To derive a formula that converts ADC values to mV (millivolt) values, we can assume a linear relationship between the ADC values and the voltages. The general formula for converting ADC values to voltages is given by the equation of a line:

$V = m \times \text{ADC} + b$

Where:

• $V$ is the voltage in mV.
• $\text{ADC}$ is the ADC value.
• $m$ is the slope of the line.
• $b$ is the intercept (offset) on the voltage axis.

We can calculate the slope $m$ using the two extreme points provided (assuming the relationship is linear). Let's choose the points corresponding to $-2000 \, \text{mV}$ and $2000 \, \text{mV}$:

Given points:

• $(-2000, 7174)$
• $(2000, 58360)$

Step 1: Calculate the slope $m$

The slope of the line is calculated as:

$m = \frac{\Delta V}{\Delta \text{ADC}} = \frac{2000 - (-2000)}{58360 - 7174} = \frac{4000}{51186}$

$m \approx 0.07815 \, \text{mV per ADC unit}$

Step 2: Calculate the intercept $b$

Now, use one of the points (e.g., $(-2000, 7174)$) to calculate $b$:

$-2000 = 0.07815 \times 7174 + b$

Solving for $b$:

$b = -2000 - (0.07815 \times 7174) = -2000 - 560.6 = -2560.6 \, \text{mV}$

Final Formula:

The formula for converting ADC values to mV is:

$V = 0.07815 \times \text{ADC} - 2560.6$

This formula should give you the approximate millivolt value for any ADC reading in the given range.

Would you like further clarification or details on how this formula was derived?

Related Questions:

1. How accurate is this formula for values outside the given ADC range?
2. Can you apply this method to non-linear data, and how?
3. How does ADC resolution affect the precision of this formula?
4. What assumptions were made in deriving the linear relationship?
5. How can we improve the precision of the intercept calculation?

Tip:

Always verify the linearity of your data points before assuming a linear model for conversions like ADC to voltage.