Use resistor noise to characterize a low-noise amplifier
Measure gain or noise with an AC voltmeter.
Joe Geller, Whitesboro, NY; Edited by Martin Rowe and Fran Granville -- EDN, June 23, 2011
If you know or can estimate a
low-noise amplifier’s gain or
noise bandwidth, you can measure the
other spec using only a handful of resistors
and an ac voltmeter (Reference 1).
The method in this Design Idea uses the
Johnson Equation, which describes the
amount of noise a resistor generates
(Reference 2). To find the missing
parameter, measure an amplifier’s output-noise voltage, first for a shorted
input and then using a few resistors of
different values. You can download an
Excel spreadsheet that can calculate
gain or noise bandwidth here.
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Using each of the measured resistance
values, the spreadsheet plots a
theoretical “blue” curve representing
the Johnson noise in normalized units of 
(Figure 1). You can compensate the blue curve for any low-noise-amp
input resistance. The graph also shows
a “green” curve that represents the
amplifier’s calculated “excess” output
noise—the measured output minus the
amplifier’s uncorrelated input-referred
noise. The input-referred noise is an uncorrelated noise signal that adds to
any excess input noise as the square root
of the sum of the squares of the noise
voltages. You can find the amplifier’s
input-referred noise using its effective-noise-bandwidth and gain values and
measuring the output-noise voltage by short-circuiting the amplifier’s input
terminals.
(Figure 1). You can compensate the blue curve for any low-noise-amp
input resistance. The graph also shows
a “green” curve that represents the
amplifier’s calculated “excess” output
noise—the measured output minus the
amplifier’s uncorrelated input-referred
noise. The input-referred noise is an uncorrelated noise signal that adds to
any excess input noise as the square root
of the sum of the squares of the noise
voltages. You can find the amplifier’s
input-referred noise using its effective-noise-bandwidth and gain values and
measuring the output-noise voltage by short-circuiting the amplifier’s input
terminals.
Enter the input parameters and measured output-noise values into the spreadsheet. Take a guess at the unknown parameter’s initial value and then vary it until the green curve almost exactly overlaps the theoretical blue curve. When the curves overlap, you’ve found the missing parameter. You can then try what-if scenarios by varying both parameters.
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References |
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Talkback
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The upcoming noise battles will be won with reductions of current noise now that voltage noise is below 1 nv/hz/sq on many new opamp designs.
Since voltage and current noise are additive, one can get very low voltage noise in a low level audio app for microphones. Bench measurements will not get you where you expect due to the higher current noise in many of these same devices. That is their trade-off.
JFET input opamps solve the current noise dilemma but cannot get the lower levels of voltage noise.
The current solution still involves low voltage noise discretes which have far less current noise than similar spec'ed opamps.
Jim Williams - 2011-3-7 10:09:15 PDT -
Use of different source resistors as suggested in the article could create the following problems:
1. Measurement bandwidth variations for different resistors values.
2. resistor noise source quality due to limited resistor material choices. Looks like only wirebound resistors could be use, but they have inductance and maybe should be compensated.
3. The principal noise source for these resistors is at their end termination. So you need to have very good attachments to the input and ground terminals of amplifier under test. It will be hard to use some switching for connecting them in place.
Seems to me there could be missing some components that usually used for such measurements. There are a low-noise preamplifier and a filter that should be connected before RMS voltmeter.
Vladimir Doubovis - 2011-28-6 20:20:10 PDT -
Amplifier input capacitance, as the resistance of the test resistor rises is definitely something to look out for. For example, once the R-C roll-off is dominant, increasing R can bring the roll-off point inside of the bandwidth of the amplifier, reducing the measured noise voltage. Then the cruel irony is that as the R increases further, the roll-off point moves further into the bandwidth of the amplifier under test, in some cases giving a fixed output noise value for increasing R.
Many thanks for the comments on current noise. The test setup certainly has some limitations, e.g. probably for bipolar input stages as mentioned in the comments, low gain amplifiers, high capacitance inputs, etc. We found it helpful in our application and wanted to share it with others. Sometimes, some of the following conversation can be quite good and helpful as well.
To be clear, I only argue that Johnson noise, according to the Johnson noise equation, can be observed under some test conditions, for a resistor with no additional stimulus. Of course different types of Rs are going to have different noise spectra for different types of materials, construction, power levels, thermal effects, etc.
Also, from private communications, I notice that some observers are losing context for the JCan Johnson noise measurement experiment that I mentioned earlier. By focusing our JCan measurements at zero resistor current (as nearly as practical) our goal was to be able to replicate a Johnson noise measurement across a range of resistances, -at very low cost- with a -relatively simple circuit-. Of Course, when any resistor is powered, different types of resistors can and do exhibit widely different noise characteristics (noise power, noise spectra, etc). When we added some bias current at the end of the JCan experiment, the point was simply to show that such differences can be observed (not necessarily accurately quantified) with a relatively simple experiment. We also showed why you cannot simply place a resistor on the input terminals of a standard AC voltmeter or DMM to measure the Johnson noise from a resistor. We hope that perhaps, in part because of our JCan experiment, more students and hobbyists are thinking more about Johnson noise. Is that such a bad thing?
Joe Geller - 2011-28-6 14:55:19 PDT -
Note, by the way, that a more complicated function which incorporates the effects of amplifier parallel noise as well as voltage noise can be used to get both.
However, the evaluation of the measurement bandwidth in each case gets more critical. If one of the test resistors is a lot larger, the fixture and amplifier input capacitance will reduce the bandwidth compared to the one determined for smaller resistor values.
Brad Wood - 2011-28-6 12:11:45 PDT -
Besides resistor excess noise, this discussion makes no mention of amplifier parallel noise, i.e. the amplifier's equivalent input noise current.
Now, some amplifiers may have negligible parallel noise in the bandwidth of interest, e.g. FET input amps at frequencies below a hundred kHz or so. But bipolars will have quite significant parallel noise ---indeed, the optimal source resistance is given by e sub n/i sub n.
Brad Wood - 2011-27-6 21:14:52 PDT
