# How much is the noise of a multiplexer for analog inputs?

I have 4 sensors, each have with two differential output (S- and S+) that I need to use in a differential amplifier (with a gain equals to 1000 in my case).

The difference between S- and S+ is between 0V and 5mV and I would like to have a 0.005mV precision.

As I want to used just one amplifier, I thought about using a multiplexer (like this CD4052BM96) before amplifying the signal, but I was wondering if the multiplexer's noise would allow or not a 0.005mV precision.

How can I calculate how much noise the multiplexer (CD4052BM96 for example) will add to my signal?

Thanks a lot.

• What accuracy do you need to maintain? What bandwidth are you wanting? What source impedance are your sensors? Also what input amplifier are you using? – Andy aka Apr 12 '14 at 20:06
• @Andyaka I think my question was not so clear, sorry. The impedance of my sensors are 1kohm (it is a loadcell), its output shouldn't vary much (really low frequency). The accuracy I want at the output of the multiplexer is +-0.0025mV (if S+ is 1.535mV, the output of the multiplexer should be (1.535+-0.0025)mV. Maybe I should'n be asking about noise, but about distortion. – koike Apr 13 '14 at 13:49

## 1 Answer

You can calculate the thermal (Johnson-Nyquist) noise of the switch easily. That's broadband noise.

$v_{n} = \sqrt{ 4 k_B T R \Delta f }$

where T is the temperature in Kelvin, R is the resistance, $k_B$ is Boltzman's constant, and $\Delta f$ is the bandwidth.

Leakage current could cause some disturbance, especially to DC levels of your signal, you'll have to work that out from the impedances of both the switch and the rest of your circuit, and datasheet leakage current guarantees.

For much more detail, you can refer to this paper.

There might be a slight thermocouple voltage, but likely insignificant since they don't get warm, so the thermal gradients tend to be minimal.

CMOS multiplexers do not have offset, hysteresis, shot noise (except a tiny bit from the body diode leakage) or other bad characteristics, just leakage and some (nonlinear) resistance that can cause distortion if care is not taken, but since your question is about noise I'll ignore that.

Generally the 4052 is better than advertised in leakage, since it's a cheap part it's not tested to very low leakage levels. It has quite a large internal resistance, especially when operated at lower voltages.

Better guaranteed performance is available (at a price) by using analog multiplexers such as the ADG series.

• Thanks for you reply. I think you are right, I should be asking about the deformation in the output of the multiplexer (I never know if I should open/make another question about this, asking the right thing, what do you think?) – koike Apr 13 '14 at 13:52
• Another question.. It's different and a good size. – Spehro Pefhany Apr 13 '14 at 14:03