Question on input noise current

[Christer]

Noise was recently discussed in another thread, but since
that thread ended up discussing everything but the original
topic (which wasn't noise) I thought it better to start
a new thread. In the other thread I posted the following links
to documents on noise, which also others may perhaps find
useful.

http://www.national.com/an/AN/AN-104.pdf
(deals with noise on amplifier level and defines the basic
theory needed for this)

http://www.eie.polyu.edu.hk/~ensury...h3/Chapter3.htm
(defines and discusses noise sources in semiconductor devices)

http://www.teicontrols.com/notes/El...cCircuitsII.pdf
(actually a compilation of diagrams and formulae on various
things, but also briefly defines the basic types of noise.)

http://www.teicontrols.com/notes/El...iseReferral.pdf
(Another document discussing referral of noise sources to the
input, also covered in the National app note).


Now, I think I have spotted an error in the last of these
documents, but I don't trust my own analysis enough to
convince myself to 100% that it is indeed an error, so I
would appreciate your opinion.

The first document (National app note 104) defines the eq. noise
input current as a current source between the inputs of an amp.
This seems reasonable to me and I trust the people at National
to know what they are talking about, so I accept this as the
standard definition, unless somebody protests. In many cases
it will be convenient to split this current source into two current
sources, one between the positive input and ground and one
between the negative input and ground. These two sources
will both have the same value (the value being a function over
time) but opposite directions. Since they have the same value,
their respective contributions to the eq. input noise must, as far
as I can understand, be summed using plain standard addition.
However, document 4 assumes these two sources to be
independent noise currents and sum them in rms fashion.
Is this an error in document 4, or do I go astray somewhere in
my reasoning??

This will probably only make a difference in the case current
noise is the dominant noise source and the source and feedback
resistances are on the same order, but then it does make
quite a difference.

[john curl]

Folks, input 'current noise' is the noise made by the electrons crossing a junction. It is formally called shot noise. It has a formula, but usually low noise transistors will have it graphed in their spec sheet. It is usually spec'd with picro amps/rt-Hz. Now what you do is to get a number off the graph and MULTIPLY it by the effective source resistance(this includes any resistors in both the base and the emitter, including local feedback resistors). For example, a noise current of 1pA/rt-Hz and a 1K source would have an effective input noise contribution of 1nV/rt-Hz. This might make a LM394 about 3dB noisier.

[SY]

And if we parse John's first sentence, you can see that noise across two junctions will be independent. They can be added in an RMS way to get the single current noise source of the National paper.

BTW, that National app note saved me a year of grief when I was a student. A really understandable analysis.

[Christer]

John and SY,

Perhaps I was a bit unclear, I am sorry for that. My question
was not about calculating the input noise current for a design,
but rather on how to use the given figure for an opamp. (Well,
John says something on this thay may perhaps be understood
as confirming how I understand this, but I am not sure if that
is the way to understand him). More particularly, I should have
said that I was considering an op amp used in non-inverting
config.

Now, according to the National app note., the input noise figure
is by definition referring to a virtual current source between the
two inputs (the reference direction is, of course, arbitrary since
it is noise, so let's say it is from neg. input to pos. input). Let's
denote this noise current by i(t), which is a random function over
time. This currents causes noise voltages over the source
resistance and over the feedback resistance. When calculating
the corresponding equivalent input noise voltage, it may simplify
the analysis to split this current source into two, one from ground
to the pos. input and one from the neg. input to ground. These
two currents must be identical, both having the value i(t), or
else we would violate KCL (as far as I can see, Kirchoffs laws
must hold also for random currents and voltages, ie. noise).
Hence, the way to go about would be to make this split, and
then by superposition find the eq. input voltage for each
current and add these voltages. This is ordinary addition since
the two currents are identical rather than independent. Then,
this sum can be treated as an independent noise voltage
corresponding to the one original noise current. However,
document 4 (which is about noise referral) uses two separate
current sources, one for the pos. input and one for the new.
input, and treats these as independent noise sources, which
would seem to be wrong if my reasoning above is correct. In
fairness, it should be pointed out that this document does not
define how to derive values for the two noise currents from one
single noise current as given in a datasheet. However, it seems
not obvious that one could derive two independent noise
currents from a single one, such that the net results are
identical.

[MarcelvdG]

I haven't been able to read the second, third or fourth document, because the links don't seem to work on this computer. That is why I don't know how much of the following applies to the case analysed in Christer's fourth reference.

Anyway, in theorectical analyses, the amplifier is often assumed to be a two-port with (by definition) a perfectly floating input port. For practical amplifiers with a differential input, it does not necessarily make sense to define a single equivalent input noise current. In general, you need two different equivalent input noise currents to get an adequate model when you have a differential input.

For the case of a bipolar differential pair without base current compensation and with a symmetric load, assuming the shot noise of the base current to be dominant, the noise current can be described with two uncorrelated sources with a power spectral density of 2qIB (RMS value sqrt(2qIB*DELTAf) over a bandwidth DELTAf), one going to one base, the other to the other base. You can transform these into an equivalent differential input noise current source and two fully correlated common-mode input noise current sources if you like, but unless the impedances driving the positive and negative inputs are equal, it makes no sense to use only a differential source.

In general, base current shot noise is only one of many contributions to the equivalent input noise current or currents. Others which are often significant are base current 1/f-noise and in some cases base current compensation circuit noise.

[Christer]

Marcel,

sorry about the links. Some piece of "intelligent" software
somewhere along the way must have abbreviated them
without me noticing it. Here are the links again:

http://www.national.com/an/AN/AN-104.pdf
http://www.eie.polyu.edu.hk/~ensurya...3/Chapter3.htm
http://www.teicontrols.com/notes/Ele...CircuitsII.pdf
http://www.teicontrols.com/notes/Ele...seReferral.pdf

What you say makes sense, but I am not sure it it answers
my question. Although it may not be reasonable to treat the
current noise as one differential source, as you say, that is
what we are given to work with from the datasheet, assuming
datasheets adhere to the definition in the National app note,
that is. (I just checked a few datasheets, and except for CFB
amps, none of them defined what the noise current figure
refers to). The question then is how to best make use of
this figure.

[Christer]

Sorry again, but it seems to be the forum software that
pretends to be intelligent and abbreviates the links

I'll make a new attempt and split the links to see if that works

http://www.eie.polyu.edu.hk/~ensurya...3/Chapter3.htm

http://www.teicontrols.com/notes/Ele...CircuitsII.pdf

http://www.teicontrols.com/notes/Ele...seReferral.pdf


Edit: It seems the problem is only with displaying the URLs
correctly, so maybe there is some problem with Internet
Explorer rather than the forum software, so perhaps only
some of us got the links abbreviated. Anyway, I have reported
the problem to the admins.

[MarcelvdG]

I usually first look if there is some additional information hidden in the data sheet, like the noise current measurement set-up or a graph of the total noise versus unmatched source impedance.

If I can't find anything, I look at the internal schematic. If the op-amp has a bipolar input stage without base current compensation, normally each input has a noise current with twice the power spectral density (3dB more) of the differential noise current. As base shot noise and 1/f noise usually dominate in bipolar op-amps without base current compensation, you should also be able to calculate the white part of the input noise current in A/sqrt(Hz) from sqrt(2q times the input bias current), where q is the electron charge (1.6022E-19 C).

If the op-amp does have base current compensation, depending on the exact circuit, there may be a very large common-mode input noise current component. In this case, if the datasheet doesn't provide any additional information, it's anybodies guess how much noise it will generate with unequal impedances driving the positive and negative inputs.

[SY]

In this case, if the datasheet doesn't provide any additional information, it's anybodies guess how much noise it will generate with unequal impedances driving the positive and negative inputs.

Well, presumably, the two transistors in the input diff amp will be the same (or close to it). Same bias comp. So I would think that the noise contribution from each source can be calculated independently, then RMSed to get total noise.

[Christer]

Marcel,

Thanks, although perhaps not quite the answer I asked for, it
is probably the answer I should have asked for, since it
goes deeper than just trusting and using a single figure from
the datasheet. It is probably a sensible thing to follow your
procedure when an as exact results as possible is desired.
In other cases, it is still interesting to make the best of the
given figure, without losing more accuracy than is already lost
in such a compund figure.

when I said I checked a number of datasheets before,
I must confess I didn't check those for the usual low-noise
op amps, since I didn't find those particular datasheets at
the moment. I have now checked LT1028, LT115 and AD797,
and these datasheets do contain som further info. LT mentions
the test procedure, as using equal balanced source resistors,
measuring the noise voltage, and, after compensating for the
thermal noise, dividing the remaining voltage by the sum of
the resistors. Similaryly, AD says that the noise voltage produced
by the current noise is the current noise multiplied by the sum
of source resistances for the two inputs. This is, as far as I
understand, consistent with my line of reasoning that the
differential current source can be replaced by two identical ones,
that is, not two independent ones as suggested in the fourth
document I linked to.