noise optimization in sensor signal conditioning circuit part i
TRANSCRIPT
ADI JAN1608
Slide 1:
Gary Cocker:
Good morning, good afternoon, or good evening, depending on where
you are in the world, and welcome to today’s webinar, “Noise
Optimization in Sensor Signal Conditioning Circuits.” This is
part one, presented by Analog Devices. I’m Gary Cocker. I’ll be
your moderator today. We have just a few announcements before we
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our technical support helpline, which is also located in the
webcast help guide. Now, onto the presentation, “Noise
Optimization in Sensor Signal Conditioning Circuits," part one.
Noise is a term that is broadly used in signal path design, but
in many cases there is a level of confusion as to what it exactly
means and how to deal with it. Today, in this first of a two-
part series, we will explore the topic in detail and get insight
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and answers on the sometimes intimidating subject of noise.
Making this presentation today is Reza Moghimi, applications
engineering manager in Analog Devices Precision Amplifier Group.
Reza, welcome, and over to you.
Reza Moghimi:
Thanks, Gary. Let’s start. There have been many papers written
on the topic of noise and, as you said, still there is -- the
term is used broadly with some levels of confusion. A person
yelling is asked not to make too much noise. A person standing
next to a highway might say that it is too noisy. Some engineers
think of DC errors, such as offset voltage and bias current as
noise, but others refer AC parameters such as current noise and
voltage noise densities as noise. We will establish a definition
of noise from an electrical engineering point of view. But for
now, generally speaking, we can say that noise is any unwanted,
undesirable signal that affects the quality of the useful
information.
Slide 2:
So I know that my audience today comes from a very diverse
background. Some of you come from a digital background and are
not familiar with the analog concepts, and some of you are very
strong in analog design. But I can assure you that you will be
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getting something out of this and the next session, which is
scheduled for the month of February. If I do not get to all
questions or give satisfactory answers to your questions, or
don’t know the answer to your questions, I promise you that ADI
has enough experts in this field that I can consult with and get
back to you, so please do not hesitate to send us email. So
after explaining why design for low noise and defining noise and
its types, I will introduce a general formula to calculate noise
of a signal condition circuit. Next, I will introduce a low
noise design process, and in my February session I will explain
deeper into this low noise design process and share with you dos
and don’ts, and a number of ways to use and optimize common
signal conditioning circuits.
Slide 3:
So let’s see what changes have come about and why, more than
ever, every system designer needs to know about low noise design.
So, why low noise?
Slide 4:
Let’s look at the types of applications that are in the
mainstream these days and need low noise signal conditioning. A
typical signal chain is shown over here. On the left, there are
many sensor types, and the rest of the circuit is a single
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conditioning path. Making high-resolution measurements
accurately depends on the noise floor of the system. A parameter
I’m sure you’re all familiar with, called an S signal to noise
ratio, gives a good idea as to how much noise we have in a
system. So the question is, what are the major sources of noise?
Is it the sensor, signal conditioning circuits themselves, or a
pickup or radiated noise, as it is called? Remember that sensors
have their own noise and they are supposed to detect small
signals which cannot be distorted. So to attain best noise
floor, designers need to understand component levels noise
sources, pick the best signal processing architecture, and
prevent external noise sources that might interfere with the
application circuit.
Slide 5:
Why low noise signal conditioning? Popular applications have
moved toward lower operating supply voltages. It used to be
common to have +/- 22V, and now it’s pretty common to have +/-
0.9 V or +/- 1.5 V, and more applications are requiring higher
precision and accuracy. As an example, car industry has moved
from an 8-bit system to 12 bits or higher. Lower supply
operations, combined with higher accuracy requirements -- meaning
the number of bits -- has made measurements of microvolts quite
challenging. We used to point out the LSB size for 5 V and 10 V
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full-scale data acquisition systems, as it is shown here, and we
used to say that these were very small and we needed low noise
signal conditioning. For example, we used to point out, for a
14-bit system, where the full scale was 5 V, the LSB size was 305
μV. But remember that this is the amount of error that we are
allowed after signal conditioning circuits. The situation is
worse when we look at the output of the sensors, as I showed you
in the previous slide -- signal chain. Sensors have, or produce,
very small signal.
Slide 6:
So, as an example, imagine a real-world signal that generates
signals of 30 mV maximum, full-scale. The half an LSB for a 12-
bit system is 3.5 μV, and if you have 1μV of input referred error
or noise from the amplifier, would invalidate the measurement.
Eliminating noise is very critical since this usually sets the
lower limit of usable signal level in a circuit.
Slides 7, 8, 9:
Something else that we need to know when we have a driver for an
ADC is the signal to noise ratio of an ADC can degrade as the
result of the goodness of the amplifier driving it. Designing
low-noise signal conditioning is critical, since the noise
generated by an ADC driver needs to be kept as low as possible in
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order to avoid worsening the signal to noise ratio. In this
slide, I show how the SNR gets degraded if you pick a wrong
amplifier. As an example, when using the AD7671, which is the
16-bit, 20μV RMS noise and 10 mHz of bandwidth, if you pick this
ADC let’s see how we can degrade its SNR by picking different
amplifiers. Shows us amplifiers that have different noise specs,
and we see the SNR loss as a result of the amplified noise. So
let’s get a better understanding of what noise is, how we define
noise, and what are the noise sources.
Slide 10:
I explained that sensor signals are small, the need for
resolution has gone up, power supply voltages have shrunk, and in
order to make meaningful signal conditioning we need to learn
about low noise design. It is critical to optimize the signal
conditioning circuitry so we get rid of the noise and measure the
real signal. So let’s see how we define noise and what are the
noise types that that we need to worry about.
Slide 11:
So what is noise? One can define noise to fall into two
categories, either an extrinsic or interference, and intrinsic or
inherent. Electrical, magnetic are forms of extrinsic noise.
They can be periodic, intermittent, or random, and system
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designers can reduce the effect of these through a number of
ways. Thermal agitations of electrons and random
generations/recombinations of electron-hole pairs are examples of
inherent noise, which IC manufacturers have tried to reduce by
better processes or better circuit design techniques.
Slide 12:
And intrinsic noise is what I will be talking about today. We
will cover the extrinsic noise and how to deal with it in the
future.
Slide 13:
So I mentioned earlier, in loose terms, that noise is any
unwanted signal. So what is really noise in the electrical
engineering term? Let’s define it. Engineers define noise as a
random process due to quantum fluctuations inherent in all
resistors and semiconductor devices, specifically P-N junctions
that create voltages and currents in any application. Noise is
an instantaneous, has an instantaneous value, and is
unpredictable, it’s possible to predict it in terms of
probabilities, which we will talk about. Most noise sources are
treated as uncorrelated and have a Gaussian distribution. When
it comes to defining noise, we use terms such as peak to peak,
RMS, and we show noise in the peak to peak and, many times, in
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spectral noise density graphs.
Slide 14:
So here is how noise looks like over a 0.1 to 10 Hz, and over a
much wider frequency of 10 Hz to 10 kHz, as it is shown on the
right-hand figure. It is difficult to mathematically
characterize amplifier noise at low frequencies due to 1/f,
temperature, and aging drifts, and possibly even popcorn. This
is why it is easier for us to just show 0.1 to 10 Hz photographs
in our datasheets, and move on. Peak to peak is really only
meaningful for 0.1 to 10 Hz of bandwidth.
Slide 15:
So here is a noise signal, and unlike AC signals, whose power is
concentrated at just one frequency, noise power is spread all
over the frequency spectrum. Instantaneous value of noise is
unpredictable, but possible. It is possible to predict in terms
of probabilities. I’ve shown here -- as I mentioned earlier,
most noise has a Gaussian distribution.
Slides 16, 17, 18:
Derivative of noise power, which is the mean square voltage of
the voltage noise, the frequency is called the noise power
density, and is denoted as En2 or E2 in the case of the voltage
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noise. When specifying noise, as we can see, we should always
specify the frequency band that we are talking about.
Slide 19:
So let’s see what RMS means. Here is how we define RMS
mathematically.
Slide 20:
Let’s say that we have a pure sine wave. To get the RMS, we have
to square the signal, and once we do we get a signal like this.
Slide 21:
We have to do the average. Again, it’s the root mean square. We
have done the squaring. We have to do the mean.
Slide 22:
And this is how it looks like after averaging. If you take the
root of the signal, that’s what happens. So a sine wave in a
root, RMS fashion, is just going to look like as it is shown on
the bottom figure on this slide.
Slide 23:
So the graph on the left shows a peak-to-peak noise value of a
part over the broadband frequencies. It is very difficult to
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read peak-to-peak values accurately and consistently, as I
mentioned, from the graph on the left. When noise power density
is plotted versus frequency, it provides a visual indication of
how power is distributed over a frequency. In ICs, as you can
see on the right-hand figure, the two most common forms of power
density distributions are what is called the 1/f and white noise.
The flat part of the graph is called the white noise, and when it
starts going up it is a 1/f noise. The quantities of the voltage
noise and the current noise are noise spectral densities and
expressed in nV per root Hz and peak A per root Hz. In some
cases, μA per root Hz per root Hz. The noise spectral density
shows the noise energy at a given frequency, while an RMS gives
an RMS value over a given bandwidth or time interval.
Slide 24:
It is always good to know the peak-to-peak noise value. Because
noise is random, there is always a probability the voltage could
exceed the peak-to-peak value. This probability is shown here,
in terms of a new term, crest factor, which we define as the
ratio of the peak-to-peak value over the RMS value of the noise.
RMS values are easy to measure repeatedly and are the most usual
form for presenting noise data. One can use the table above to
estimate the probabilities of exceeding peak values, given the
RMS values. A very common number to convert from an RMS to a
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peak to peak is using a factor of 3.3 or 6.6 times. The
probability of a peak-to-peak value exceeding 6.6 times the RMS
noise value is 0.1%.
Slide 25:
It was mentioned earlier that noise spectral density of an IC is
composed of white noise and 1/f noise. I referred to these two
terms without really going through them. But there are other
contributors to IC noise, and these are popcorn noise, shot
noise, and avalanche noise. We cover all of these parameters one
by one. Also, in addition to ICs, there are other components
such as resistors, capacitors, and inductors, that are commonly
used in system designs and these elements have their own noise
sources for noises. So let’s get a better understanding of each
one of these terms.
Slide 26:
So the white noise mentioned is the flat part of the noise’s
spectral density, as it is shown over here.
Slide 27:
It is also called the broadband noise, and the voltage noise
density is constant over a frequency.
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Slide 28:
And this is how we show it mathematically in the RMS form.
Slide 29:
Remember I mentioned that you need to have the bandwidth
specified, and the f2 minus f1 is the bandwidth that we have in
mind in this example.
Slide 30:
If f1 is a lot smaller than, let’s say, ten times of the f2 --
let’s say we pick f1 to be 100 Hz and the f2 to be 10 mHz or
something, then the f1 is really irrelevant.
Slide 31:
Then we can approximate the noise to be just the En times the
square root of the f2 frequency. Remember, this is the noise
floor of the systems and a limiting factor for system resolution.
This is what is called the broadband noise, or the white noise.
Slide 32:
Another noise term that we define, or we mention, is the pink
noise -- also called the flicker, or 1/f noise. At low
frequencies, as is shown over here, noise goes up inversely
proportional to the frequency. And that’s why the term -- 1/f
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term. One over f is always associated with current and is caused
due to traps, which, when current flows, capture and release
charge carriers randomly, therefore causing random fluctuations
in current itself. In the BJTs, it is caused by contamination
and imperfect surface conditions at the base-emitter junction of
a transistor. In CMOS, it is mostly associated with extra-
electron energy states at the boundary between silicon and
silicon dioxide. The 1/f corner frequency, which is a figure of
merit, is a frequency above which the amplitude of noise is
relatively flat and independent of frequency.
Slide 33:
To measure, or to calculate the 1/f noise, the equations are
shown over here, as you can see. Please note that the corner
frequency for a voltage noise is different, or might be
different, than the corner frequency of a current noise. I
mentioned earlier that the unit for voltage noise is nV/root Hz,
and for a current is sometimes μA per root Hz.
Slide 34:
One characteristic of a 1/f noise is that the power content in
each decade is equal, and this is what is shown in this slide.
As you see, we have bandwidths that are apart from each other by
one decade. I showed you the formula earlier, and squaring both
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sides of that equation gives 1/f noise power, which is
proportional to the log ratio of the bandwidth, regardless of the
band location. So if you pick 200 Hz and 20 Hz is a factor of 10
and the log of 10 is always 1, as I showed in that equation.
Slide 35:
So here is -- some interesting facts, which I like to share with
you. White noise has equal energy per frequency.
Slide 36:
And we mentioned that the f2, when it is very large compared to
f1, RMS noise is set by the f2.
Slide 37:
Pink noise has equal energy per octave.
Slide 38:
RMS noise is set, I showed you in the equation, by the ratio of
the f2 to f1.
Slide 39:
So I just want to give you a little bit of bonus.
Slide 40:
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And that is, I ask you which do you think sounds louder?
Slide 41:
Why do they call it white noise?
Slide 42:
Why do they call it pink noise? I give you the answers for two
of them, and you can give me an answer for another one, for the
third one, later, because I don’t know the answer to that
question myself. White noise sounds louder. It has more energy
at wider bandwidth than pink noise. Our ears are much more
sensitive to frequencies from 500 to 2 kHz. White light has all
frequencies with equal energy from each frequency. White light
has equal energy per frequency. And I mentioned that I don’t
know why it is called pink noise. If you know, please let me
know.
Slide 43:
To give you a feel as to how broadband noise and 1/f noise look
like -- we actually get a lot of questions related to noise all
the time, and one of the things that I usually ask my customers
to do is look at the noise on the scope and interpret the
results, or if they don’t understand they can send us a picture.
So here are those two references that you can use. The upper
15
figure is the broadband noise, and the one shown below it is the
1/f noise. The broadband noise is the furry shape, and 1/f noise
is more rough and grassy. That’s how you can say it.
Slide 44:
So now the question is, what happens when we have spectral noise
density and not the peak-to-peak graph in a data sheet? This has
happened sometimes in some of the data sheets that we have done
over the past 40 or 50 years. Here, I show you a formula that
you can use to arrive at the peak-to-peak value.
Slide 45:
Assuming you are given the graph on the left, you can use this
formula. You can find out the corner frequency and, given the
two frequencies for the f1 and f2 of 0.1 and 10 Hz, you can find
out what the peak-to-peak value would be based on the noise
spectral density that you have. If you go through the
calculation, as I have here, you get the peak-to-peak noise to be
218 nV.
Slide 46:
And here is the graph, which is in the data sheet, showing the
peak-to-peak noise to be 200 nV. They come pretty close, and we
have a good idea. We can move on.
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Slide 47:
Another noise term is called, or noise type, is called the
popcorn noise, also called the burst noise. It causes the step
function voltage changes at the output of an amplifier. It is
caused by transistors jumping erratically between two values of
beta. In the early days, popcorn noise was a serious issue that
resulted in random discrete offset shifts in a timescale of a few
tens of milliseconds. Today, although popcorn noise can still
occasionally occur during manufacturing, the phenomenon is
sufficiently well understood and parts are scrapped during
limited testing. Popcorn noise is a part of the 1/f noise and
remember it happens at very low frequencies. It’s purely a
function of the process. It was more of a problem in the old
days and not as big of a deal these days, although every once in
a while you have some issues. We have done extensive in this
area and we have experts who have done great amount of work who
can help in case you need any more information.
Slide 48:
The noise that is called the shot noise, also called a
[Schottky?] noise, occurs whenever a current passes through PN
junctions and there are many junctions, as you know, in our
parts. Barrier crossing is purely random and the DC current
17
that’s observed is the sum of many random elementary current
pulses. So this is the current noise, and it has a uniform power
density. It’s a part of white noise. And remember, white noise
is constant over all frequencies. The equation to find the value
of a shot noise is given over here, which is the square root of 2
qI delta f -- I in the case of an amplifier is the Ib that you
are talking about. There is a handy number that you can use if I
is given in the peak amps, which, for our J FET parts and CMOS
parts, the Ibs are in the [pento arm?], you can use the
simplified equation to quickly find out what is the amount of
shot noise based on that current.
Slide 49:
I mentioned that this is when the current passes through a PN
junction, so here I have used -- I give you an example of two
diodes operating at two different currents -- at one micron and 1
nA, and I have calculated the noise based on those currents
crossing the PN junction. As a result, the noise is generated
and the signal to noise -- the signal being the current that I
forced through the diodes and the noise generated as a result of
those currents -- the signal to noise ratio, as you can see, is
65 dB and 35 dB.
Slide 50:
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Another noise type is the avalanche noise, and it is found in PN
junctions in reverse breakdown modes. We don’t really have this
in our parts and I have the slide here to be complete. I just
have a couple of bullets on these. I’m not going to spend too
much time on this.
Slide 51:
The thermal noise, also called Johnson noise, found in all
resistors, even a resistor sitting in a drawer in the lab
somewhere. This noise is generated as a result of temperature
changes or whatever else that might be happening. It’s the
thermal agitation of electrons in resistors that cause random
movement of charge, causing a voltage to appear, and thermal
noise is part of the white noise, or the broadband noise, that we
just talked about earlier. The equation to find the thermal
noise is given right in the middle of this slide, which is the
square root of 4 kTR times the bandwidth that we are working on,
and I have every term defined there. the way to reduce the
thermal noise is, of course, to pick a small resistor -- as it is
shown over here, the smaller the resistor the less noise. If we
can control the temperature, if we can cool the temperature that
will be smaller, and as one of my friends, Mr. James Bryant,
says, there isn’t anything you can do with the Boltman constant
because he’s dead and that constant is fixed. So, remember,
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doubling the resistance increases the noise by 3 dB because it’s
under the square root term. So four times the resistance equals
to doubling the noise.
Slide 52:
One of my characteristics is that I always want to make sure that
we all understand what we are talking about. So here is a
question to you: What is the noise contribution of a 10 k
resistor room temperature?
Slide 53:
Is it A, B, C, or D?
Slide 54:
I give you a hint: Remember that the 1 k resistor has 4 nV per
root Hz of noise.
Slide 55:
So, knowing that information and using this equation, by looking
at this you will find out that the answer is C, which is 12 nV.
And this way you can quickly look at your circuits and your
components that you have picked and find out what the noise of a
resistor is right off the top of your head. So remember, the 1 k
resistor has 4 nV per root Hz and then from that point on it’s
20
just the square root of -- you use that if you want to pick the
10 -- square root of 10 is almost 3, 3 times 4 is 12.
Slide 56:
And if you cannot remember the equation or you don’t want to be
bothered, I am giving you a graph here that plots the resistor
noise based on the resistor value and, as you see, as the
resistor value goes up its noise up. It’s very critical to
notice things, because in the next session, when we go and design
the signal conditioning circuit, we need to account for all the
errors, or all the noise sources that come into picture.
Slide 57:
So now the question is, what’s the sum of two noise sources? How
do we add up the two noise sources? If the noise sources are
uncorrelated -- as I mentioned, the majority of the noise sources
are recombined in a root-sum-square as it is shown over here.
Slide 58:
This means that adding tow noise sources that have the same
energy only increases the overall noise by 1.4 or 3 dB.
Slide 59:
That’s the square root of 2, remember that. Two equal noise
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sources added up have a 1.4 factor.
Slide 60:
And this works for audio, as well. Two people talking the same
volume about two totally different things only add 3 cB of sound
pressure levels to the party, and it’s not going to be 2 times as
much. So remember the RSS or the root-sum-square fashion for
adding uncorrelated noises.
Slide 61:
So, let me just say, go back to a signal conditioning circuit
that’s interfacing a sensor and give you a handy formula that you
can always use to calculate the two different noise of your
signal conditioning circuit.
Slide 62:
So what we have done so far is that -- I have explained that all
ICs have some inherent noise within them. In case of an
amplifier, those noise sources can be modeled as zero impedance
voltage generator en noise source in series with the input, and
infinite impedance current sources parallel with the input, as I
have shown in.
Slide 63:
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Do not worry too much about the direction of the arrows here -- I
just drew something. Each of these terms vary with frequency, as
I have shown, and the type of amplifiers that you have picked for
your signal conditioning. I mentioned that the voltage noise
density unit is nV per root Hz and the current noise density is
pA or μA per root Hz. Both of these sources can be treated as
uncorrelated noise sources and the amplifier here that I have
shown, I am treating it as a noiseless amplifier. This is an
ideal amplifier that I wish we had, which we don’t have yet. So
now if you put the ideal amplifier and its noise sources there,
we come up with the signal conditioning as it is shown here with
a sensor, which I show a sensor on the left-hand side of the
figure with its noise resistance and resistor, as we mentioned,
has a noise. All the resistors around the amplifiers have noise
associated with them, as I have shown here. So now to look at
the noise -- the total noise on the input, as it is called, the
refer to inputs, we can use the equation that I show on the
bottom of the slide. In general form, these are all noise
sources that I could think of in a typical signal conditioning
circuit. Total output noise referred to input is given by
resistor noises, op amp noise, which are current and voltage
noise sources. It’s not going to be -- there are some terms here
that need a bit of explanation. And we will talk about these
things later on. What I was just going to point out here is the
23
term called noise gain as it is defined, what is called the
bandwidth, or the effective bandwidth, as I explain to you later
on what that is. So if you want to look at the noise on the
output, you have to know the referred to input noise and multiply
that by the noise gain and not really the signal gain. I’ll
explain to you what this is and how we define this.
Slide 64:
So what is really the noise gain? How do we define this? This
is how much the noise and whatever garbage and extra useless
information is gained up by. Regardless of the configuration,
whether the amplifier is an inverting or non-inverting
configuration, the noise gain, as I showed you earlier, is equal
to 1 plus R2 over R1. Here, I show two circuits. The one on the
left-hand side is a non-inverting configuration. The one on the
right-hand side is an inverting configuration. In an inverting
configuration, as I state here, the signal gain is minus R3 over
R4; the noise gain is 1 plus R3 over R4. In the left-hand side,
where we have a non-inverting configuration, as you all know, the
signal gain is 1 plus R2/R1 and the noise is 1 plus R2 over R1.
So in both configurations the noise gain is 1 plus the feedback
resistor over the R1, or actually R4 in this case. Sorry --
there is an error in my drawing here. Instead of R4 over R3, I
had mentioned R2 and R1. Those are easy to understand.
24
Slide 65:
And I mentioned the term called noise effective bandwidth. White
noise is passed as if the filters were a brick wall type, but
with a cutoff frequency of 1.57 times as large. The 0.57
accounts for the transmitted noise above the cutoff frequency as
a consequence of gradual roll-off.
Slide 66:
We can think of the amplifier as a single-pole low-pass filter,
which is a good approximation, and that -- you can use the
equations to come up with the noise of a first-order low-pass
filter, meaning you have to multiply the noise by the square root
of 1.57 times that corner frequency.
Slide 67:
And if you want to design a higher order of filters, and just
figure out the noise effective bandwidth, here is the equation
that you can use.
Slide 68:
The N is the order of the filter and once you use this -- I give
you an example here, that if N is equal to 1, as it is the first
order filter that I just explained in the previous slide, the
25
factor is 1.57 and as you go higher and higher in the order you
get closer to the brick wall and the bandwidth is narrowed, and
less noise is passed through, which is a desirable feature, but,
again, there is a price to pay to go to a higher-order filter.
You get rid of the noise, but there is a price to pay. That’s
how life is in the amplifier world, and in our world. There’s
always a tradeoff that you have to make.
Slide 69:
I say here that the high-order filter is good and as you can see
it can make an improvement to our signal to noise ratio.
Slide 70:
So assume that I have used the circuit in the previous slide for
the signal conditioning that I showed you, where I showed you the
noise calculation equation and all the noise sources. So assume
that I have used that circuit and I am using a 10 mHz amplifier
in an inverting gain of 1000, using the resistor values of 100 k
in the feedback and 100 ohm as a source, and what I have done
here is I have plotted amplifier noise -- meaning, if I picked
different amplifiers that have different voltage noise densities,
put it in this configuration, the amount of noise that I will get
at the output is just going to look like this. So if you pick an
amplifier that has a large value for its voltage noise density,
26
then the output noise will be higher even if it 10 mHz. So you
need to make sure you’re picking the right component. This is
something that we talk about later on, in the next session. You
have to know how to go about picking the right component, whether
it is a capacitor, a resistor, an amplifier, or anything that’s
just going to be used for signal conditioning. You have to
exercise a good discipline and good practice. And it is very
important to pick the right component, and I explain about this
later on in the next session.
Slide 71:
Here, just to be complete -- here we look at the noise gain of a
second-order system. The shape of the noise gain is going to be
different, of course, because of the resistors because of the
capacitors. At very low frequency, noise gain is a function of
the resistors, as I have shown here, and at higher frequency is
the function of the capacitors. Capacitors do not generate noise
themselves, but the current noise of an amplifier drops across
the capacitor and creates a voltage noise error.
Slide 72:
So how do we go about designing a low noise circuit? My
suggestion is always to build in low-noise design ideas and
concepts, rather than designing something and then trying to
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reduce the noise by shielding, layout, and other techniques that
you try to figure out at the end of your design process. So you
have to build it in. So what process do I suggest?
Slide 73:
So here is the process that I suggest. I will say you have to
know which frequency range or which frequency band are you
interested in? Are you working in the 1/f region? Is your
application requiring a broadband region? That’s the very first
thing you need to understand -- where your signals, or what’s the
bandwidth of your signals. And then you have to design -- my
suggestion is, for the best performance that you can find.
Today’s amplifiers have noise range of 0.9 nV to 60 nV.
Understanding about the input architecture and the amplifier
helps you pick the right amplifiers. So you pick the right
amplifier, you pick the right target components, and you know the
bandwidths. You design around that. Then you worry about the
other things that are non-noise requirements, like the input
impedance or how much current you have to use in your system and
what gain, and stuff like that. And if noise specs is not met
after going through this process, then you need to go back again
and pick a different component, maybe a different amplifier, and
go through this situation several times. So, it’s very important
to understand a little bit about the amplifier -- how it is put
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together, and my goal is to show you in the next few slides how
noise sources inside of an op amp power and what benefits do you
get if you go with a bipolar or a CMOS or a J FET amplifier.
Slide 74:
So what are the noise sources in the bipolar amplifiers? If a
data sheet tells you that the noise is 3 nV, it’s not good
enough. You need to know how these 3 nV is achieved, since, as I
mentioned earlier, there is always a tradeoff that has to be made
and that tradeoff might affect your application.
Slide 75:
So here is the input structure of an amplifier on bipolar
process. Thermal noise, shot noise, and 1/f noise are the three
noise sources that you need to worry about, or a designer needs
to worry about, inside of the power, but you need to be aware of
these things. And voltage noise, I mentioned earlier, is made up
of 1/f and broadband noise.
Slide 76:
So if you want to know the complete story in what factors in
bipolar transistors, or what elements in bipolar transistors,
contribute to the voltage noise density or the voltage noise of a
bipolar op amp, here is the complete equation. And I mentioned
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there is always a tradeoff. And here is the current noise
density equation that you can use as a reference. So, to get,
say, a low-voltage noise density you need to use a very high
beta, as it is shown in that equation, in the denominator. But
that requires a light doping and very thin Rb on the input, and
Gm and Ibs, as you know, are directly proportional to the IC, and
therefore the current noises can go.
Slide 77:
So what works to minimize the en is the opposite of what is good
for low-current noise density, which represents the fundamental
tradeoff in bipolar design.
Slide 78:
There are a number of parts that have super beta or Ib
cancellation circuits in them that introduce correlated noise.
Ib cancelled ports -- not, still, as good as FET for bias
currents, but they bring in a lot of good benefits. This is the
compensation for bias current error term and we have a number of
parts, and I will talk briefly about the compensated parts, what
to do with them, in the next session.
Slide 79:
The noise in CMOS parts -- we have many, many CMOS, many, many J
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FETs, and many bipolar parts that we have designed over the past
40-50 years.
Slide 80:
So when we look at the noise sources inside of a CMOS part, here
is how it looks like. There are three noise associated, and
these are the gate leakage, which I show as the Ing 1/f noise,
which I show as If, and the current noise, which is another shot
noise term, which is shown as Ind.
Slide 81:
Noise contributors are different in different regions of this
graph. There are process dependencies or design tweaks that can
be used to get better noise specs, but each have their
implications on the approximation application level.
Slide 82:
Flicker noise is inversely proportional as an example to the
transistor WL, so to reduce the noise one has to use input stage
transistors with large geometries. So here we see, as we use
larger geometries for W and L in the denominator the noise is
just going to go down, but this has implications that you need to
be aware of when we go to the application level.
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Slide 83:
Bigger transistor geometries are just going to have larger
capacitances that come into the end applications, and you need to
worry about this and compensate the amplifiers correctly to get
the performance that you need to get out of it.
Slide 84:
Here's an equation to measure the current spectral density -- is
just showing you the equation for the corner frequencies. And
what designers can do inside of the IC companies like mine.
Slides 85-86:
We can, of course, operate the FET where gm is large. We can do
that to get lower noise.
Slide 87:
We can use high values of the static current.
Slides 88-89:
Again, we get the noise down but we are consuming a lot of power,
a lot of current, as it is shown over here, or, as I mentioned,
we can use a large geometries to get the noise down. Each one of
these we will talk about later on, as to what implication it may
have in the final design.
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Slide 90:
Briefly, I talk about the corner frequency in CMOS.
Slide 91:
We know where a corner frequency is, where the flat part and 1/f
noise are equal to each other --
Slide 92:
-- and if you recall the equations for the CMOS part you get the
corner frequency if you use this equation. This, again, has
significance to us, as significance to the equation, as I showed
you there, that finding the right corner frequency, or pushing
the lower corner frequency to very close to DC is very important.
Slide 93:
And here is the noise in the J FET. Compared to bipolar
transistors, J FETs have much lower gm. Therefore, FET op amps
tend to have a higher voltage noise for similar operating
conditions. We have some J FET parts that are very low noise,
also, but when we do a one-to-one comparison we can make a
statement like that. And remember, at room temperature, the
current noise density, like the CMOS parts, is not a problem. It
is negligible. Many times in the μA per root Hz -- but one
33
drawback here is that it doubles for every 10 to 20 degrees and
that may become a bit of a problem over temperature, if you need
to operate over wide temperatures, like middle temperature
ranges.
Slide 94:
So, in a tabulated form, here I compare the bipolar, CMOS, and J
FET input amplifiers for the processes that the amplifiers are
on, and I give you an idea as to which amplifier process to pick
if you have an interest in the voltage noise or a current noise,
and this way make it easy for you.
Slide 95:
So, in summary, what I have done is I have explained as to why it
is important to understand the low-noise design. I built some
foundations and fundamentals on the noise definitions and the
noise types that are available. I gave you a general formula
that can be used for an inverting, non-inverting, different sound
amplifiers under many configurations, and how to calculate the
noise of a typical signal conditioning circuit, and I very
briefly introduced you to a low-noise design process. I will go
through these things a bit further in my next talk, and I show
you a lot of dos and don'ts and different ways of optimizing a
typical circuit in my February talk. This ends my talk. Gary?
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Gary Cocker:
Thank you, Reza, for that very nice presentation. We are running
a bit long, so we're going to have to truncate our Q & A a bit.
I'm going to ask you to please bear with us on that score. Reza,
how does popcorn noise behave with time?
Reza Moghimi:
Wow, that's a great question and, actually, we get that quite
often. Occurrence of the popcorn is quite random. An amplifier
may exhibit several pops per second during one observation
period, and then it remains popless for several minutes. We
don't really have a screening -- I don't think anyone has a
screening -- a perfect screening, to remove all noisy poles,
although we have a pretty good understanding that what causes it
and how we can catch the parts with very high probability.
Gary Cocker:
Reza, I'm afraid our production team has given me the time-out
signal. That's all we have time for today. I wish we could get
more questions answered. But I do want to wrap up with --
everyone, we will be getting to all of your questions here. All
of your submitted questions will be answered by Reza via email
shortly after the conclusion of this broadcast. So if you send
35
in a question, it is not in vain. It will be answered. So look
to your email for that. And that's going to wrap up our show
today. And thank you for attending today's webinar, "Noise
Optimization in Sensor Signal Conditioning Circuits." This was
part one, presented by Analog Devices. Don't forget to catch
part two, which is going to be scheduled for next month. So I
hope you'll join us there. and, again, look to your email for
your Q & A answers. And thank you very much, Reza, again. For
additional information and documentation, please direct your
attention to the Analog Devices resource page that's opened
before you at www.analog.com. This webinar is copyright 2008 by
CMP Media. The presentation materials are owned and copyrighted
by Analog Devices, Incorporated, which is solely responsible for
its content. The individual speakers are solely responsible for
their content and their opinions. On behalf of our panelist
today, Reza Moghimi, and our entire webinar production team, I'm
Gary Cocker. Thank you for joining us, and have a great day.
END OF TRANSCRIPT
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