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When designing a PCB, is it sensible to use a pin jumper in the pathway of a small current signal (around 0.8 uA) or could there be issues with noise? I would use the jumper to select between different transimpedance amplifiers.

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Jumpers are no more noisy than any other simple male/female connector. As long as the jumper is a nice and tight fit and there is a good electrical contact made there will be no connector noise.

The general structure of a jumper, being wide and flat, means it's not much of an antenna like a raised loop of wire would be, so it won't pick up much in the way of induced noise.

The main issues are with badly fitting jumpers. Bad electrical contacts can result in additional resistances, which themselves can generate noise, or in a worst case scenario you get a diode effect, which can not only itself corrupt your signal, but under certain conditions act like a radio receiver (aka cats whisker) picking up EM interference from the environment.

But in general with a good fitting jumper you get no more noise than say a jack plug, or a Molex KK connector, which is to say a pretty much immeasurable amount.

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It sounds like there will just be a steady DC value on it. You may have a small amount of noise introduced temporarily while the person fiddles with the jumper, but otherwise, it'll be a very quiet area. If you can handle a little extra noise for short periods of time, then go for it. If you're needing no noise all the time, even when you're selecting the other amplifier, then you'll want move the pin jumper elsewhere.

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If you're switching the input to a transimpedance amplifier you may need to be a bit careful as to the capacitance and coupling you're adding. You don't mention what the impedance is at that node- I've seen megohms, hundreds of megs, and G ohms, as well as lower values. Also frequencies can be Hz or VHF.

If the jumper is horizontal to the board and has a ground plane under it you shouldn't have troubles on that account, but it might add a few pF to the input, which could be enough to destabilize the amplifier.

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