adc.txt

ADC_VREF value for STM32F407 at 168MHz : 1523-1536 

Vref, V  for 3.3V reference VCC : 3.3 * ADC_VREF / 4095 =  3.3*1536/4095  = 1.2375

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To determine VCC based on known Vref = 1.2375 

VCC = 4095 * Vref / ADC_VREF  = 4095 * 1.2375 / ADC_VREF

For example if ADC_VREF = 1800,   VCC = 4095 * 1.2375 / 1800 = 2.815 

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To determine VBAT:   

VBAT is divideved by 2  for STM32F407 

VBAT = ADC_VBAT * 2 * VCC / 4095


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General formula to determine V, for example on a resistor voltage divider: 

V = ADC conversion result * VCC / 4095

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V external battery connected to a voltage divider R1/R2: 

Vext = Vcc/4095 * ADC_R2  * (R1+R2) / R2

Example:  
R1=2K  R2=4.87K

3.77/4095*3131*6.87/4.87