# Low noise low pass

## Main Question or Discussion Point

Is a low pass with an inductance less noisy than one with a resistor due to thermal noise? Will an RC low pass between two op amps necessarily be less noisy when the C is large and the R is small? Does this matter in real life circuits?

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Neither inductances nor capacitances produce any thermal noise. The thermal noise voltage in a resistor is sqrt(4kBTR), and can be modeled as a noise voltage generator in series with the resistor. Thermal noise minimization is especially important in the first amplifier stage. Sometimes the amplifier is cooled to liquid nitrogen temperature and lower. See
http://en.wikipedia.org/wiki/Johnson–Nyquist_noise

berkeman
Mentor
Neither inductances nor capacitances produce any thermal noise.
Is that true? You gave the formula for the thermal noise, which depends on the value of resistance...

From Bob S
"Neither inductances nor capacitances produce any thermal noise."
Is that true? You gave the formula for the thermal noise, which depends on the value of resistance...
I believe that in circuits with resistors, capacitors, and inductors, only real impedances, or real components of reactive impedances, can produce thermal (KTB) noise. This would include copper wire in an inductance but not the inductance itself, excepting Barkhausen noise (which is not thermal). .See
http://en.wikipedia.org/wiki/Barkhausen_effect

berkeman
Mentor
Oh rats, sorry. I misread your post to say neither inductances nor resistances.... I'm brain fried. :tongue2:

http://en.wikipedia.org/wiki/Johnson–Nyquist_noise
but actually it is due to the thermal resistor noise in the RC circuit. The "R" drops out of the equation during derivation. There is also shot and flicker (1/f) noise, but neither are thermal noise.

There's a lot that goes into understanding why a particular circuit is noisy, or how to minimize the noise. I do an awful lot of specialty interface work, and noise is consistently an issue of optimizing the first (and occasionally second) amplifier stage

Passing through the first gain stage, the signal from the sensor (microphone, pick-up-coil, capacitive sensor, pin diode, etc...) will have a measure of noise added to it. At the same time, the signal, as well as the added noise, will be amplified. With any luck, any noise contributed by later stages will be less of an issue than the noise from the first stage.

The key is to minimize the noise of the first amplifier. First, find the appropriate amp for your sensor's impedance - at the frequency of interest. Lower impedance sensors, like coil microphones, will do best with bipolar amplifiers. They tend to have a lot of noise current on the input, but very little noise voltage. For higher impedance sensors (>10K), like capacitance microphones, JFET amplifiers are better. They have negligible current on the inputs, but a great deal more noise voltage. The values for these voltage and noise currents are listed as en and in in the data sheets of op amps.

As for noisy resistors, that comes from two areas:

1. Large resistance values
2. Resistors which have current flowing through them.

For case one, you generally don't need large value resistors for feedback circuits, and the sensor should have the largest of the impedances seen at the inputs.

In some cases, like bridge circuits, current through resistors can create undesired noise. In these cases, the construction of the resistor is important. Metal film (thin film) and wire wound resistors are excellent for these applications.

By the time you get around to doing any filtering, hopefully you've amplified your signal enough that any noise at this stage is minor.

I hope this helps a bit, feel free to ask questions,

- Mike

There's a lot that goes into understanding why a particular circuit is noisy, or how to minimize the noise. I do an awful lot of specialty interface work, and noise is consistently an issue of optimizing the first (and occasionally second) amplifier stage
I am optimizing the second amplifier stage, where I should be in the microvolts. I am quite confident, that I cannot do much better then what I do with the instrumentation amplifier. But it introduces high frequency noise that needs to be filtered.
[...]
As for noisy resistors, that comes from two areas:

1. Large resistance values
2. Resistors which have current flowing through them.

For case one, you generally don't need large value resistors for feedback circuits, and the sensor should have the largest of the impedances seen at the inputs.

In some cases, like bridge circuits, current through resistors can create undesired noise. In these cases, the construction of the resistor is important. Metal film (thin film) and wire wound resistors are excellent for these applications.
My signals have very low frequency, so I am fighting with things like dc offset and dc drift. Right now I have the dogmas:
- The less active components the better.
- Inductances stink in a high field experiment

My final lock in amplifier can do most of the work, it was expensive enough. I amplify early, but I need to do some signal cleansing to reject dirt that I pick up on the cable, and some more dirt that the first instrumentation amplifier sends.
So a low pass it is. I build a triple low pass with a 3dB knee at 100Hz with increasing impedances, so the first part does not load the next too much, but this way the first capacitor and the last resistor are very large. I wonder if I do more harm then good, with the large resistor, and if I should go with two poles or even just one. What do you think?

Would you say I should do all the amplification myself, as long as my op amps are expensive enough and use an active low pass? I don't really want to use Butterworth or other stronger filters because I want to measure phase shifts, but maybe I am to conservative here. There is hardly any current through the resistors except for the rejected dirt.

Last question: How do I have to understand 1/f noise? This noise must end somewhere right? We cannot have giant kilovolts noise close to DC can we?

If you can give me a few more details, perhaps I can help.

Can you tell me what your signal source? What sort of source impedance does it have, does it have an excitation source that can it be modulated, can it be shorted out on a regular interval to re-zero, and what bandwidth does it operate over.

You mentioned difficulties with cable. Are you have difficulties due to triboelectric effects? You also mentioned difficulties with strong fields. Are these magnetic, electric, or traveling? What sort of frequencies.

As for 1/f, one must remember that as the frequency decreases, the available bandwidth becomes less (.1Hz is ALL the bandwidth from DC to .1Hz). So, There isn't an infinite event. However, it does look more and more like drift as you go lower in frequency. The ability to turn off, or short out, the source gives you an opportunity to zero out the drift between repetitive test cycles.

Generally, the processing circuitry isn't very expensive - though the first stage amp may proved demanding. It usually costs a couple of hundred dollars for a custom PCB and a few tens of dollars for associated components.

Well the setup so far:
We have thermocouples periodically excited, to use an expensive lock in amplifier. The problem is, that the signal levels will be insanely low: around 10nV to 300 nV, but we can trade some accuracy for more signal. The frequency is somewhere around .1Hz to 20Hz we don't really want to take more than two minutes per measurement. The magnetic fields are high, but outside the cryostat at around .5T max fairly static, the direct and obvious danger would be swinging cable. I didn't have obvious problems with microphonic effects yet as far as I can tell.

When the lock in is connected directly and we crank up the amplification, then it starts clipping digitally due to noise, before we reach the desired accuracy. So the first thing we do is amplification as early as possible, with an INA333 (zero drift instrumentation amp) by a factor of 1000. Either by itself or because of some other electronics we get some high frequency noise on the line, which will have to get filtered. Accordingly my low pass' input is the INA333.

So what I really want to get is a low total input signal, and hope for the lock in to do the rest. So I was wondering, if the resistors in a low pass could do more harm then good, although I have never heard of RC low passes being a noise source.

Otherwise I cannot tell you much about my noise yet. The final setup is not ready, and the preliminary prototypes basically showed that there is signal in principle, but that noise is an issue, and that things matter that shouldn't, like the input channel of the lock in.

Btw. do you have recommendations for a good difference amplifier with drift compensation.

Ouch! Your not in the mud, you're well below it! My first thought would be to run for another sensor...

But, if your stuck with what you have, than there's a couple of useful things I can see immediately:
1. Your source impedance is low, thus you can run parallel amplifiers to gain a 1/sqrt(N) noise improvement, where N is the number of input amps. Just tie the outputs of each stage together with resistors (i.e. 1K), so they don't fight one another.
2. If you go with an op amp scheme, you can gain a 1/sqrt(2) improvement just by the doing away with series front end components associated with the instrument amp.

I've never had to go as low on a DC reading as your asking for. Just the temperature gradients on the circuit board could totally wipe out your accuracy. The lowest I've ever gone used the LTC1052. Linear Tech has some good points regarding the use of this part, circuit board issues, and resistor issues. Analog devices used to have some good notes on these as well. When I've gone low, I plated everything in sight around the circuitry to keep the temperature gradients low. In the end it sums up to - don't expect much consistency below 1 uV.

I know you have to fight this thing yourself, but if I were you, I'd look into another type of sensing device, like maybe a four wire RTD. Through pulsed modulation, you can keep the self heating low, gain excellent signal to noise by shifting the bandwidth away from the 1/f dominated area, do away with DC offset, and make excellent use with the lock in.

As to the original RC question, I suspect that you have so much more noise and drift from the front end, that this isn't the worst of your worries...