About the noise question for datasheet

generally, we always see that some OPs with low bias curret, such as several fA, have high input impedance up to 10^15 ohm. consider the Johnson noise only, the noise will be as high as 4mV/sqrt(Hz). However, I see that in the datasheet, the spectral voltage noise density is tens of nV/sqrt(Hz).
typical chip is AD549!
can any body explain to me what is wrong to this?
thank you for your guys explaination!

the input impedance is not the resistor only.
it's the small resistor in series with a capacitor.

So what about the DC resistance of the capacitor? at low frequency, A capacitor can look as a parallel large resistor with a capacitor, this make me confuse!

there is no model that take the capacitor as a parallel large resistor with a capacitor. the capacitor is a resistor in series with a capacitor.at low frequency the impedance of the capacitor is very large. the serial resistor is called ESR.

To renwl:
I read from a book name " Capacitive sensors", in the book, a parallel model(Large DC resistor parallel with the capacitor) is introduced for capacitive sensor at low frequency. I know your model is the one we always use for capacitor, But for low frequency case, it is another case, right?
thanks for discussion.

I aslo will use the parallel model(Large DC resistor parallel with the capacitor) . but it's the discrete capacitor. and the large dc resistor is only for the dc leakage current.
maybe you can provide some information about " Capacitive sensors".
I am very glad to have a chance to discuss some interesting questions like this.

I read from the Franco's books on the chapter about noise, It mention that the thermal noise is present in all "passive" resistive element! I think the word "passive" here has its meaning, So, to the semiconductor's case, I think we should turn to another consideration!

Hi, xzp,

I have just posted at

the exact answer to your question.

You simply have to distinguish among the input impedance, Zin, source impedance, Zs, and noise resistance, Rn.

Zin does not affect SNR (some books say a different thing, including “The Art of electronics,” do not believe!).

Zs*In gives you the input noise component due to the OpAmp noise current.

Rn=Vn/In.

Zs=Rn gives you the lowest noise factor, or figure (noise contribution of the OpAmp), NF, but not the highest SNR.

Zeroing the reactive part in Zs, such that Zs=Rs, is called noise tuning.

Equating Rn to Rs with a transformer or by connecting a number, n, of OpAmps in parallel [such that Vnp=Vn/sqrt(n*Vni), Inp=In*sqrt(n Ini)] is called noise matching.

Noise tuning and noise matching give you the highest SNR.

Thank you so much, I've ever read this paper, but not that carefull, I will read through it again and find more information, thank you so much!