e-book
`
`Fundamentals of
`Precision ADC Noise Analysis
`
`Design tips and tricks to reduce noise with delta-sigma ADCs
`
`ti.com/precisionADC September | 2020
`
`IPR2021-00294
`Xilinx, Inc. v. Analog Devices, Inc.
`Analog 2003
`
`

`

`Table of contents
`
`About the author . . . . . . . . . . . . . . . . . . . . . . . . 3
`
`Introduction from the author . . . . . . . . . . . . . . 4
`
`Introduction to ADC noise
`1.1 Types of ADC noise . . . . . . . . . . . . . . . . . . . . . . . . . 5
`
`
`
`
`
`
`1.2 ADC noise measurement methods
`and parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
`
`
`1.3 Defining system noise performance . . . . . . . . . . . . 15
`
`Effective noise bandwidth
`2.1 Effective noise bandwidth fundamentals . . . . . . . . 21
`
`
`
`2.2 Calculating the effective noise bandwidth . . . . . . . 25
`
`Amplifier noise, dynamic range and gain
`3.1 How amplifier noise affects delta-sigma ADCs . . . 29
`
`
`
`
`3.2 An amplifier-plus-precision delta-sigma
` ADC design example . . . . . . . . . . . . . . . . . . . . . . 33
`
`
`Special note
`These articles were originally published as a series in
`All About Circuits and have been reused with permission.
`
`Voltage reference noise
`4.1 How voltage reference noise affects
` delta-sigma ADCs . . . . . . . . . . . . . . . . . . . . . . . . . 39
`
`
`
`
`
`
`
`4.2 Reducing reference noise in delta-sigma
`ADC signal chains . . . . . . . . . . . . . . . . . . . . . . . . . 43
`
`
`Clock noise
`5.1 How clock signals affect precision ADCs . . . . . . . . 48
`
`Power-supply noise
`6.1 Power-supply noise and its effect on
`delta-sigma ADCs . . . . . . . . . . . . . . . . . . . . . . . . . 53
`
`
`
`
`
`
`
`6.2 Reducing power-supply noise in
`delta-sigma ADCs . . . . . . . . . . . . . . . . . . . . . . . . . 58
`
`
`Fundamentals of Precision ADC Noise Analysis
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`

`

`About the author
`
`Bryan Lizon is a product marketing
`engineer for the Precision Analog-to-
`Digital Converter (ADC) team at Texas
`Instruments (TI). In this role, Bryan has
`been responsible for the marketing
`functions for TI’s factory automation and
`control, test and measurement, medical and automotive
`ADCs. He joined TI in 2014 as part of the Precision ADC
`team after receiving his Bachelor of Science degree in
`electrical engineering from the University of Arizona.
`
`Bryan became interested in the topic of ADC noise soon
`after joining the ADC team, seeing that many disparate
`questions seemed like they could be traced back to
`
`Other contributors include:
`
`Christopher Hall, applications engineer, Precision ADCs
`
`Ryan Andrews, applications engineer, Precision ADCs
`
`Joachim Wuerker, systems manager, Precision ADCs
`
`challenges with noise, precision and resolution. Specifically,
`he found many customers had difficulty understanding
`the relationship between noise and gain, as well as how
`that related to data-sheet performance. To explore this
`relationship further and provide insight to engineers, Bryan
`wrote and illustrated a three-part blog post series framed as
`a whodunit mystery. From there, he took a more technical
`approach and expanded this topic to include multiple noise
`sources and how they interact with precision ADCs. Bryan
`turned this content into an internal presentation to educate
`TI’s sales team, followed by an online series of 12 articles,
`which TI assembled into this e-book.
`
`Fundamentals of Precision ADC Noise Analysis
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`

`Introduction from the author
`
`When I first began working in the semiconductor industry, I
`had never heard of a delta-sigma analog-to-digital converter
`(ADC). My university training focused heavily on digital
`design, and the only ADCs we used were low-resolution
`successive-approximation-register (SAR) ADCs integrated
`into microcontrollers (MCUs). As a result, it was somewhat
`daunting to be assigned to the Precision ADC team, where
`digital knowledge is certainly useful, but analog design
`is king. As my training ramped up, I noticed that despite
`a variety of issues that engineers raised, many of their
`challenges arose from what seemed like a very obvious
`question: How do you get the best noise performance out
`of a 16-bit, 24-bit or even 32-bit ADC?
`
`Now, I should note that this is a simple question with a
`complicated answer. And as is typical for most engineering
`questions, the answer is “It depends.” “Depends on what?”
`you might ask—and exploring that question is the basis
`for this e-book. What affects a high-resolution ADC’s noise
`performance? How does each component contribute noise
`to the system, and how do these noise sources interact with
`each other? Which noise source dominates, and how do
`you apply these principles to your specific application?
`
`If you’ve ever been tasked with designing a signal chain that
`uses a delta-sigma ADC, you have likely had to ask yourself
`these questions. Regardless of your efforts to minimize
`power consumption, decrease board space or reduce cost,
`noise levels greater than the input signals render any design
`effectively useless. As a result, this e-book is designed to
`provide fundamental knowledge to help any analog designer
`understand signal-chain noise, its effect on analog-to-digital
`conversion, and how to minimize its impact and maintain
`high-precision measurements. I will examine common
`noise sources in a typical signal chain and complement this
`understanding with methods to mitigate noise and maintain
`high-precision measurements.
`
`Before continuing, I’d like to mention that this e-book covers
`precision (noise), not accuracy. While the two terms are
`often used interchangeably, they refer to different—though
`related—aspects of signal-chain design. When designing
`high-performance data-acquisition systems, you must also
`consider errors due to inaccuracy, such as offset, gain error,
`integral nonlinearity and drift, in addition to minimizing noise.
`
`Fundamentals of Precision ADC Noise Analysis
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`

`

`Chapter 1: Introduction to ADC noise
`
`Chapter 1 encompasses three sections. In Section 1.1,
`I’ll focus on analog-to-digital converter (ADC) noise
`fundamentals while answering questions and discussing
`topics such as:
`
`• What is noise?
`
`• Where does noise come from in a typical signal chain?
`
`• Understanding inherent noise in ADCs.
`
`• How is noise different in high-resolution vs. low-
`resolution ADCs?
`
`In Section 1.2, I’ll shift the focus to these topics:
`
`• Measuring ADC noise.
`
`• Noise specifications in ADC data sheets.
`
`• Absolute vs. relative noise parameters.
`
`In Section 1.3, I’ll step through a complete design example,
`using a resistive bridge to help illustrate how the theories
`from Sections 1.1 and 1.2 apply to a real-world application.
`
`(a) High-resolution image example
`Noisy image example
`
`1.1 Types of ADC noise
`Noise is any undesired signal (typically random) that adds
`to the desired signal, causing it to deviate from its original
`value. Noise is inherent in all electrical systems, so there is
`no such thing as a “noise-free” circuit.
`
`Figure 1 depicts how you might experience noise in the real
`world: an image with the noise filtered out and that same
`image with no filtering. Note the crisp detail in Figure 1a,
`while Figure 1b is almost completely obscured. In the
`analog-to-digital conversion process, the result would be
`information loss between the analog input and the digital
`output—much like how the two images in Figure 1 bear
`virtually no resemblance to each other.
`
`In electronic circuits, noise comes in many forms, including:
`
`• Broadband (thermal, Johnson) noise, which is
`temperature-dependent noise caused by the physical
`movement of charge inside electrical conductors.
`
`• 1/f (pink, flicker) noise, which is low-frequency
`noise that has a power density inversely proportional
`to frequency.
`
`(b) Noisy image example
`Hi-res image example
`
`Figure 1. A noise-free image (a) and the same image with noise (b).
`
`• Popcorn (burst) noise, which is low frequency in nature
`and caused by device defects, making it random and
`mathematically unpredictable.
`
`These forms of noise may enter the signal chain through
`multiple sources, including:
`
`• ADCs, which contribute a combination of thermal noise
`and quantization noise.
`
`• Internal or external amplifiers, which can add
`broadband and 1/f noise that the ADC then samples,
`allowing it to affect the output code result.
`
`• Internal or external voltage references, which also
`contribute broadband and 1/f noise that appears in the
`ADC’s output code.
`
`• Nonideal power supplies, which may add noise into
`the signal you’re trying to measure with several means
`of coupling.
`
`Fundamentals of Precision ADC Noise Analysis
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`

`Chapter 1: Introduction to ADC noise
`
`• Internal or external clocks, which contribute jitter that
`translates into nonuniform sampling. This appears as an
`additional noise source for sinusoidal input signals and is
`generally more critical for higher-speed ADCs.
`
`• Poor printed circuit board (PCB) layouts, which
`can couple noise from other parts of the system or
`environment into sensitive analog circuitry.
`
`• Sensors, which can be one of the noisiest components in
`high-resolution systems.
`
`Figure 2 depicts these noise sources in a typical
`signal chain.
`
`Each ADC noise source has particular properties that are
`important when understanding how to mitigate inherent
`ADC noise.
`
`Figure 3 depicts the plot of an ADC’s ideal transfer function
`(unaffected by offset or gain error). The transfer function
`extends from the minimum input voltage to the maximum
`input voltage horizontally and is divided into a number of
`steps based off the total number of ADC codes along the
`vertical axis. This particular plot has 16 codes (or steps),
`representing a 4-bit ADC. (Note: An ADC using straight
`binary code would have a transfer function that only includes
`the first quadrant.)
`
`Power supply noise
`
`- +
`
`Reference noise
`VREF
`
`Amplifier
`
`Delta-Sigma/
`SAR ADC
`
`Sensor noise
`
`1/f noise &
`BB noise
`
`Thermal noise &
`quantization noise
`
`Layout noise
`
`Clock jitter
`
`Figure 2. Common noise sources in a typical signal chain.
`
`2N
`codes
`
`-FS
`
`Code clipped
`
`Code clipped
`
`LSB size =
`
`FSR
`2N
`
`Input
`voltage
`
`+FS
`
`Output code
`
`0111
`0110
`0101
`0100
`0011
`0010
`0001
`
`1111
`1110
`1101
`1100
`1011
`1010
`1001
`1000
`
`In the three sections that make up Chapter 1, I’ll focus
`on inherent ADC noise only. For a more comprehensive
`understanding of signal-chain noise, Chapters 3–6 discuss
`sources of noise in the remaining circuit components.
`
`Inherent noise in ADCs
`
`You can categorize total ADC noise into two main sources:
`quantization noise and thermal noise. These two noise
`sources are uncorrelated, which enables the root-sum-
`square method to determine the total ADC noise, NADC,Total,
`as shown in Equation 1:
`
`Figure 3. An ADC’s ideal transfer function.
`
`Quantization noise comes from the process of mapping
`an infinite number of analog voltages to a finite number
`of digital codes. As a result, any single digital output can
`correspond to several analog input voltages that may differ
`by as much as ½ least significant bit (LSB), which is defined
`in Equation 2:
`
`LSB size (V) =
`
`FSR
`N
`
`2
`
`(2)
`
`N
`ADC,Total
`
`=
`
`N
`ADC,Thermal
`
`2
`
`+
`
`N
`ADC,Quantization
`
`2
`
`(1)
`
`where FSR represents the value of the full-scale range (FSR)
`in volts and N is the ADC’s resolution.
`
`Fundamentals of Precision ADC Noise Analysis
`
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`September 2020 I Texas Instruments
`
`

`

`Chapter 1: Introduction to ADC noise
`
`If you map this LSB error relative to a quantized AC signal,
`you’ll get a plot like the one shown in Figure 4. Note the
`dissimilarity between the quantized, stair-step-shaped digital
`output and the smooth, sinusoidal analog input. Taking the
`difference between these two waveforms and plotting the
`result yields the sawtooth-shaped error shown at the bottom
`of Figure 4. This error varies between ±½ LSB and appears
`as noise in the result.
`
`Unfortunately, you cannot affect your ADC’s thermal noise
`because it is a function of the device design. Throughout the
`rest of this section, I’ll refer to all ADC noise sources other
`than quantization noise as the ADC’s thermal noise.
`
`Figure 5 depicts thermal noise in the time domain, which
`typically has a Gaussian distribution.
`
`Time-domain noise
`
`Noise distribution
`
`Voltage (V)
`
`0.04
`
`0.03
`
`0.02
`
`0.01
`
`0 -
`
`0.01
`
`-0.02
`
`-0.03
`
`-0.04
`150
`
`0
`
`50
`
`100
`
`150
`
`200
`
`250
`
`300
`
`350
`
`400
`
`450
`
`500
`
`0
`
`50
`
`100
`
`Time (ms)
`
`# of samples
`
`0.04
`
`0.03
`
`0.02
`
`0.01
`
`0
`
`-0.01
`
`-0.02
`
`-0.03
`
`-0.04
`
`Voltage (V)
`
`Analog
`Digital
`
`1.0
`
`0.5
`
`0.0
`
`-0.5
`
`-1.0
`
`1
`0.5
`0
`-0.5
`-1
`
`Signal (V)
`
`LSB error
`
`0
`
`200
`
`400
`600
`Sample #
`
`800
`
`1000
`
`Figure 4. Analog input, digital output and LSB error waveforms.
`
`Similarly, for DC signals, the error associated with
`quantization varies between ±½ LSB of the input signal.
`However, since DC signals have no frequency component,
`quantization “noise” actually appears as an offset error in
`the ADC output.
`
`Finally, an obvious but important result of quantization noise
`is that the ADC cannot measure beyond its resolution, as it
`cannot distinguish between sub-LSB changes in the input.
`
`Unlike quantization noise, which is a byproduct of the
`analog-to-digital (or digital-to-analog) conversion process,
`thermal noise is a phenomenon inherent in all electrical
`components as a result of the physical movement of charge
`inside electrical conductors. Therefore, you can measure
`thermal noise even without applying an input signal.
`
`Figure 5. Thermal noise in the time domain with Gaussian distribution.
`
`Although you cannot affect the ADC’s inherent thermal noise,
`you can potentially change the ADC’s level of quantization
`noise due to its dependence on LSB size. Quantifying the
`significance of this change depends on whether you’re
`using a “low-resolution” or “high-resolution” ADC, however.
`Let’s quickly define these two terms so that you can better
`understand how to use LSB size and quantization noise to
`your advantage.
`
`Low- vs. high-resolution ADCs
`
`A low-resolution ADC is any device whose total noise
`is more dependent on quantization noise such that
`NADC,Quantization >> NADC,Thermal. Conversely, a high-
`resolution ADC is any device whose total noise is more
`dependent on thermal noise, such that
`NADC,Quantization << NADC,Thermal. The transition between low
`and high resolution typically occurs at the 16-bit level, with
`anything <16 bits considered low resolution and anything
`>16 bits considered high resolution. While not always true,
`I’ll keep this general convention throughout the remainder of
`this e-book.
`
`Fundamentals of Precision ADC Noise Analysis
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`September 2020 I Texas Instruments
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`

`

`Chapter 1: Introduction to ADC noise
`
`Why make the distinction at the 16-bit level? Let’s look at
`two ADC data sheets to find out. Table 1a shows the actual
`noise tables for the TI ADS114S08, a 16-bit delta-sigma
`ADC, while Table 1b shows the noise tables for its 24-bit
`counterpart, the ADS124S08. Other than their resolutions,
`these ADCs are identical.
`
`Data Rate
`(SPS)
`
`2.5
`5
`10
`16.6
`20
`50
`60
`100
`200
`400
`800
`1000
`2000
`4000
`
`Gain
`1
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (76.3)
`76.3 (95)
`
`Data Rate
`(SPS)
`
`2.5
`5
`10
`16.6
`20
`50
`60
`100
`200
`400
`800
`1000
`2000
`4000
`
`Gain
`1
`0.32 (1.8)
`0.40 (2.4)
`0.53 (3.0)
`0.76 (7.2)
`0.81 (4.8)
`1.3 (7.2)
`1.4 (8.0)
`1.8 (9.2)
`2.4 (13)
`3.6 (19)
`5.0 (29)
`6.0 (32)
`7.8 (45)
`15 (95)
`
`(a)
`
`(b)
`
`Table 1. Input-referred noise for the 16-bit ADS114S08 (a) and 24-bit
`ADS124S08 (b) in μVRMS (μVPP) at VREF = 2.5 V, G = 1 V/V.
`
`In the noise table for the 16-bit ADS114S08, all of the input-
`referred noise voltages are the same regardless of data rate.
`Compare that to the 24-bit ADS124S08’s input-referred
`noise values, which are all different and decrease/improve
`with decreasing data rates.
`
`While this doesn’t result in any definitive conclusions by
`itself, let’s use Equations 3 and 4 to calculate the LSB size
`for each ADC, assuming a 2.5-V reference voltage:
`
`LSB
`ADS114S08
`
`=
`
`2×V
`REF
`N
`
`=
`
`2 2.5×
`
`16
`
`2
`
`2
`
`=
`
`76.3 μV
`
`ADS124S08 =
`LSB
`
`2×V
`REF
`N
`
`=
`
`2 2.5×
`
`24
`
`2
`
`2
`
`=
`
`0.298 μV
`
`(3)
`
`(4)
`
`Combining these observations, you can see that the low-
`resolution (16-bit) ADC’s noise performance as reported
`in its data sheet is equivalent to its LSB size (maximum
`quantization noise). On the other hand, the noise reported in
`the high-resolution (24-bit) ADC’s data sheet is clearly much
`larger than its LSB size (quantization noise). In this case, the
`high-resolution ADC’s quantization noise is so low that it’s
`effectively hidden by the thermal noise. Figure 6 represents
`this comparison qualitatively.
`
`Low-resolution ADCs
`
`High-resolution ADCs
`
`Thermal
`
`Quantization
`Quantization
`(a)
`(b)
`Figure 6. Qualitative representation of quantization noise and thermal
`noise in low- (a) and high-resolution (b) ADCs.
`
`Thermal
`
`Fundamentals of Precision ADC Noise Analysis
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`September 2020 I Texas Instruments
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`

`

`Chapter 1: Introduction to ADC noise
`
`How can you use this result to your advantage? For low-
`resolution ADCs where quantization noise dominates, you
`can use a smaller reference voltage to reduce the LSB size,
`which reduces the quantization noise amplitude. This has
`the effect of lowering the ADC’s total noise, represented by
`Figure 7a.
`
`For high-resolution ADCs where thermal noise dominates,
`use a larger reference voltage to increase the input range
`(dynamic range) of the ADC, while ensuring that the
`quantization noise level remains below the thermal noise.
`Assuming no other system changes, this increased reference
`voltage enables a better signal-to-noise ratio, which you can
`see in Figure 7b.
`
`Low-resolution ADCs
`
`High-resolution ADCs
`
`Thermal
`
`Quantization
`Quantization
`(a)
`(b)
`Figure 7. Adjusting quantization noise in low- (a) and high-resolution (b)
`ADCs to improve performance.
`
`Thermal
`
`Now that you understand the components of ADC noise and
`how they vary between high- and low-resolution ADCs, let’s
`build on that knowledge.
`
`Key takeaways
`
`Here is a summary of important points to better
` understand types of ADC noise:
`
`1.
`2.
`3.
`
`Noise is inherent in all
` electrical systems.
`
`Noise is introduced via all signal
`chain components.
`
`There are two main types of
`ADC noise:
`
`• Quantization noise, which scales with the
` reference voltage.
`• Thermal noise, which is a fixed value for a
`given ADC.
`
`4.
`
`One type of noise generally dominates
`depending on the ADC’s resolution:
`
`• High-resolution ADC characteristics:
`• Thermal noise-dominated.
`• The resolution is typically >1 LSB.
`• Increase the reference voltage to increase
`the dynamic range.
`• Low-resolution ADC characteristics:
`• Quantization noise-dominated.
`• The resolution is typically limited by
`LSB size.
`• Decrease the reference voltage to decrease
`the quantization noise and increase
`the resolution.
`
`Fundamentals of Precision ADC Noise Analysis
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`

`

`a range of AC input signals at multiple sample rates, but
`also the ADS127L01’s DC performance using the input-
`short test.
`
`Noise specifications in ADC data sheets
`
`If you look at the ADS127L01’s data sheet—or almost
`any ADC data sheet, for that matter—you’ll see noise
`performance reported in two forms: graphically and
`numerically. Figure 9 shows a fast Fourier transform (FFT)
`of the ADS127L01’s noise performance using an input
`sine wave with an amplitude of –0.5 dbFS and a 4-kHz
`frequency. This plot makes it possible to calculate and report
`important AC parameters such as the signal-to-noise ratio
`(SNR), total harmonic distortion (THD), signal-to-noise ratio
`and distortion (SINAD) and effective number of bits (ENOB).
`
`Signal
`
`ADS127L01
`
`Harmonics
`
`Noise floor
`
`0
`
`40
`
`80
`
`120
`160
`Frequency (kHz)
`
`200
`
`240
`
`0
`-20
`-40
`-60
`-80
`-100
`-120
`-140
`-160
`-180
`
`Amplitude (dB)
`
`fIN = 4 kHz, VIN = –0.5 dBFS, HR mode, WB2, 512 kSPS,
`32768 samples
`Figure 9. Example ADS127L01 FFT with a 4-kHz, –0.5-dBFS
`input signal.
`
`For DC performance, a noise histogram shows the
`distribution of output codes for a specific gain setting,
`filter type and sample rate. This plot makes it possible
`to calculate and report important DC noise performance
`parameters such as input-referred noise, effective resolution
`and noise-free resolution. (Note: Many engineers use the
`terms “ENOB” and “effective resolution” synonymously
`to describe an ADC’s DC performance. However, ENOB
`is purely a dynamic performance specification derived
`from SINAD and is not meant to convey DC performance.
`Throughout the rest of this e-book, I will use these terms
`accordingly. For more comprehensive parameter definitions
`and equations, see Table 2 later in this section, Section 1.2.)
`
`Chapter 1: Introduction to ADC noise
`
`1.2. ADC noise measurement methods
`and parameters
`
`Before I explain how ADC noise is measured, it’s important
`to understand that when you look at ADC data-sheet
`specifications, the goal is to characterize the ADC, not the
`system. As a result, the way that ADC manufacturers test
`ADC noise and the test system itself should demonstrate
`the capabilities of the ADC, not the limitations of the testing
`system. Therefore, using the ADC in a different system or
`under different conditions may lead to noise performance
`that varies from what the data-sheet reports.
`
`There are two methods ADC manufacturers use to
`measure ADC noise. The first method shorts the ADC’s
`inputs together to measure slight variations in output
`code as a result of thermal noise. The second method
`involves inputting a sine wave with a specific amplitude and
`frequency (such as 1 VPP at 1 kHz) and reporting how the
`ADC quantizes the sine wave. Figure 8 demonstrates these
`types of noise measurements.
`
`Power supply
`
`- +
`
`Reference
`VREF
`
`Power supply
`
`- +
`
`Reference
`VREF
`
`VCM
`
`Delta-Sigma/
`SAR ADC
`
`ADC
`
`(a)
`
`VCM
`
`Delta-Sigma/
`SAR ADC
`
`ADC
`
`(b)
`
`Figure 8. Input-short test setup (a) and sine-wave-input test setup (b).
`
`Typically, ADC manufacturers choose an individual ADC’s
`noise measurement method based on its target end
`application(s). For example, delta-sigma ADCs that measure
`slow-moving signals such as temperature or weight use the
`input-short test, which precisely measures performance at
`DC. Delta-sigma ADCs used in high-speed data-acquisition
`systems generally rely on the sine-wave-input method,
`where AC performance is critical. For many ADCs, the data
`sheet specifies both types of measurements.
`
`For example, the 24-bit ADS127L01 from TI has a high
`maximum sampling rate of 512 kSPS and a low pass-band
`ripple wideband filter, both of which enable high-resolution
`AC signal sampling for test and measurement equipment.
`However, these applications often require accurate
`measurement of the signal’s DC component as well. As a
`result, TI characterizes not only the ADC’s performance with
`
`Fundamentals of Precision ADC Noise Analysis
`
`
`
`
`
`10
`
`September 2020 I Texas Instruments
`
`

`

`In Figure 11b, the teal-shaded region depicts the peak-to-
`peak (VN,PP) noise performance of the ADC. Peak-to-peak
`noise is given as 6 or 6.6 standard deviations due to the
`crest factor of Gaussian noise, which is the ratio of the peak
`value to the average value. Peak-to-peak noise defines the
`statistical probability that the measured noise will be within
`this range. If your input signal also falls in this range, there is
`a chance that it will be obscured by the noise floor, resulting
`in code flicker. Additional oversampling will help reduce
`peak-to-peak noise at the cost of a longer sampling time.
`
`You’ll also find the aforementioned AC and DC specifications
`numerically in the electrical characteristics section of most
`ADC data sheets. An exception to this rule involves ADCs
`with integrated amplifiers, where noise performance varies
`with gain as well as data rate. In such instances, there
`is generally a separate noise table for parameters such
`as input-referred noise (RMS or peak-to-peak), effective
`resolution, noise-free resolution, ENOB and SNR.
`
`Chapter 1: Introduction to ADC noise
`
`Figure 10 shows the noise histogram for the ADS127L01.
`
`ADS127L01
`
`-3.1
`
` -2
`
` -1
`
` 0
` 1
`Voltage (μV)
`
` 2
`
`3.1
`
`4.1
`
`6500
`6000
`5500
`5000
`4500
`4000
`3500
`3000
`2500
`2000
`1500
`1000
`500
`0
`-3.9
`
`Number of occurrences
`
`Inputs shorted, HR mode, LL, 8 kSPS, 32768 samples
`
`Figure 10. Example ADS127L01 noise histogram.
`
`Like the FFT plot, the noise histogram provides important
`graphical information about DC noise performance.
`Since the noise histogram has a Gaussian distribution,
`the definition of average (root mean square [RMS]) noise
`performance is typically one standard deviation—the red-
`shaded region in Figure 11a.
`
`RMS noise
`
`Peak-to-peak noise
`
`ADS127L01
`
`-3.1
`
` -2
`
` -1
`
` 0
` 1
`Voltage (μV)
`
` 2
`
`3.1
`
`4.1
`
`(b)
`
`6500
`6000
`5500
`5000
`4500
`4000
`3500
`3000
`2500
`2000
`1500
`1000
`500
`0
`-3.9
`
`Number of occurrences
`
`ADS127L01
`
`-3.1
`
` -2
`
` -1
`
` 0
` 1
`Voltage (μV)
`(a)
`
` 2
`
`3.1
`
`4.1
`
`6500
`6000
`5500
`5000
`4500
`4000
`3500
`3000
`2500
`2000
`1500
`1000
`500
`0
`-3.9
`
`Number of occurrences
`
`Figure 11. ADS127L01 RMS (a) and peak-to-peak noise (b).
`
`Fundamentals of Precision ADC Noise Analysis
`
`
`
`11
`
`September 2020 I Texas Instruments
`
`

`

`Chapter 1: Introduction to ADC noise
`
`Table 2 summarizes AC and DC noise parameters, their definitions, the applicable noise test and equations.
`
`Noise parameter
`Input-referred noise
`
`SNR
`
`THD
`
`SINAD
`
`Ratio of the RMS value of the output signal to the RMS value of all other spectral
`components, not including DC.
`
`Input sine wave (AC)
`
`10log
`
`10
`
`(
`
`(
`
`S
`
`V
`
`Signal(RMS)
`)
`+ V
`
`V
`Harmonics
`
`Noise(RMS)
`
`Effective resolution
`
`Dynamic range figure of merit using the ratio of full-scale range (FSR) to RMS
`noise voltage to define the noise performance of an ADC.
`
`Noise-free resolution
`
`Dynamic range figure of merit using the ratio of FSR to peak-to-peak noise
`voltage to define the maximum number of bits unaffected by peak-to-peak noise.
`
`Noise-free counts
`
`ENOB
`
`Figure of merit representing the number of noise-free codes (or counts) that you
`can realize with noise.
`Figure of merit relating the SINAD performance to that of an ideal ADC’s
`resolution with a certain number of bits (given by the ENOB).
`
`DC-input (DC)
`
`DC-input (DC)
`
`DC-input (DC)
`
`Input sine wave (AC)
`
`(
`
`2 V
`
`FSR
`
`N,RMS
`
`)
`
`log
`
`(bits)
`
`FSR(
`
`V
`N,PP
`
`)
`
`log
`
`2
`
`(bits)
`
`Noise-free resolution (counts)
`)
`2 (
`
`SINAD(
`
`
`
`)–1.76dBc
`
`dB
`
`6.02
`
`(bits)
`
`If you choose a system input signal that is not referenced to
`the same full-scale voltage, or if the input signal amplitude
`varies from the value defined in the data sheet, you should
`not necessarily expect to achieve data-sheet performance,
`even if all of your other input conditions are identical.
`
`Similarly, for DC noise parameters, you can see from Table 2
`that effective resolution is relative to the ADC’s input-referred
`noise performance at the given operating conditions, as
`well as at the ADC’s FSR. Since FSR depends on the ADC’s
`reference voltage, using a reference voltage other than
`what’s listed in the data sheet has an effect on your ADC’s
`performance metrics.
`
`For high-resolution ADCs, increasing the reference voltage
`increases the maximum input dynamic range, while input-
`referred noise stays the same. That is because high-
`resolution ADC noise performance is largely independent of
`the reference voltage. For low-resolution ADCs, where noise
`is dominated by LSB size, increasing the reference voltage
`actually increases input-referred noise, while the maximum
`input dynamic range remains approximately the same.
`Table 3 on the following page summarizes these effects.
`
`Table 2. Typical ADC noise parameters with definitions and equations.
`
`Absolute vs. relative noise parameters
`An important characteristic of all of the equations in Table 2
`is that they involve some ratio of values. These are “relative
`parameters.” As the name implies, these parameters provide
`a noise performance metric relative to some absolute value,
`usually the input signal (decibels relative to carrier [dBc]) or
`the FSR (decibels relative to full scale [dBFS]).
`
`Figure 12 shows an output spectrum of the ADS127L01
`using an input signal at –0.5 dBFS, where full scale is 2.5 V.
`
`ADS127L01
`
`0
`
`40
`
`80
`
`120
`160
`Frequency (kHz)
`
`200
`
`240
`
`0
`-20
`-40
`-60
`-80
`-100
`-120
`-140
`-160
`-180
`
`Amplitude (dB)
`
`fIN = 4 kHz, VIN = –0.5 dBFS, HR mode, WB2, 512 kSPS,
`32768 samples
`Figure 12. ADS127L01 FFT, with the input voltage (VIN ) referenced to
`full scale.
`
`Fundamentals of Precision ADC Noise Analysis
`
`
`
`
`
`12
`
`September 2020 I Texas Instruments
`
`Noise test
`n/a
`
`Equation (units)
`
`Measured (V
`,V )
`RMS PP
`
`V V
`
`Signal(RMS)
`
`Noise(RMS)
`
`Input sine wave (AC)
`
`(
`
`10
`
`10log
`
`Definition
`Resolution or internal noise of the ADC (plus programmable gain amplifier [PGA]
`noise for integrated devices) specified as a noise voltage source applied to the
`ADC’s input pins (before gain).
`Ratio of the output signal amplitude to the output noise level, not including
`harmonics or DC.
`
`V S
`
`Harmonics
`
`ignal(RMS)
`
`S(
`V
`
`Indication of a circuit’s linearity in terms of its effect on the harmonic content of a
`signal, given as the ratio of the summed harmonics to the RMS signal amplitude.
`
`Input sine wave (AC)
`
`(
`
`10log
`
`10
`
`)
`
`(dBc)
`
`)
`
`)
`
`(dBc)
`
`)
`
`(dBc)
`
`

`

`However, using a 1-V reference voltage reduces the FSR
`to 2 V. You can use this 2-V value to calculate the new
`expected effective resolution (dynamic range), given by
`Equation 5:
`(
`
`FSR
`
`log
`
`2
`
`V
`Noise,RMS
`
`)
`
`= log
`
`2
`
`(
`
`2 V
`1.34×10 V
`
`–6
`
`)
`
`= 20.51 bits
`
`(5)
`
`Chapter 1: Introduction to ADC noise
`
`Reference voltage
`
`Increases
`
`Decreases
`
`Parameter
`Dynamic range
`
`Input-referred noise
`Dynamic range
`Input-referred noise
`
`Low-resolution
`ADCs
`Stays the same
`
`Increases
`Stays the same
`Decreases
`
`High-resolution
`ADCs
`Increases
`
`Stays the same
`Decreases
`Stays the same
`
`Table 3. Effect of changing reference voltage on ADC noise parameters.
`
`Therefore, to characterize an ADC’s maximum dynamic
`range, most ADC manufacturers specify effective resolution
`and noise-free resolution, using the assumption that the FSR
`is maximized. Or, in other words, if your system does not
`use the maximum FSR (or whatever FSR the manufacturer
`used to characterize the ADC), you should not expect to
`achieve the effective or noise-free resolution values specified
`in the data sheet.
`
`Let’s illustrate this point by using a 1-V reference voltage
`with an ADC whose data-sheet noise is characterized with a
`reference voltage of 2.5 V. Continuing with the ADS127L01
`as an example, Table 4 shows that using a 2.5-V reference
`voltage and a 2-kSPS data rate in very low power mode
`results in 1.34 μVRMS of input-referred noise and an effective
`resolution of 21.83 bits.
`
`Mode
`
`High resolution (HR)
`
`Low power (LP)
`
`Very-low power
`(VLP)
`
`Data rate
`(SPS)
`512,000
`
`128,000
`32,000
`8,000
`256,000
`64,000
`16,000
`4,000
`128,000
`32,000
`8,000
`2,000
`
`VRMS_noise
`(μVRMS)
`7.40
`
`5.12
`2.74
`1.41
`7.22
`4.97
`2.65
`1.37
`6.97
`4.80
`2.57
`1.34
`
`ENOB
`19.37
`
`19.90
`20.80
`21.76
`19.40
`19.94
`20.85
`21.80
`19.45
`19.99
`20.89
`21.83
`
`Table 4. ADS127L01 noise performance: low-latency filter, AVDD = 3V,
`DVDD = 1.8 V and VREF = 2.5 V.
`
`Changing the reference voltage reduces the ADC’s FSR,
`which in turn reduces its effective resolution (dynamic range)
`compared to the data-sheet value by more than 1.3 bits.
`Equation 6 generalizes this loss of resolution:
`
`resolution (dynamic
`range) loss
`
`= log (%
`
`utilization
`
`) = log
`
`2
`
`2
`
`(
`
`2 V
`V5
`
`)
`
`= –1.32 bits
`
`(6)
`
`where % utilization is simply the ratio of the actual FSR to
`the FSR at which the ADC’s noise is characterized.
`
`While this apparent resolution loss may seem like a
`drawback to using high-resolution delta-sigma ADCs, recall
`that while the FSR is decreasing, the input-referred noise
`is not. Therefore, I suggest performing ADC noise analysis
`using an absolute noise parameter, or one that is measured
`directly. Using an absolute noise parameter eliminates the
`dependence on the input signal and reference voltage
`characteristic of relative noise parameters. Additionally,
`absolute parameters simplify the relationship between ADC
`noise and system noise.
`
`For ADC noise analysis, I recommend using input-
`referred noise. I’ve bolded this phrase because it’s not
`common practice to use input-referred noise to define
`ADC performance. In fact, a majority of en