A 41.5% Bar Hides a 38 dB Power Gap

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

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.

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.