Turn a link budget into a maximum data rate in the sandbox, and predict — before you read it off the screen — the link SNR, the spectral efficiency, and the Shannon capacity C = B log2(1 + SNR) the channel can carry.
A link budget tells you the received power; Shannon tells you the most that power can buy. Take the received power the demo computes and subtract the thermal-noise floor kTB it prints, and you have the link SNR in dB. Convert it to a linear ratio with SNR = 10^(SNR_dB/10), and the Shannon–Hartley law C = B log2(1 + SNR) gives the maximum error-free bit rate for a channel of bandwidth B. Bandwidth enters linearly and SNR through a logarithm — which is why widening the channel pays far more than adding power, and why at high SNR a 3 dB gain buys only about one more bit/s/Hz.
Open the sandbox and pick the Office WiFi 2.4 GHz preset from the scenario dropdown — the same worked link as the M9 lab, read this time for its data-rate ceiling. Each step names the one thing to read or compute; leave everything else alone.
Scenario preset -> Office WiFi 2.4 GHz Channel bandwidth B -> 20 MHz
Open the NOISE panel -> read Prx and the thermal-noise floor kTB (both dBm)
Watch the received-power readout Prx and the thermal-noise-floor readout kTB, both in dBm — their difference is the link SNR that sets the capacity.
With the Office WiFi 2.4 GHz preset, the budget delivers a received power of Prx = -56.83 dBm, and the thermal-noise floor in the 20 MHz channel is kTB = -100.96 dBm. Predict the link SNR = Prx - kTB, then read it off the noise panel.
The link SNR = Prx - kTB = -56.83 - (-100.96) = 44.13 dB — the received signal sits 44.13 dB above the thermal floor. This is the demo's own received power minus its own noise floor, not a typed number.
Shannon's formula needs the SNR as a linear power ratio, not decibels. Convert the 44.13 dB with SNR = 10^(SNR_dB/10). Predict that ratio, then check it against the panel.
The linear ratio is SNR = 10^(44.13/10) = 25882.97 — a signal roughly twenty-six thousand times stronger than the noise. This is the same SNR, only unlogged; it is what goes inside log2(1 + SNR).
Spectral efficiency is capacity per hertz, C/B = log2(1 + SNR) in bit/s/Hz — the number of bits each hertz of bandwidth can carry. Predict log2(1 + 25882.97), then read it.
The spectral efficiency is C/B = log2(1 + 25882.97) = 14.66 bit/s/Hz — this WiFi link could in principle carry about 14.66 bits in every hertz of its channel.
Now multiply by the bandwidth. The channel is B = 20 MHz wide, so C = B log2(1 + SNR) = 20 MHz x 14.66 bit/s/Hz. Predict the capacity in Mbit/s, then read it.
The Shannon capacity is C = 20 MHz x 14.66 = 293.2 Mbit/s — the theoretical ceiling for this link against thermal noise. Because B enters linearly, doubling the channel to 40 MHz would double the ceiling; the demo's own bandwidth and SNR set this figure.
Bandwidth is linear but SNR is inside a logarithm, so power has sharply diminishing returns. Raising the SNR by 3 dB doubles the linear ratio; predict how much that adds to the spectral efficiency, log2(1 + 2·SNR) - log2(1 + SNR).
At this high SNR the gain is log2(1 + 2·SNR) - log2(1 + SNR) = 1 bit/s/Hz — a 3 dB power gain adds only about one more bit per hertz. To double the capacity through power alone you would have to square the SNR; widening the channel is the cheaper lever.
Everything above is waiting in the sandbox. Switch presets and watch the SNR and the capacity move together: the wide 80 MHz WiFi 5 channel and the narrow 125 kHz LoRa link sit at opposite ends of the bandwidth-vs-SNR trade, and dragging the required SNR or the distance shows the capacity ceiling rise and fall in real time.
- Read the link SNR straight off the budget: Prx - kTB = -56.83 - (-100.96) = 44.13 dB
- Converted it to a linear ratio, SNR = 10^(44.13/10) = 25882.97
- Found the spectral efficiency log2(1 + SNR) = 14.66 bit/s/Hz and the Shannon capacity C = 20 MHz x 14.66 = 293.2 Mbit/s
- Saw why bandwidth beats power: at high SNR, +3 dB buys only 1 bit/s/Hz
- Every value is the demo's own budget arithmetic, not a picture