A 41.5% Bar Hides a 38 dB Power Gap

A 41.5% Bar Hides a 38 dB Power Gap

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

A 41.5% Bar Hides a 38 dB Power Gap

The diagnostics lab maps an RSSI of -68 dBm onto a friendly 41.5% quality bar, drawn as a straight line from -95 dBm at the floor to -30 dBm for excellent. The percentage reads reassuring, but decibels are logarithmic, so that same reading actually sits a 38 dB gap below the excellent reference. This audit converts the linear bar into real power to show what a 41.5% reading hides.

Companion to the chapter Lab: Network Diagnostics — every number here comes from that chapter.

See the relationship before changing it

The figure reads from left to right. The blue card is received signal strength. The middle card applies this page's rule. The green card is power gap to excellent. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only received signal strength, so the numeric fixture does not switch without explanation.

Received signal strength changes power gap to excellent An input card leads through the rule power gap = 10^((-30 dBm - RSSI) / 10) to the power gap to excellent result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. A linear-looking quality bar hides an exponential power gap because decibels are logarithmic.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is -68 dBm.

  2. 2

    Name the relationship. power gap = 10^((-30 dBm - RSSI) / 10)

  3. 3

    Substitute with units. 10^((-30 - -68) / 10) = 6,310 times

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change received signal strength

Try Predict the direction of power gap = 10^((-30 dBm - RSSI) / 10). Test another received signal strength, then compare power gap to excellent.

-68 dBm
Chapter baseline
Power gap to excellent

Observe A linear-looking quality bar hides an exponential power gap because decibels are logarithmic. Reset received signal strength to -68 and compare power gap to excellent.

Explain A linear-looking quality bar hides an exponential power gap because decibels are logarithmic.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only received signal strength moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only received signal strength. It is not a field prediction.

TryChoose Check derivation for -68 dBm on the bar spanning -95 to -30 dBm.
ObserveThe linear quality display reads 41.5%, yet the power-gap evidence remains 38 dB or about 6,310x below the excellent reference.
ExplainThe bar linearly interpolates decibel labels, but physical power follows 10 raised to dB divided by 10, so percentage distance is not power ratio.

Ready: use the stated baseline inputs, then compare each displayed result.

Ada: The lab converts an RSSI of -68 dBm into a “41.5% quality” reading using a linear scale from -95 dBm (floor) to -30 dBm (excellent). That percentage is honest for a progress bar, but it quietly flatters the link, so let me compute it and then convert the same gap into actual power.

The quality figure is a straight-line interpolation between the two anchors:

  • Numerator: -68 - (-95) = 27 dB above the floor.
  • Span: -30 - (-95) = 65 dB from floor to excellent.
  • Quality: 27 / 65 = 0.41538, i.e. 41.5%.

Now the same distance in real power. Decibels are logarithmic, so a gap of -30 - (-68) = 38 dB is a power ratio of:

  • 10^(38 / 10) = 10^3.8 = 6309.6, about 6,310x.

So the “excellent” reference carries roughly 6,310 times the received power of the -68 dBm sensor, even though the linear bar shows the sensor as only 58.5% short of the top. The design meaning is that a friendly linear percentage understates how marginal a weak link is: “41.5% quality” is really a signal sitting almost four orders of magnitude below the excellent reference, which is exactly why link budgets are kept in decibels and why a few dB of extra path loss can tip a “usable” bar into dropped packets.

Every number above is taken from the chapter’s own material and re-derived step by step.

Technical boundaries. Receiver calibration, fading, noise variation, packet delivery, antenna orientation, and temporal averaging are omitted from this fixed display-versus-power comparison.