10 bit ADC Conversion Formula and Calculator

This tool provides the ADC resolution and the digital value for an analog input signal.

Enter:

  • Input Voltage Vin
  • Reference Voltage Vref
  • Number of bits

Formula for 10-bit ADC

The analog resolution or the smallest value that can be measured by the ADC is given by the formula:

(Vref)/210

where

  • Vref is the reference voltage

The digital output from an ADC is given by the following formula for a 10-bit ADC.

Digital output = 210 * (Vin)/(Vref)

where

  • Vin is the analog input
  • Vref is the analog reference

Example Calculation for 10-bit ADC

For example, if an 10-bit ADC has a reference voltage (Vref) of 5V, the smallest change it can detect (quantum) is Vref / 210 = 5V / 1024 ≈ 4.88 mV. This means each step of the digital output corresponds to a change of about 4.88 mV in the input signal.

Analog input voltage of 1 Volt gives a digital output level of 11001101.

Background

What is a 10-bit ADC?

An 10-bit Analog-to-Digital Converter (ADC) is a device that converts analog signals into digital signals. The “10-bit” part refers to the resolution of the ADC, meaning it can produce 210 = 1024 discrete values. This process involves several key steps and concepts which are important to understand how ADCs work.

  • Sampling: The first step in the ADC process is sampling the analog signal at regular intervals. The frequency at which the signal is sampled is determined by the Nyquist theorem, which states that the sampling rate should be at least twice the highest frequency present in the analog signal to accurately represent the signal.
  • Quantization: After sampling, each sampled analog value is assigned to the nearest value represented by the 8-bit resolution. Because an 8-bit ADC can only represent 256 discrete levels, this step introduces a quantization error, as the analog value might not match exactly with the discrete levels available. The range of the analog signal that the ADC can convert is determined by its reference voltage (Vref); the resolution determines how finely it can divide this range.
  • Digital Representation: The result of the quantization step is a digital representation of the analog input. For a 10-bit ADC, this digital representation will be a number between 0 and 1023, where 0 represents the lowest possible input (often 0V or GND) and 1023 represents the highest (equal to Vref).
  • Resolution and Accuracy: The resolution of an ADC determines how many discrete values it can produce and affects the precision of the digital output. However, accuracy also depends on other factors such as noise, linearity errors, and the stability of the reference voltage.
  • Voltage Range and Scaling: The input voltage range of an ADC is determined by its design and the reference voltage used. Sometimes, input signals need to be scaled down or conditioned through amplifiers or attenuators to fit within the ADC’s input range. Voltage dividers are used to scale a voltage down.

A 10-bit ADC is widely used in various applications due to its balance between simplicity, resolution, and cost. Applications range from simple data acquisition systems to complex embedded systems, audio processing, and more.