TL;DR: If we have a VREFH other than the typical value VTEMP25 is calculated at, how do we find the new typical VTEMP25 without running calibration procedures?
I am a long-time user of the HCS08 processor line. Specifically, our company uses the MC9S08DZ128 in many of its applications. Recently, we were confused while reading AN3031 (HCS08 Temperature Sensor) and did some testing to determine whether the bandgap and temperature readings were generated from VDD, VDDA, or VREFH (the note continuously says VDD). After determining that the note assumes all 3 are the same thing and finally figuring out that it is based off VREFH, it then brought into question how we are calculating the internal temperature.
My question is: how is VTEMP25 affected by VREFH? AN3031 keeps saying that VTEMP25 is based off of a VDD of 3V, but the MC9S08DZ128 data sheet says that the value given for VTEMP25 is based on VREFH = VDDA = VDD = 5V. So how do we take the typical value for 5V and scale it for our own purposes? We have different values for VREFH for different applications (5V, 3V, and 3.3V, specifically). Further, the graphs in AN3031 show that constant changes in VREFH result in exponential changes in the resulting ADC values.