ADC resolution and reference voltage in Embedded C

Introduction

ADC resolution and reference voltage help convert real-world signals into numbers a microcontroller can understand.

Measuring temperature with a sensor that outputs voltage.

Reading battery level to check how much charge is left.

Detecting light intensity using a photoresistor.

Measuring sound levels with a microphone.

Reading joystick position for a game controller.

Syntax

Embedded C

digital_value = (analog_voltage / reference_voltage) * ((1 << resolution) - 1);

resolution is the number of bits the ADC uses (e.g., 10 bits means values from 0 to 1023).

reference_voltage is the maximum voltage the ADC can measure (e.g., 5V or 3.3V).

Examples

This example calculates the digital value for 2.5V input with 10-bit ADC and 5V reference.

Embedded C

resolution = 10;
reference_voltage = 5.0;
analog_voltage = 2.5;
digital_value = (analog_voltage / reference_voltage) * ((1 << resolution) - 1);

Here, a 12-bit ADC with 3.3V reference converts 1.65V input.

Embedded C

resolution = 12;
reference_voltage = 3.3;
analog_voltage = 1.65;
digital_value = (analog_voltage / reference_voltage) * ((1 << resolution) - 1);

Sample Program

This program calculates the digital output of a 10-bit ADC with 5V reference for an input voltage of 2.5V.

Embedded C

#include <stdio.h>

int main() {
    int resolution = 10; // 10-bit ADC
    float reference_voltage = 5.0; // 5V reference
    float analog_voltage = 2.5; // example input voltage

    int max_digital = (1 << resolution) - 1; // 1023 for 10-bit
    int digital_value = (int)((analog_voltage / reference_voltage) * max_digital);

    printf("Analog voltage: %.2f V\n", analog_voltage);
    printf("Digital value (ADC output): %d\n", digital_value);

    return 0;
}

Important Notes

Higher resolution means more precise measurements but may take longer to convert.

Reference voltage sets the maximum voltage the ADC can read; using a stable reference improves accuracy.

Always scale your input voltage to be within 0 and reference voltage to avoid incorrect readings.

Summary

ADC resolution defines how many steps the analog input is divided into.

Reference voltage is the maximum voltage the ADC can measure.

Digital value = (input voltage / reference voltage) x (2^resolution - 1).

Practice

1. What does the ADC resolution represent in an embedded system?

easy

A. The power consumption of the ADC

B. The maximum voltage the ADC can measure

C. The speed at which the ADC converts analog to digital

D. The number of discrete steps the analog input voltage is divided into

Solution

1. Step 1: Understand ADC resolution meaning

   ADC resolution defines how many discrete digital values the analog input voltage can be divided into.

2. Step 2: Differentiate from reference voltage

   Reference voltage is the max voltage measurable, not the number of steps.

3. Final Answer:

   The number of discrete steps the analog input voltage is divided into -> Option D

4. Quick Check:

   ADC resolution = number of steps [OK]

Hint: Resolution means how many steps ADC splits the input into [OK]

Common Mistakes:

• Confusing resolution with reference voltage
• Thinking resolution is speed or power
• Mixing up digital output range with voltage

2. Which of the following C code snippets correctly calculates the digital output value from an ADC input voltage?

easy

A. digital_value = input_voltage * reference_voltage / resolution;

B. digital_value = (reference_voltage / input_voltage) * (resolution - 1);

C. digital_value = (input_voltage / reference_voltage) * ((1 << resolution) - 1);

D. digital_value = (input_voltage + reference_voltage) / resolution;

Solution

1. Step 1: Recall the formula for ADC digital value

   Digital value = (input voltage / reference voltage) x (2^resolution - 1).

2. Step 2: Match formula with code

   digital_value = (input_voltage / reference_voltage) * ((1 << resolution) - 1); uses (1 << resolution) - 1 which is 2^resolution - 1, correctly applying the formula.

3. Final Answer:

   digital_value = (input_voltage / reference_voltage) * ((1 << resolution) - 1); -> Option C

4. Quick Check:

   Use (input/reference) * (2^resolution - 1) [OK]

Hint: Use bit shift for 2^resolution minus 1 in code [OK]

Common Mistakes:

• Dividing reference voltage by input voltage
• Using addition instead of multiplication
• Incorrectly calculating 2^resolution

3. Given an ADC with 10-bit resolution and a reference voltage of 5V, what is the digital output value for an input voltage of 2.5V?
resolution = 10;
reference_voltage = 5.0;
input_voltage = 2.5;

medium

A. 1023

B. 512

C. 256

D. 1024

Solution

1. Step 1: Calculate max digital value for 10-bit ADC

   Max value = 2^10 - 1 = 1023.

2. Step 2: Calculate digital output for 2.5V input

   Digital value = (2.5 / 5.0) * 1023 = 0.5 * 1023 = 511.5, rounded to 512.

3. Final Answer:

   512 -> Option B

4. Quick Check:

   Half of max 1023 is about 512 [OK]

Hint: Half input voltage gives about half max digital value [OK]

Common Mistakes:

• Using 1024 instead of 1023 as max value
• Not rounding the result
• Confusing input and reference voltage ratio

4. Identify the error in the following code snippet for calculating ADC digital value:

int resolution = 8;
float reference_voltage = 3.3;
float input_voltage = 1.65;
int digital_value = (input_voltage / reference_voltage) * (1 << resolution);

medium

A. Missing parentheses around (1 << resolution) - 1

B. Using float division instead of integer division

C. Incorrect variable types for voltage

D. No error, code is correct

Solution

1. Step 1: Check formula correctness

   The formula should use (2^resolution - 1), which is (1 << resolution) - 1, not just (1 << resolution).

2. Step 2: Identify missing subtraction

   Code misses the '- 1', so max digital value is off by one.

3. Final Answer:

   Missing parentheses around (1 << resolution) - 1 -> Option A

4. Quick Check:

   Max digital value = 2^resolution - 1 [OK]

Hint: Remember max ADC value is 2^resolution minus 1 [OK]

Common Mistakes:

• Forgetting to subtract 1 from 2^resolution
• Confusing integer and float division
• Assuming no parentheses needed

5. You have a 12-bit ADC with a 3.3V reference voltage. You want to measure an input voltage range from 0 to 1.65V only. How should you adjust the calculation to get the correct digital output value for this limited range?

hard

A. Use 1.65V as the reference voltage in the formula instead of 3.3V

B. Keep 3.3V as reference and multiply digital value by 2

C. Double the resolution to 24 bits in the formula

D. Divide input voltage by 2 before calculation

Solution

1. Step 1: Understand reference voltage role

   Reference voltage sets the max measurable voltage for ADC conversion.

2. Step 2: Adjust reference voltage for limited input range

   Since input max is 1.65V, use 1.65V as reference to scale digital output correctly.

3. Final Answer:

   Use 1.65V as the reference voltage in the formula instead of 3.3V -> Option A

4. Quick Check:

   Reference voltage = max input voltage [OK]

Hint: Set reference voltage to max input voltage for correct scaling [OK]

Common Mistakes:

• Using full 3.3V reference for smaller input range
• Trying to adjust resolution instead of reference voltage
• Incorrectly scaling input voltage before calculation