Contents

**Introduction**

In this post we provide two calculators.

- The first calculator gives the oversampling ratio when you provide it with 1) the actual Sampling rate and 2) Nyquist rate. It uses this ratio to find the Signal-to-Noise Ratio (SNR) and resulting improvement in the Effective Number of Bits (ENOB)
- The second calculator gives the sampling rate required to achieve a desired increase in ENOB

Also provided is background information on oversampling and its benefits.

**Calculator** 1

Use this calculator to find the oversampling ratio **k** for a given 1) Sampling rate and 2) Nyquist rate.

The tool also provides:

- SNR Improvement
- Extra bits of resolution achieved from oversampling

**Example Calculation**

If the sampling rate is 40 kHz for a Nyquist rate of 10 kHz, the oversampling ratio k = 4. The SNR improvement is 6 dB and this results in an extra bit of resolution. In other words, the ENOB improves by one bit. For an 8 bit ADC, that’s quite significant.

**Calculator 2**

This calculator gives the sampling rate required to achieve a desired increase in ENOB.

To use the calculator enter 1) Required ENOB improvement 2) Nyquist Sampling Rate

**Example Calculation**

To achieve an ENOB improvement of 1 bit with a Nyquist rate of 100 kHz, requires a sampling rate of 400 kHz.

**Background**

Analog-to-digital converter (ADC) oversampling is a technique used to improve the effective resolution and signal-to-noise ratio (SNR) of analog-to-digital converters.

An ADC converts analog signals into digital data for processing and storage in digital systems. The conversion process introduces quantization noise because of the finite resolution of the ADC. This limits the precision of the digital representation of the analog signal.

Here’s how oversampling helps improve things:

**Increased Resolution**: Oversampling involves sampling the input signal at a significantly higher frequency than the Nyquist rate (twice the highest frequency present in the signal). With this the signal’s information is spread over more digital samples than what is minimally required. This extra information can then be processed to increase the effective resolution of the ADC beyond its nominal bit depth, allowing for finer detail to be captured in the digital representation of the analog signal.**Improved Signal-to-Noise Ratio (SNR)**: Oversampling also helps in reducing the impact of quantization noise on the signal. When the signal is oversampled, the quantization noise is spread across a wider range of frequencies. Then, by applying (low pass) digital filtering to this data, it’s possible to remove a significant portion of the noise while retaining the desired signal. This process effectively concentrates the signal’s power into a narrower bandwidth, thereby improving the SNR.**Noise Shaping**: In conjunction with oversampling, techniques like delta-sigma modulation can be used to shape the noise spectrum, pushing quantization noise into higher frequencies that are less relevant to the signal of interest. This further improves the SNR in the frequency range that matters for the application, allowing even lower resolution ADCs to achieve high fidelity in specific frequency bands.

ADC oversampling enhances the quality of digital representations of analog signals. This helps achieve both higher precision and better SNR than what the ADC’s raw specifications might suggest. This is particularly useful in applications requiring high accuracy and low noise, such as audio processing, high-precision measurements, and scientific research instruments.