How to Calculate Sampling Rate of Adc

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ADC Sampling Rate Calculator

Hz kHz MHz GHz
The highest frequency component present in your analog signal.
Must be ≥ 2.0 (Nyquist Limit). Engineers typically use 2.5x to 10x for practical filter design.
Used to calculate the required data throughput rate.
Please enter a valid positive frequency.
Nyquist Rate (Theoretical Min): 0 Hz
Recommended Sampling Rate (fs): 0 Hz
Signal Bandwidth: 0 Hz
Data Throughput: 0 Mbps
function formatFrequency(hz) { if (hz >= 1000000000) { return (hz / 1000000000).toFixed(3) + ' GHz'; } else if (hz >= 1000000) { return (hz / 1000000).toFixed(3) + ' MHz'; } else if (hz >= 1000) { return (hz / 1000).toFixed(3) + ' kHz'; } else { return hz.toFixed(2) + ' Hz'; } } function calculateSamplingRate() { var freqInput = document.getElementById('maxFrequency').value; var unitMult = parseFloat(document.getElementById('frequencyUnit').value); var factorInput = document.getElementById('oversamplingFactor').value; var bitsInput = document.getElementById('bitDepth').value; var errorDiv = document.getElementById('error-msg'); var resultDiv = document.getElementById('result-area'); var datarateRow = document.getElementById('datarate-row'); // Validation if (freqInput === "" || isNaN(freqInput) || parseFloat(freqInput) <= 0) { errorDiv.style.display = "block"; resultDiv.style.display = "none"; return; } var oversampling = parseFloat(factorInput); if (isNaN(oversampling) || oversampling 0) { var bits = parseFloat(bitsInput); var bitsPerSecond = recommendedHz * bits; var throughputText = ""; if (bitsPerSecond >= 1000000000) { throughputText = (bitsPerSecond / 1000000000).toFixed(2) + " Gbps"; } else if (bitsPerSecond >= 1000000) { throughputText = (bitsPerSecond / 1000000).toFixed(2) + " Mbps"; } else if (bitsPerSecond >= 1000) { throughputText = (bitsPerSecond / 1000).toFixed(2) + " kbps"; } else { throughputText = bitsPerSecond.toFixed(0) + " bps"; } document.getElementById('dataRate').innerHTML = throughputText; datarateRow.style.display = "flex"; } else { datarateRow.style.display = "none"; } }

How to Calculate Sampling Rate of ADC

Calculating the correct sampling rate for an Analog-to-Digital Converter (ADC) is a fundamental step in digital signal processing and embedded systems design. Choosing the right rate ensures that the analog signal is reconstructed accurately in the digital domain without data loss or distortion known as aliasing.

The Nyquist-Shannon Sampling Theorem

The calculation relies primarily on the Nyquist-Shannon Sampling Theorem. This theorem states that to perfectly reconstruct a signal, you must sample it at a rate (frequency) at least twice the maximum frequency component present in the signal.

The formula for the minimum theoretical sampling rate (Nyquist Rate) is:

fs ≥ 2 × fmax
  • fs: Sampling Rate (samples per second).
  • fmax: The highest frequency component in the analog signal.

Why Use Oversampling?

While the Nyquist rate (2x) is the theoretical minimum, practical engineering usually requires a higher rate. This is called oversampling. Using a multiplier (often 2.5x to 10x) provides several benefits:

  • Anti-Aliasing Filter Design: Real-world analog filters cannot cut off frequencies instantly at fmax. A higher sampling rate creates a "transition band," making filter design cheaper and simpler.
  • Noise Reduction: Oversampling can improve the Signal-to-Noise Ratio (SNR) by spreading quantization noise over a wider bandwidth.
  • Phase Linearity: Higher sampling rates preserve the phase information of high-frequency components more accurately.

Calculation Example

Let's say you are sampling an audio signal. The human ear can hear up to approximately 20 kHz.

  1. Identify fmax: 20 kHz (20,000 Hz).
  2. Calculate Nyquist Rate: 20 kHz × 2 = 40 kHz.
  3. Apply Safety Margin: Standard audio uses 44.1 kHz or 48 kHz. 44.1 kHz is roughly 2.2x the max frequency, allowing room for the anti-aliasing filter to roll off.

Calculating Data Throughput

Once you determine the sampling rate, you often need to know the required data bandwidth (Bit Rate). The formula is:

Data Rate = Sampling Rate × Bit Depth

For example, a 48 kHz sampling rate with a 16-bit ADC resolution results in:
48,000 × 16 = 768,000 bits per second (768 kbps).

Common Applications and Rates

  • Telephone Voice: fmax ≈ 3.4 kHz → Sampling Rate: 8 kHz.
  • CD Audio: fmax ≈ 20 kHz → Sampling Rate: 44.1 kHz.
  • Professional Audio: fmax ≈ 24 kHz → Sampling Rate: 48 kHz or 96 kHz.
  • Biomedical (ECG): fmax ≈ 150 Hz → Sampling Rate: 500 Hz to 1 kHz.

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