# Maximum Quantization Error for ADCs Calculator

In this post we provide a tool to calculate the maximum quantization error for Analog-to-Digital converters. This error depends on the input voltage range and the resolution of the ADC.

The post also includes additional background and explanatory information on quantization errors.

## Calculator

Enter the max and min input voltage values and number of ADC bits.

## Formula

Max Quantization Error = + [(VMax-VMin)/(2N+1)]

Where

• VMax is the maximum input analog voltage level
• VMin is the maximum input analog voltage level
• VMax – VMin represents the Full scale range of the ADC
• N is the number of ADC bits

## Example Calculation

For a 12-bit ADC with a full-scale range of 0 to 5V:

• The number of levels is 212=4096
• The value of one LSB is 5V/4096 â‰ˆ 1.22â€‰mV
• Thus, the maximum quantization error is Â± 0.61 mV.

## Background

Quantization error in an Analog-to-Digital Converter (ADC) refers to the difference between the actual analog input signal and the digitized output value produced by the ADC.

This error is inherent in the process of quantization, where a continuous range of analog values is mapped to a limited set of discrete digital levels.

The picture below shows the effect of quantization where a range of analog values are mapped to a digital word thereby resulting in an approximation and associated error value. For instance input voltage values of 0.125 to 0.375 Volt are mapped to 001.

Increasing the number of bits in the ADC reduces the error value and as the number of bits approaches infinite, the step converges to the straight line associated with the Ideal ADC.

### Key Aspects of Quantization Error

• Nature of Error: Quantization error is essentially a form of rounding error. It occurs because an ADC can only represent an analog signal by a finite number of digital levels. The finer the levels (higher resolution), the smaller the quantization error.
• Magnitude of Error: The maximum quantization error for an ADC is generally Â±1/2 of one Least Significant Bit (LSB). This is because the analog signal can fall anywhere within the range defined by one LSB, leading to a maximum deviation when the signal is midway between two adjacent quantization levels.
• Resolution Dependency: The resolution of an ADC, typically measured in bits, directly affects the quantization error. A higher-resolution ADC, with more bits, can produce a more accurate representation of the analog signal, resulting in a smaller quantization error. For example, an 8-bit ADC has 256 discrete levels, while a 16-bit ADC has 65,536 levels.

### Implications

While quantization error is unavoidable in digital systems, its impact can be minimized by using ADCs with higher resolution or employing techniques like dithering, which adds a small amount of noise to the signal before conversion to spread the quantization error across a broader spectrum, making it less noticeable in certain applications.