Engineering
Shannon-Hartley channel capacity (Mbps) & RF dBm-to-milliwatt formulas
Calculate theoretical maximum wireless throughput B * LOG(1 + 10^(SNR_dB/10), 2) and convert RF link-budget power between dBm and milliwatts.
Convert decibel SNR_dB to linear SNR before applying Shannon-Hartley!
The Shannon-Hartley expression C=B*LOG(1+S/N,2) describes an ideal band-limited additive white Gaussian noise channel with an average power constraint. Capacity is the limiting rate for arbitrarily small error with suitable coding, not a guarantee of zero errors or real Wi-Fi throughput. Protocol overhead and multi-antenna channels require additional modeling.
Convert SNR from dB to a linear power ratio using 10^(SNR_dB/10). Bandwidth in MHz gives capacity in Mbps. Link budgets add gains and losses in dB to a referenced power in dBm; do not add two dBm powers directly. The example 20 dBm + 6 dBi - 90 dB + 4 dBi gives -60 dBm under its assumed path model.
| RF / Wireless Calculation | Formula | Result |
|---|---|---|
| 20 MHz Channel @ 20 dB SNR (Linear 100) | 20 * LOG(1 + 10^(20/10), 2) | 133.16 Mbps |
| Spectral Efficiency (bits / s / Hz) | LOG(1 + 10^(20/10), 2) | 6.66 bps/Hz |
| Transmit Power +20 dBm -> Milliwatts | 10 ^ (20 / 10) | 100.0 mW |
| Link Budget: 20 dBm + 6 dBi - 90 dB + 4 dBi | Sum of dBm + dBi - Loss_dB | -60.0 dBm |
Shannon-Hartley channel capacity (Mbps) from MHz and SNR (dB)
A2=Bandwidth_MHz (20) and B2=SNR_dB (20); LOG(..., 2) computes base-2 logarithm.
=IF(OR(COUNT(A2:B2)<>2,A2<=0),"Invalid inputs",ROUND(A2 * LOG(1 + 10 ^ (B2 / 10), 2), 2))Convert dBm to milliwatts
C2 holds power in dBm. Use 10^(C2/10) without fixed decimal rounding so very small powers are not rounded to zero. Negative dBm and negative SNR in dB are valid. This example requires positive bandwidth.
=IF(NOT(ISNUMBER(C2)),"Invalid inputs",10^(C2/10))Try the example
Use the original values or change them to test your understanding.