the circuit is balanced (in equilibrium). The offset can be calculated from this equation:
Vos = kT/q ln(IR3/IR2) ~ kT/q ln((Vdd - VGS3)R2/((Vdd - Vbe)R3)) , where kT/q ~ 26mV @ room temp
The offset is a requirement since without it the circuit will attempt to keep the Vds across Q3 near zero which will force Q3's gate to be near ground any time there is current flowing into the output. That will cause long turn-off times for Q3 when the input voltage drops below the output. The circuit will behave more like a comparator if the two resistor values are equal.
The main concern of this circuit is how it is compensated to be stable under all conditions. Usually there is a dominate pole compensation capacitor - either the 47uF load capacitor or the Cgs of Q3 - that keeps the circuit from oscillating. I'm assuming that the designers have done their job well and it is stable.