Signal-to-Noise Ratio (SNR)
The Signal-to-Noise Ratio (SNR) compares the power of a desired signal to the power of background noise. It is usually expressed in decibels (dB); higher SNR indicates a cleaner, more reliable link.
Definition and Formulas
Linear: SNR = P_s / P_n
Power-based (dB): SNR_dB = 10 * log10(P_s / P_n)
Voltage-based (same impedance, dB): SNR_dB = 20 * log10(V_s / V_n)
where:
P_s = signal power
P_n = noise power
V_s = signal RMS (Root Mean Square) voltage (same impedance as V_n)
V_n = noise RMS voltage
SNR Calculator
Note: This calculator is for illustration and quick estimates. It assumes 290 K thermal noise and idealized conditions. For design, link planning or regulatory submissions, perform a full link-budget.
Formulas Used
SNR = P_s - P_n (both in dBm)Where:
P_s = signal power in dBm
P_n = noise power in dBm
Quick Examples
Signal: -50.0 dBm, Noise: -80.0 dBm
→ SNR = 30.0 dB
C: -70.0 dBm, NF: 6.0 dB, B: 20 MHz, R_b: 54 Mbps
→ SNR ≈ 23.0 dB
Typical SNR Requirements
| Modulation | Typical SNR (dB) | Application |
|---|---|---|
| BPSK | ~9-10 | Satellite, GPS |
| QPSK | ~12-13 | LTE, WiFi 802.11b |
| 16-QAM | ~20-21 | LTE, WiFi 802.11a/g |
| 64-QAM | ~28-29 | WiFi 802.11n/ac |
| 256-QAM | ~35-36 | WiFi 802.11ac/ax, 5G |
Practical Meaning and Units
SNR is unitless in linear form; in practice it is reported in dB.
A +3 dB increase roughly doubles the power ratio; +10 dB is a tenfold increase.
Negative SNR means the noise power exceeds the signal power within the measurement bandwidth.
Measurement in Practice
Define bandwidths clearly. Noise power scales with bandwidth. When comparing SNR values, keep measurement bandwidths consistent or normalize.
Use proper filtering and averaging. On spectrum analyzers, set RBW/VBW appropriately; average noise is usually reported with linear averaging.
Account for instrument noise figure and preamps. Front-end NF and gain affect measured noise floors; correct if necessary.
Ensure impedance match. The 20 * log10 voltage formula assumes equal impedance for signal and noise paths.
Document conditions. Frequency, bandwidth, detector settings, averaging time, and temperature improve result repeatability.
Relationship to C/N and C/N_0
Carrier-to-Noise ratio (C/N) compares carrier power to noise power within a specified noise bandwidth B_n.
Mapping: in linear terms, SNR = (C/N) * (B_s / B_n), where B_s is the signal bandwidth after filtering or demodulation.
In dB:
SNR_dB = (C/N)_dB + 10 * log10(B_s / B_n)
Carrier-to-Noise density (C/N_0) uses noise power spectral density N_0 (W/Hz). It relates to bit energy-to-noise density:
E_b/N_0 (dB) = C/N_0 (dB-Hz) - 10 * log10(R_b)
where:
B_s = signal (post-detection) bandwidth
B_n = noise bandwidth used for C/N
R_b = bit rate in Hz
Example Calculation
A receiver measures P_s = 1 mW and P_n = 1 µW in the same bandwidth.
SNR_dB = 10 * log10(1e-3 / 1e-6) = 10 * log10(1000) ≈ 30 dB.
Common Pitfalls
Comparing SNR values taken with different bandwidths or detector settings.
Using the 20 * log10 formula for voltages when impedances differ.
Ignoring adjacent-channel interference and treating it as noise without noting the source.
Reporting SNR without frequency and bandwidth context.