Hi @Steve_Mayze, that circuit is not going to get you what you want. It is still just a voltage divider with the Teensy measuring the drop across the 30k resistor. The voltage across that resistor will range from 0 - 3.3V for an input of 0 - 15.4V so it won't improve the resolution.
I would suggest you use a 7.5V - 8.2V zener diode in series with a voltage divider, then there is no current flowing through the divider until you reach the zener voltage. With a 8.2V zener diode choose values for the two resistors in the divider such that 15V - 8.2V gives you 3.3V. You just need to watch that the divider values are such that the zener's minimum current requirements are met at low voltages, around 8.5V - 9V. Until the required minimum current is flowing through the zener you won't get a linear output voltage so choose a zener with a low minimum current. You should be able to get a linear output above about 9V. Or use a 7.5V zener for a linear output from about 8V.
Hope that helps.
Edit: For example, if you use 14.8V as an upper limit, 14.8V - 8.2V = 6.6V and if your divider divides that by 2 (ie. both resistors are equal) then the output would be 3.3V for an input of 14.8V. You can vary the resistors to obtain whatever upper voltage limit you want.