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SNR and Eb/N0 Relationship

#SNR#Eb/N0#digital communications#BER#modulation

SNR and Eb/N0 Relationship

Eb/N0 (energy per bit to noise power spectral density ratio) is the fundamental measure of digital communication system performance. This formula relates it to the more commonly measured SNR.

EbN0=SN⋅BRb\frac{E_b}{N_0} = \frac{S}{N} \cdot \frac{B}{R_b}

Alternative Forms

In dB
EbN0dB=SNRdB+10log⁡10(BRb)\frac{E_b}{N_0}_{dB} = SNR_{dB} + 10\log_{10}\left(\frac{B}{R_b}\right)
Decibel form for practical calculations
With Spectral Efficiency
EbN0=SNR⋅1η\frac{E_b}{N_0} = SNR \cdot \frac{1}{\eta}
Using spectral efficiency η = Rb/B

Input Variables

dB

Measured SNR in the channel bandwidth(Range: -10 – 60 dB)

MHz

Channel bandwidth(Range: 0.001 – 1000 MHz)

Mbps

Data rate in megabits per second(Range: 0.001 – 10000 Mbps)

Results

Energy per Bit to Noise Density (Eb/N0)
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📖 Example: Wi-Fi Link Analysis

Calculate Eb/N0 for 10 Mbps in 20 MHz channel with 10 dB SNR

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