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.
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.
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.
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.
BTW, that National app note saved me a year of grief when I was a student. A really understandable analysis.
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.
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.
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.
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.
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/lect_notes/commun_cir/Ch3/Chapter3.htm
http://www.teicontrols.com/notes/ElectronicCircuitsIIEE338K/ElectronicCircuitsII.pdf
http://www.teicontrols.com/notes/ElectronicCircuitsIIEE338K/NoiseReferral.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.
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/lect_notes/commun_cir/Ch3/Chapter3.htm
http://www.teicontrols.com/notes/ElectronicCircuitsIIEE338K/ElectronicCircuitsII.pdf
http://www.teicontrols.com/notes/ElectronicCircuitsIIEE338K/NoiseReferral.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.
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/lect_notes/commun_cir/Ch3/Chapter3.htm
http://www.teicontrols.com/notes/ElectronicCircuitsIIEE338K/ElectronicCircuitsII.pdf
http://www.teicontrols.com/notes/ElectronicCircuitsIIEE338K/NoiseReferral.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.
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/lect_notes/commun_cir/Ch3/Chapter3.htm
http://www.teicontrols.com/notes/ElectronicCircuitsIIEE338K/ElectronicCircuitsII.pdf
http://www.teicontrols.com/notes/ElectronicCircuitsIIEE338K/NoiseReferral.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.
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.
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.
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.
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.
Folks, let's not complicate the issue. Noise figure is mostly useless. I know, I know, you have been told that it is important, but for audio, with today's circuits, it is mostly useless. However, an IC op amp works just like an individual transistor, or fet, except you have to add the effect of the op amp topology, to get the answer to the noise produced.
If you look at an IC op amp data sheet, you will all be able to find the VOLTAGE NOISE of the op amp. If the op amp is FET input, that is all you need to know.
If the op amp has a bipolar input, then you HAVE to pay attention to the CURRENT NOISE, because the current noise will always be pretty high. This is BECAUSE the voltage noise is low, and that implies the base current is relatively high. Of course, extremely hi beta input devices will lower the base current, BUT there is always the trade-off with base resistivity, that would increase the VOLTAGE NOISE, if taken too far. This is what designers live for. The trade-offs in design for best performance.
So you have to look at the data sheet for the current noise contribution and realize that any source over 1Kohm and even 100 ohms in many cases is going to see the current source noise contribution as important as the voltage noise. More later.
If you look at an IC op amp data sheet, you will all be able to find the VOLTAGE NOISE of the op amp. If the op amp is FET input, that is all you need to know.
If the op amp has a bipolar input, then you HAVE to pay attention to the CURRENT NOISE, because the current noise will always be pretty high. This is BECAUSE the voltage noise is low, and that implies the base current is relatively high. Of course, extremely hi beta input devices will lower the base current, BUT there is always the trade-off with base resistivity, that would increase the VOLTAGE NOISE, if taken too far. This is what designers live for. The trade-offs in design for best performance.
So you have to look at the data sheet for the current noise contribution and realize that any source over 1Kohm and even 100 ohms in many cases is going to see the current source noise contribution as important as the voltage noise. More later.
I looked at the AD797 and found the current noise. It is 2pA. The voltage noise is about 1nV. Now, 2pA multiplied by 500 ohms is 1nV, so the best noise figure would be about 500 ohms and it would get significantly noisier if used with a higher source impedance. A 2SK389 can do better than this, but it needs a higher operating current to work well.
SY,
The problem with base current compensation is that often a single transistor is used to generate the compensating current for both inputs. Often, this transistor has a smaller size and smaller collector current than the input devices. An amplifying current mirror with two outputs is then used to get the right compensating currents.
For example, suppose the input transistors are each biased at 1mA of collector current. You can then compensate for the base currents using a ten times smaller transistor biased at 100uA and a current mirror with two outputs with ten times gain. However, in this case, the base current shot noise from the transistor biased at 100uA and the noise from the input transistor of the current mirror will be amplified and injected (fully correlated) in both inputs.
Measure with equal impedances driving the + and - inputs and you don't see this common-mode noise current. Use unequal impedances, as in most real-life applications, and this current noise term will be much greater than the base current shot noise of the input transistors.
An LT1028 is a good example. The noise current is specified as 1pA/sqrt(Hz) with equal impedances, but you should count on 3.25pA/sqrt(Hz) with unequal impedances...
The problem with base current compensation is that often a single transistor is used to generate the compensating current for both inputs. Often, this transistor has a smaller size and smaller collector current than the input devices. An amplifying current mirror with two outputs is then used to get the right compensating currents.
For example, suppose the input transistors are each biased at 1mA of collector current. You can then compensate for the base currents using a ten times smaller transistor biased at 100uA and a current mirror with two outputs with ten times gain. However, in this case, the base current shot noise from the transistor biased at 100uA and the noise from the input transistor of the current mirror will be amplified and injected (fully correlated) in both inputs.
Measure with equal impedances driving the + and - inputs and you don't see this common-mode noise current. Use unequal impedances, as in most real-life applications, and this current noise term will be much greater than the base current shot noise of the input transistors.
An LT1028 is a good example. The noise current is specified as 1pA/sqrt(Hz) with equal impedances, but you should count on 3.25pA/sqrt(Hz) with unequal impedances...
Bias compensation
Bias compensation for op amps is very common the get the both speed and DC precision required for op amp applications.
For an input transistor have 1 mA to have the typical input bias current of 0.25 micro amps (with the AD797), the Hfe would have to be 4.e9 for an uncompensated. This is a good indication of how well the bias current compensation is implemented on this part, This is a reduction of the uncompensated bias current of about 7 orders of magnitude and also has to track extremely well with temperature and common mode voltage changes. Some pretty good engineering!
http://www.analog.com/library/analogDialogue/Anniversary/6.html
Bias compensation for op amps is very common the get the both speed and DC precision required for op amp applications.
For an input transistor have 1 mA to have the typical input bias current of 0.25 micro amps (with the AD797), the Hfe would have to be 4.e9 for an uncompensated. This is a good indication of how well the bias current compensation is implemented on this part, This is a reduction of the uncompensated bias current of about 7 orders of magnitude and also has to track extremely well with temperature and common mode voltage changes. Some pretty good engineering!
http://www.analog.com/library/analogDialogue/Anniversary/6.html
Fred,
Don't you mean that hFE would have to be 4000 (rather than 4E9) to get a 0.25uA typical input bias current with 1mA of collector current without base current compensation? I'm sure the AD797 is well-designed, but getting the base current matching between two transistors on an integrated circuit much better than 1% or so is nearly impossible, even with large devices and very careful design.
Don't you mean that hFE would have to be 4000 (rather than 4E9) to get a 0.25uA typical input bias current with 1mA of collector current without base current compensation? I'm sure the AD797 is well-designed, but getting the base current matching between two transistors on an integrated circuit much better than 1% or so is nearly impossible, even with large devices and very careful design.
Looks like Fred slipped a digit ;-) No big thing. I analyzed, without actually proof from AD, that the quiescent current could be about .5mA per device. That would help the noise current a little, but it would assume very, very low Rbb'. I thought that the excess current noise could be from the bias compensation circuit. I could be wrong on this, and 1mA might be design center for each input device.
Give or take 6 orders of magnitude
On most days I do know the difference between micro and pico. I guess today wasn't one of them. If one is going to make a mistake why not be off by a factor of a million..... Thanks for the heads up. The point is still valid that bias current is still much smaller than one would get without compensation. The link describes bias compensation and even a little bit about the effect of the bias compensation on current noise current .
For some of the lowest input bias current op amps:
The OP97 has bias currents of less the 250pA over the full itemperature range with bipolar inputs. One of the lowest bias current jfet op amps the AD549L has an input bias current of 60 fA !
http://www.analog.com/library/analogDialogue/Anniversary/6.html
micro 10e-6
nano 10e-9
pico 10e-12
femto 10e-15
atto 10e-18
PS Mr. Curl is either a master of under statement or has exceedingly good manners rivaling those of Mr. Pass
On most days I do know the difference between micro and pico. I guess today wasn't one of them. If one is going to make a mistake why not be off by a factor of a million..... Thanks for the heads up. The point is still valid that bias current is still much smaller than one would get without compensation. The link describes bias compensation and even a little bit about the effect of the bias compensation on current noise current .
For some of the lowest input bias current op amps:
The OP97 has bias currents of less the 250pA over the full itemperature range with bipolar inputs. One of the lowest bias current jfet op amps the AD549L has an input bias current of 60 fA !
http://www.analog.com/library/analogDialogue/Anniversary/6.html
micro 10e-6
nano 10e-9
pico 10e-12
femto 10e-15
atto 10e-18
PS Mr. Curl is either a master of under statement or has exceedingly good manners rivaling those of Mr. Pass
- Status
- This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.