How to measure Johnson Noise precisely practically?
I tried using opamp/ low noise amplifier in cascade with band pass filter followed by multiplier circuit (squaring signal) and measured output which deviates from expected by nearly 10^(3 to 4) order.
Electronic – Johnson Noise Measurement
noise
Related Solutions
Yes, we only want to eliminate 1kHz
A notch filter can be used for this: -
This is a 10 kHz design and note figure 6 - how it responds as you get between 9 kHz and 11 kHz with the input signal.
This article describes the circuit in more detail and provides examples of other notch filters across the audio range. The article is by TI and is entitled: -
An audio circuit collection, Part 2
Regarding the op-amps, because you are using a lock-in amplifier it's not critical BUT just in case go for op-amps that are below 10 nV/\$\sqrt{Hz}\$ specified on noise. Devices that spring to mind are OP1177, AD8605, ADA4528 but there are plenty with lower noise.
There are a number of problems with this circuit:
- The input to the reference is not filtered.
R5 and R4 make half the supply voltage, but also transfer half of whatever noise is on the supply. There should be cap to ground across R4. I'd start with around 2 µF.
- There is no bias supply for the microphone.
You said this was a electret, so there should be a pullup to 5 V. Usually these should be a few kΩ. Check the datasheet of your mic.
You should also filter the pullup voltage to keep power supply noise from being fed directly into the mic. Perhaps 1 kΩ from 5 V followed by 20 µF to ground, then 2 kΩ to the mic. Again, see the mic datasheet.
- There are no bypass caps anywhere!
The above shows the power to only one opamp, but all of them have the same problem. For even better noise rejection, especially for the first stage amp shown above, put a ferrite chip inductor in series followed by 10 µF or so ceramic to ground. That reduces high frequencies, like from radio station pickups, that the active circuitry in the opamp can't handle well.
- Low gain. The first stage amplifies by a bit over 6. That by itself is OK, although I'd like to see a bit more from the first stage if the opamp can handle it. You didn't provide a link to the opamp datasheet, so I didn't look it up. In any case, there are certainly opamps available that can run from 5 V and provide a closed loop gain of 30 or so at 20 kHz with plenty of gain headroom for the feedback to do its job.
A microphone amp usually needs a gain of around 1000 at full volume to get to line level signals. Two gain stages at front with a gain of 30 each is usually about right, with a volume control between the two of them.
After the signal has been amplified, any noise added is a much lower fraction of the whole.
- Decouple the Vref inputs to each stage. U5 isn't perfect. It will have some noise. It's output impedance also isn't 0, so there will be some cross talk between stages. Even just 1 kΩ in series followed by 20 µF to ground at each point of use would help.
- Do you really need all that filtering? This is way excessive for any normal audio. Eliminating filter stages will reduce noise. Everything adds noise, so don't put more stuff in the signal path than you really need.
Best Answer
Johnson noise is the white noise of resistors.
1) You can measure the integrated noise voltage: sample the voltage with a digital multimeter and process the statistics. The standard deviation will be the integrated voltage noise. You might need to know the bandwidth of the multimeter and its own noise if the noise levels are very low. 1) b) use an oscilloscope and check the noise in the waveform. They can calculate the RMS noise as well. Though the resolution of an oscilloscope is inferior to a multimeter, but it is much faster.
2) spectrum analyser, i.e. bandpass filtering many small parts of the spectrum and measure the energy in there. Basically it is the same method you described as well. If you built it for yourself you need to know the noise added by your components and calibrate them out from your measurement.
+1: noise is messy. It is hard to distinguish where the deviations are coming from. They can be radio stations (I've debugged some strange weak waveforms in a circuit of mine for more than an hour until finally I checked its FFT and it became clear that it picked up FM radio), wifi, bluetooth, etc. or SMPS in nearby computers or instruments... Therefore you need to shield your DUT and its connection to your instruments as much as you can.