Calculator Inputs
Example Data Table
| Bandwidth | SNR | Capacity | Spectral Efficiency | Required Eb/N0 |
|---|---|---|---|---|
| 1 MHz | 10 dB | 3.4594 Mbps | 3.4594 bits/s/Hz | 4.61 dB |
| 2 MHz | 20 dB | 13.3164 Mbps | 6.6582 bits/s/Hz | 11.77 dB |
| 5 MHz | 15 dB | 25.1390 Mbps | 5.0278 bits/s/Hz | 7.99 dB |
| 10 MHz | 30 dB | 99.6723 Mbps | 9.9672 bits/s/Hz | 20.01 dB |
Formula Used
C = B × log2(1 + S/N)
η = C / B = log2(1 + S/N)
B = C / log2(1 + S/N)
S/N = 2(C/B) - 1
Eb/N0 = (2η - 1) / η
In these formulas, C is channel capacity in bits per second, B is bandwidth in hertz, S/N is linear signal-to-noise ratio, and η is spectral efficiency in bits per second per hertz. The well-known asymptotic Shannon floor is approximately -1.59 dB.
How to Use This Calculator
- Select the required calculation mode first.
- Choose whether SNR comes from direct dB input or power values.
- Enter bandwidth, data rate, spectral efficiency, or power data as needed.
- Press Calculate Shannon Limit to show results above the form.
- Review capacity, required SNR, required bandwidth, and required Eb/N0.
- Use the CSV and PDF buttons to export the displayed result summary.
- Study the Plotly graph to understand how capacity or Eb/N0 changes.
FAQs
1. What does the Shannon limit represent?
It represents the theoretical maximum reliable data rate for a noisy communication channel with a given bandwidth and signal-to-noise ratio.
2. Is this calculator only for wireless systems?
No. The formulas apply to any communication channel where bandwidth and noise are relevant, including wireless, wired, optical, and satellite links.
3. Why is SNR sometimes entered in dB and sometimes in linear form?
Engineers often measure SNR in dB for convenience. Shannon equations use linear SNR internally, so the calculator converts dB automatically.
4. What is spectral efficiency?
Spectral efficiency is the number of bits transmitted each second per hertz of bandwidth. Higher values require cleaner channels or more advanced coding.
5. What does required Eb/N0 mean?
It is the minimum energy-per-bit to noise-density ratio needed to support a chosen spectral efficiency under ideal Shannon assumptions.
6. Why is the Shannon floor shown as -1.59 dB?
That value is the theoretical lower bound for Eb/N0 as spectral efficiency approaches zero. Real systems usually require more.
7. Can real systems achieve the exact calculator result?
Not exactly. The calculator gives an ideal upper bound. Real modulation, coding, interference, implementation loss, and fading reduce achievable performance.
8. Why might my required SNR look very high?
A high target data rate over a narrow bandwidth raises spectral efficiency. Higher spectral efficiency demands sharply higher SNR in Shannon theory.