Signal-to-Noise Ratio
SNR = 10 × log₁₀(Ps/Pn)
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Formula
Description
Signal-to-noise ratio measures how much stronger the desired signal is compared to the background noise, expressed in decibels. Higher SNR means cleaner signal quality. In digital communications, minimum SNR thresholds determine the achievable data rate and modulation scheme. In audio, SNR defines the dynamic range available. Thermal noise (Johnson-Nyquist noise) in resistors sets a fundamental noise floor: P_noise = kTB, where k is Boltzmann's constant, T is temperature in Kelvin, and B is bandwidth in Hz.
Variables
- SNR — Signal-to-noise ratio (dB)
- Psignal — Signal power (W)
- Pnoise — Noise power (W)
Practical Notes
Typical SNR requirements: telephone quality audio 30 dB, CD quality audio 96 dB, WiFi (OFDM 64-QAM) 25 dB, cellular LTE 15-25 dB depending on modulation. Op-amp circuits typically achieve 60-100 dB SNR. To improve SNR, either increase signal power or reduce noise bandwidth through filtering.
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