Misguided testing

Tom's job was to test light sensors for the Navy. He would mount 4 sensors at a time in a test circuit, then shine a light at them and measure the output.

"Sensor #157 is clearly the best," Tom concluded. "It's signal is weak, but the relative noise is 42% lower than any of the other sensors on the board. That's really amazing!"

"I can tell right away you've made a mistake," said Tom's boss.

What was Tom's mistake?

Rules:

• Tom's boss doesn't know any more than we do.
• 42% (not 41% or 43%) must be the key clue to the answer.
• Some knowledge of electronics is involved. But it doesn't matter how you explain the electronics so long as you can say where 42% comes from.
• Does he test all four sensors on the board at once, or does he test them one at a time, in order? Jun 28 '16 at 4:30
• @Vaekor He tests them at the same time.
– Owen
Jun 28 '16 at 4:42
• He chose the other leading sensors over "tide"... Jun 28 '16 at 5:34
• I added the physics tag to this question since it apparently requires knowledge of electrical circuits. If this isn't the case feel free to remove it. Jun 28 '16 at 12:48
• What does "relative noise" mean, SNR inverted?? Jun 28 '16 at 13:11

the tester got one of the signal lines and the ground line transposed.

resulting in

one signal that's the sum of the other sensors signal currents and the other sensors having the voltage noise of the sensor 157 added to them.

the fact that 0.58 is $\sqrt{1/3}$ is probably signifigant here.

• I tried to comment "bingo" but apparently that's too short.
– Owen
Jun 30 '16 at 22:24

It seems like there are a lot of possibilities depending on things that Tom's boss knows and we don't. Perhaps

these sensors are of a known type whose signal-to-noise ratio is well understood and never varies by anything like 42%. (Or: whose sensitivity is well understood and basically never varies at all.)

Or perhaps

these sensors are known to introduce minimal noise of their own, so that SNR is almost entirely determined by the signal level (and in particular a lower-signal sensor on the same board shouldn't be able to have better SNR).

Or perhaps

as Quark suggests in his answer, relative noise in these sensors is always higher when the signal is lower (e.g., because it's almost entirely shot noise).

Or perhaps

there were fewer than 157 different sensors, so Tom must have been testing the wrong thing (perhaps another, more expensive part).

Or perhaps

the metric that actually matters for their application is sensitivity and not relative noise, so Tom's conclusion is inconsistent with his observations.

Or, for that matter, maybe

Tom's words quoted in the question were from a written report and his boss was complaining about the "It's" rather than about anything to do with the sensors.

• The last one - lol.
– TTT
Jun 28 '16 at 19:45
• Glad you like it :-). (I actually reckoned there was maybe a 10% chance that was the intended answer. But Owen has been around here since I posted it, so I think we can assume that if it were he'd have said so by now.) Jun 28 '16 at 20:30

I think that:

Tom ran sensor #157 alone, or not as one of four. (Guessing by the number, which is one more than a number divisible by four)

• It's possible that in a batch Tom had sensors 156, 157, 158, 159 Jun 28 '16 at 21:04

Possibly,

The readings are reversed, and that particular sensor is more sensitive and has more noise. This conclusion would come from the fact that signal-to-noise ratio should be lower in low lighting conditions.

Does the 42 have to do with

the "Hitchhiker's Guide To The Galaxy" ?

Just a thought

the noise is not lower, but higher.

Tom said, relative noise. so,
4 sensors was tested at the same time.
noise is 42% HIGER than 3 sensor, where each noise is 19%.
100 - 42 = 58,
58 / 3 sensors = 19%

• If I understand this right, you're suggesting that the only noise is common to all sensors. That fact would be a thing Tom's boss knows and we don't, contrary to what the questioner's told us... Jun 30 '16 at 8:18
• You right @GarethMcCaughan, I need more clue. Jus wondering, 42 is a trap. Jun 30 '16 at 9:25