About ADC Calculator

An Analog-to-Digital Converter (ADC) converts continuous analog signals into digital numbers that represent the signal’s magnitude. The accuracy of this conversion is determined by the resolution of the ADC, which is expressed in bits. A higher number of bits provides better resolution and more precise digital representation.

Mathematical Equations

The conversion of the input voltage (\(V_{\text{in}}\)) to a digital value is calculated using the formula:

\[ADC\ Value = \left\lfloor \frac{V_{\text{in}}}{V_{\text{ref}}} \cdot (2^n – 1) \right\rfloor\]

• \(n\): Number of bits of the ADC
• \(V_{\text{in}}\): Analog input voltage
• \(V_{\text{ref}}\): Reference voltage
• \((2^n – 1)\): Maximum digital value for an \(n\)-bit ADC

Key Concepts:

• Resolution: The resolution of an ADC indicates the number of bits used to represent the
  digital output. For example, a 10-bit ADC can represent \(2^{10} = 1024\) discrete levels.
• Reference Voltage (\(V_{\text{ref}}\)): This is the maximum voltage that the ADC can
  measure. Any input voltage above \(V_{\text{ref}}\) will saturate at the maximum ADC value.
• Analog Input Voltage (\(V_{\text{in}}\)): The voltage being measured. This value must
  be within the range of 0 to \(V_{\text{ref}}\) for accurate conversion.

Example Calculations

Example 1: 10-bit ADC

For a 10-bit ADC with:

• Reference Voltage (\(V_{\text{ref}}\)) = 5V
• Analog Input Voltage (\(V_{\text{in}}\)) = 2.3V

Step 1: Calculate the maximum ADC value:

\[\text{Max Value} = 2^{10} – 1 = 1023\]

Step 2: Calculate the ADC output:

\[ADC\ Value = \frac{2.3}{5} \cdot 1023 = 471.78 \approx 472\]

Result: Numeric Output = 472, Binary Output = 111011000

Example 2: 12-bit ADC

For a 12-bit ADC with:

• Reference Voltage (\(V_{\text{ref}}\)) = 3.3V
• Analog Input Voltage (\(V_{\text{in}}\)) = 0.7V

Step 1: Calculate the maximum ADC value:

\[\text{Max Value} = 2^{12} – 1 = 4095\]

Step 2: Calculate the ADC output:

\[ADC\ Value = \frac{0.7}{3.3} \cdot 4095 = 869.55 \approx 870\]

Result: Numeric Output = 870, Binary Output = 1101100110

Example 3: 16-bit ADC

For a 16-bit ADC with:

• Reference Voltage (\(V_{\text{ref}}\)) = 3.6V
• Analog Input Voltage (\(V_{\text{in}}\)) = 1.8V

Step 1: Calculate the maximum ADC value:

\[\text{Max Value} = 2^{16} – 1 = 65535\]

Step 2: Calculate the ADC output:

\[ADC\ Value = \frac{1.8}{3.6} \cdot 65535 = 32767.5 \approx 32768\]

Result: Numeric Output = 32768, Binary Output = 1000000000000000