Op amp noise from Inductors

A pure inductance *generates* no noise. That would violate conservation of energy.

At any given frequency, multiply the opamp's input current noise density (in amps per root Hz) by the inductor's impedance; that's the input noise voltage density, units of volts per root Hz. Multiply that by amp gain at that frequency to get output noise density. Looks like you'll need a fet amp here.

To get net noise voltage, you have to integrate the noise density curve over frequency. Note that, unless the opamp gain rolls off, or the coil has shunt capacitance, the output noise density (at least this In*Zin*gain thing) here will increase linearly with frequency, pretty much forever.

The resistor would add its own noise, too. At some point, in real life, pickup from ambient magnetic fields will actually dominate. That's why HF receivers don't need good noise figures: atmospheric noise is huge below about 30 MHz. A little 60 Hz hum, or one good AM station, will entirely blow away any considerations of thermal noise.

John

Hello John,

That's why it can be a good idea to use toroids or for very large inductances pot cores. They don't "talk" much.

Regards, Joerg

Thanks for info. Using that equation and lets say the input source is

100% inductive. At 1pA/SqrtHz and 600 ohms impedance = 600 pV/SqrtHz. Or using 6 M ohm impedance (from inductor) = 6 uV/SqrtHz. ... I don't understand why the noise should increase from an increase in pure inductance. If inductors don't cause noise then how would the output noise be a factor of input source impedance? If we double the inductance, then according to the above equation, the noise doubles. Is this absolutely correct?

I'm trying to understand where the noise would come from. In the case of pure inductance, wouldn't the noise only come from the op-amp itself and the input shot current noise? If by chance the output noise is a function of input current in this case, then shouldn't the noise go down by increasing the input reactance? Let me look at this from another angle. If the source impedance in this type of op-amp doubles, then the gain should cut in half. Either viewpoint, how can an increase in impedance on this op-amps input source cause an increase in output noise?

Thanks for any help, Paul

The noise you are talking about is just one source of the overal noise and it is there already in the bias current coming out(or in) of the op amp inputs, it has to go somewhere, the resultant voltage noise at the input is therefore proportional to the effective impedance seen at the input, from simple aplication of ohms law, it is not generated by the inductor, (although as already stated an inductor will introduce its own aditional noise). Hope this helps to make it clearer.

A resistor in parallel with the inductor will lower the impedance seen at the input, however it will also reduce the output, so it will not benefit the SNR however half the turns on the coil will reduce the voltage by 2, but will reduce the impedance and resultant noise by 4, at some point either the voltage noise source or the current noise source will dominate, an op amp with much lower input current ie jfet/mosfet will probably give a better compromise.

Colin =^.^=

Err... no, you missed the bit "the fact that the inductor itself does not generate any noise" then?

The input transistors generate the shot noise. This noise is dropped across the source impedance.

Well the other dudes have answerd the rest, so I'll leave it there.

Kevin Aylward snipped-for-privacy@anasoft.co.uk

SuperSpice, a very affordable Mixed-Mode Windows Simulator with Schematic Capture, Waveform Display, FFT's and Filter Design.

"There are none more ignorant and useless,than they that seek answers on their knees, with their eyes closed"

We may be a bit confused here. I was assuming, maybe wrongly, that you wanted to amplify the signal created by a magnetic-field pickup coil, from something like 1KHz to 1MHz. If that's the case, you don't want to load the coil, because that would kill the signal level at higher frequencies.

If you do connect the coil to a high-impedance amp, like the n.i. input of an opamp, the opamp input current noise (pretty constant over frequency) will produce voltage noise across the impedance of the coil, and the impedance hence noise increase linearly with frequency.

As in all such cases, it would help a lot if you explained the application, what you're trying to accomplish, and what actual circuit you propose to use. A schematic (post to a.b.s.e., or a web site) would help.

John

That seems to be the consistent answer. Great! I only need to amplify one polarity, and linearity is of very little concern. Would a simple Common-Source JFET Amp work best?

Some op-amps have 10^2 input fet resistance. That's nice due to my high input reactance and you also get some good gain. I'm wondering if that would also work well for my case?

Given R resistance, X reactance, gain of G, may I ask what the output voltage noise will be for such a jfet amp? I heard that paralleling multiple fets would decrease the noise.

Again, thanks for the great help, Paul