SNR Converter
Free Snrconverter Converter for signal & frequency units. Enter a value to see equivalent measurements across systems.
Formula
SNR (dB) = 10 * log10(P_signal / P_noise)
SNR in dB equals 10 times the base-10 logarithm of the signal-to-noise power ratio. Shannon capacity = BW * log2(1 + SNR_linear). ENOB = (SINAD - 1.76) / 6.02.
Worked Examples
Example 1: WiFi Link Budget
Problem: A WiFi signal at -50 dBm with noise floor at -90 dBm over 20 MHz bandwidth.
Solution: SNR = -50 - (-90) = 40 dB\nSNR linear = 10^(40/10) = 10,000\nShannon capacity = 20e6 * log2(1 + 10000) = 266 Mbps\nEb/No = 40 - 10*log10(20e6) = -33 dB
Result: SNR = 40 dB | Shannon capacity = 266 Mbps
Example 2: ADC Quality Assessment
Problem: A 16-bit ADC measures SINAD of 85 dB. What is the effective number of bits?
Solution: ENOB = (SINAD - 1.76) / 6.02\nENOB = (85 - 1.76) / 6.02\nENOB = 83.24 / 6.02 = 13.83 bits\nLost bits = 16 - 13.83 = 2.17 bits
Result: ENOB = 13.83 bits (2.17 bits lost to noise/distortion)
Frequently Asked Questions
What is Signal-to-Noise Ratio (SNR)?
SNR is the ratio of desired signal power to unwanted noise power, typically expressed in decibels (dB). A higher SNR means the signal is clearer relative to the noise. In dB, SNR = 10*log10(Psignal/Pnoise). For example, 20 dB SNR means the signal is 100 times more powerful than the noise. SNR is a fundamental metric in communications, audio engineering, medical imaging, and any field where signal quality matters.
What is Shannon channel capacity and how does SNR affect it?
Shannon channel capacity is the theoretical maximum data rate achievable over a noisy channel, given by C = B * log2(1 + SNR), where B is bandwidth in Hz and SNR is the linear power ratio. This means doubling the bandwidth doubles capacity, but increasing SNR has diminishing returns. For example, a 1 MHz channel with 20 dB SNR can theoretically carry about 6.66 Mbps. This theorem sets the fundamental limit that no real communication system can exceed.
What is Eb/No and how does it differ from SNR?
Eb/No (energy per bit to noise power spectral density ratio) normalizes SNR by the data rate and bandwidth. While SNR depends on the measurement bandwidth, Eb/No is a more fundamental measure of signal quality per bit of information. The relationship is Eb/No = SNR - 10*log10(bit rate/bandwidth). Eb/No is used to compare modulation schemes and coding techniques on equal footing, independent of bandwidth.
What is ENOB and how does it relate to SNR?
ENOB (Effective Number of Bits) quantifies the dynamic range of an analog-to-digital converter in terms of equivalent ideal ADC bits. It is calculated from SINAD (Signal to Noise and Distortion ratio) as ENOB = (SINAD - 1.76) / 6.02. An ideal 12-bit ADC has SINAD of 74 dB and ENOB of 12. Real ADCs always have ENOB less than their nominal resolution due to noise and distortion. ENOB is a key specification for evaluating ADC performance.
How accurate are the results from SNR Converter?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.