Freescale Semiconductor
Application Note
AN2438/D
2/2003
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ADC Definitions
and Specifications
By: J. Feddeler and Bill Lucas
8/16 Bit Division Systems Engineering
Austin, Texas
Introduction
This application note will help users of analog-to-digital converters (ADC)
understand common terminologies used in the electronics industry to define
ADC operation and performance. There are many terms and parameters used
to define the performance of ADC’s. Included in this document are common
definitions, numerical specifications, differences, and issues with the
definitions. By understanding the terminology used to specify various ADC
parameters, a systems designer can better understand how to obtain the
greatest overall system performance, based on the various performance
features of any given ADC system.
Terms and Definitions
The following terms are used in the electronics industry to define ADC
operation.
Measurement Units
There are several terms commonly used to measure ADC performance.
Improper or inconsistent use of terms may result in confusion and or
misinterpretation of performance. Common measurement units in use in the
industry are described here (The following examples assume a 10-bit, 5.12-V
ADC with an ideal 2.56-V conversion at $200):
•
Volts (V) — The error voltage is the difference between the input voltage
that converts to a given code and the ideal input voltage for the same
code. When the error is measured in volts, it is related to the actual
voltages and is not normalized to or dependent on the input range or
voltage supply. This measure is useful for fixed error sources such as
offset but does not relate well to the observed error.
•
Least Significant Bits (LSB) — A least significant bit (LSB) is a unit of
voltage equal to the smallest resolution of the ADC. This unit of measure
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approximately relates the error voltage to the observed error in
conversion (code error), and is useful for systemic errors such as
differential non-linearity. A 2.56-V input on an ADC with ± 3 LSB of error
could read between $1FD and $203. This unit is by far the most common
terminology and will be the preferred unit used for error representation.
•
Percent Full-Scale Value (%FSV) — Percent full-scale voltage is a unit
of voltage equal to 1/100th of the input range of the ADC. This unit of
error clarifies the size of the error relative to the input range, and is useful
for trimmable errors such as offset or gain errors. This unit is difficult to
accurately translate to observed error.
•
Counts — A count is a unit of voltage equal to an LSB. It is a terminology
unique to specifications of some Freescale ADC’s and may be confusing
to customers when doing cross-vendor comparisons.
•
Bits — A bit is a unit equal to the log (base2) of the error voltage
normalized to the resolution of the ADC. An error of N bits corresponds
to 2N LSB of error. This measure is easily confused with LSB and is hard
to extrapolate between integer values.
•
Decibels (db) — A decibel is a unit equal to 20 times the log (base10)
of the error voltage normalized to the full-scale value
(20*log(err_volts/input_range)). A 2.56 input on an ADC with an error of
50 db will convert between $1FD and $203. This figure is often used in
the communications field and is infrequently used in control or
monitoring applications.
ADC Transfer
Curves
The ADC converts an input voltage to a corresponding digital code. The curve
describing this behavior is the Actual Transfer Function. The Ideal Transfer
Function represents this behavior assuming the ADC is perfectly linear, or that
a given change in input voltage will create the same change in conversion code
regardless of the input’s initial level. The Adjusted Transfer Function assumes
this behavior after the errors at the endpoint are accounted for.
Ideal Transfer
Function
The Ideal Straight-Line Transfer Function of an ADC is a straight line from the
minimum input voltage (voltage reference low; VREFL) to the maximum input
voltage (voltage reference high; VREFH). The Ideal Transfer Function is then
quantized (divided into steps) by the number of codes the ADC is capable of
resolving. The input voltage range is divided into steps, each step having the
same width.
This Ideal Code Width (ICW) — also known as 1LSB — is:
ICW = 1LSB = (VREFH – VREFL)/2N
Where:
N is the “width” of the ADC, in our examples, 10 bits.
The Ideal Transfer Function is then:
Code = (VIN – VREFL) / 1LSBVIN = (Code*1LSB) + VREFL
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Quantization Error (EQ) and Method
Quantization Error (EQ) and Method
The way the Ideal transfer function is divided into steps depends on the method
of quantization the ADC uses. The two possible methods are:
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1. Uncompensated Quantization — The first step is taken at 1LSB, with
each successive step taken at 1LSB intervals and the last step taken at
VREFH – 1LSB. The Quantization Error (EQ) in this case is from 0LSB to
1LSB.
2. ½LSB Compensated Quantization – The first step is taken at 1⁄2LSB,
with each successive step taken at 1LSB intervals and the last step
taken at VREFH – 11⁄2LSB. The Quantization Error (EQ) in this case is
±1⁄2LSB.
Ideal Straight-Line TF
Conversion
Uncompensated Ideal TF
Conversion Quantization
½LSB Compensated Ideal TF
Conversion Quantization
$7
$7
$7
$6
Ideal Straight-Line
Transfer Function
$6
$5
$5
$4
$4
$3
$3
$2
$2
$1
$1
$0
VREFL 1
2
3
4
5
6
7V
REFH
Input Voltage in LSB
Error
(0 to 1LSB)
$6
Ideal Code
Width
(1LSB)
$5
Ideal Transfer
Function
$0
VREFL 1
2
3
4
5
6
7V
REFH
Error
(±½LSB)
Ideal Code
Width
(1LSB)
$2
Ideal Transfer
Function
$1
$0
VREFL 1
Input Voltage in LSB
2
3
4
5
6
7V
REFH
Input Voltage in LSB
Figure 1. Quantization Graphs
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Adjusted Transfer Function
½LSB Comp. Adjusted TF
Conversion
$7
$6
(-) Full-Scale Error
Adjusted
Code Width
$5
Adjusted Transfer
Function (Dashed)
$4
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$3
Adjusted StraightLine Transfer
Function (Solid)
$2
$1
Zero-Scale Error
4
5
6
7V
REFH
Most ADC’s exhibit some non-linearity at
the endpoints due to the difficulty in
measuring a signal that is identical to the
reference. If these errors are accounted
for, a more accurate portrayal of the ADC
behavior in application is possible. For
this reason, the Adjusted Straight-Line
Transfer Function is drawn between the
minimum input voltage plus the ZeroScale Error (VREFL + EZS) to the
maximum input voltage plus the FullScale Error (VREFH + EFS).
Input Voltage in LSB
The Adjusted Transfer Function is then quantized in the same method as the
Ideal Transfer Function. The Adjusted Code Width is therefore:
ACW = [(VREFH + EFS) – (VREFL + EZS)] / 2N
The Adjusted Transfer Function is then:
Code = (VIN – VREFL – EZS) / ACW VIN = (Code*ACW) + VREFL + EZS
Best-Fit Transfer Function
Some ADC’s exhibit low Zero- and Full-Scale
Errors but still have significant non-linearities.
(+) Best-Fit EFS
Conversion
In cases where these linearities tend to be in
Actual Transfer
$7
one direction (for example, a significantly
Function (Double)
$6
“bowed” function) the best application results
Best-Fit
Best-Fit
$5
Code Width
Transfer may be obtained if the errors are compared to
Function a Best-Fit Transfer Function. The Best-Fit
$4
(Dashed)
Straight-Line Transfer Function is the line from
$3
which the average deviation of all conversions
Best-Fit Straight
$2
Line Transfer
is minimum. Computing this function requires
$1
Function (Solid)
that the entire Actual Transfer Function be
4 5 6 7V
recorded, which is impractical in most
REFH
Best-Fit EZS
applications. Therefore, any performance
Input Voltage in LSB
parameters calculated against the Best-Fit
Transfer Function are not useful to the user. Unfortunately, many automatic
evaluation packages (software and hardware) assume this type of curve.
½LSB Comp. Best-Fit TF
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Zero-Scale Error and Full-Scale Error
Zero-Scale Error and Full-Scale Error
The non-linearities at the endpoints are considered special cases due to the
ease with which they are measured and corrected. The non-linearity at the
beginning of the Actual Transfer Function is called the Zero-Scale Error (EZS)
and the non-linearity at the top end of the function is called Full-Scale Error
(EFS). The Zero- and Full-Scale Errors have the following definitions:
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•
NOTE:
Zero-Scale Error (EZS) is the difference between actual first transition
voltage and the ideal first transition voltage (if the first transition is not
from $000 to $001, then use the difference between the actual and ideal
$001–$002 transition voltages, and so on).
The Ideal Code Width for the zero code is ½LSB for ADC’s with ½LSB
compensated quantization.
Representing this error is by code widths:
EZS = CCW(0) – ICW(0)
Or, in the case where the first “x” codes are missing,
EZS = CCW(x) – sum(i=0→x)[ICW(i)]
•
NOTE:
Full-Scale Error (EFS) is the difference between the actual last
transition voltage and the ideal last transition voltage (if the last transition
is not from $3FE to $3FF, then use the difference between the actual
and ideal $3FD–$3FE transition voltages, and so on).
The Ideal Code Width for the last code is 1½LSB for ADC’s with ½LSB
compensated quantization.
Representing this error by code widths:
EFS = CCW(last) – ICW(last)
Or, in the case where the last “x” codes are missing,
EFS = CCW(last-x) – sum(i=x→last)[ICW(i)]
Zero- and Full-Scale Error
Conversion
(-) Full-Scale Error
Offset and Gain Error
$7
$7
$6
$6
$5
Ideal Transfer
Function
$5
$4
$4
$3
$3
$2
Adjusted Transfer
Function
$1
(+) Zero-Scale Error
4
5
6
(+) Gain Error
Conversion
Adjusted
Straight-Line
Trans Func.
$2
Ideal S.L. Transfer
Function Plus Offset
$1
7V
REFH
Input Voltage in LSB
(+) Offset Error
4
5
6
7V
REFH
Input Voltage in LSB
Figure 2. Endpoints Error Graph
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Offset and Gain Error
Zero-Scale Errors and Full-Scale Errors can be used to calculate Offset and
Gain Errors. These terms are used to define the performance on many
industry-standard ADC’s but the definitions used vary and can be misleading
or inconsistent.
• Offset Error (EO), Adjusted Offset, or Zero-Scale Offset is the
difference between the actual and ideal first transition voltages. This is
the same definition as Zero-Scale Error. The term offset; however,
implies that all conversions are off by an equal amount. In the case of a
strong non-linearity near the Zero-Scale Value, this definition may be
misleading, and the less ambiguous Zero-Scale Error term is preferable.
• Best-Fit Offset is the difference between the Best-Fit Straight-Line
Transfer Function and the Ideal Straight-Line Transfer Function at
VREFL. Some definitions define the offset point at the center-conversion
((VREFH – VREFL) /2) instead of at VREFL. This offset is virtually
impossible to measure in the application and is therefore only a
laboratory curiosity. Since this yields optimistic results and is not
measurable in the application, it can be misleading and will not be used.
• Full-Scale Offset is the difference between the actual and ideal last
transition voltages. This is the same definition as Full-Scale Error, and is
misleading for the same reason that Offset is misleading with respect to
Zero-Scale Error.
• Gain Error (EG) or Adjusted Gain Error is the difference in the slope
of the Actual and the Ideal Straight-Line Transfer Functions. The error is
not measured as a slope but rather as the difference in the total available
input range from the first to the last conversions between the Ideal and
Adjusted Straight-Line Transfer Functions. It is can also be expressed
by:
EG = EZS – EFS
Gain Error is not directly measurable and the term has been
inconsistently defined in the literature. Additionally, if there are strong
non-linearities at the endpoints, this definition of Gain Error may be
misleading, so the less ambiguous Full-Scale Error term is preferred
provided a simple gain calculation (above) is possible.
• Best-Fit Gain Error is the difference in the slope of the Best-Fit and
Ideal Straight-Line Transfer Functions. The error is not measured as a
slope but rather as the difference in the total available input range from
the first to the last conversions between the Ideal and Best-Fit StraightLine Transfer Functions. Since the Best-Fit Straight-Line Transfer
Function will result in an optimistic Gain Error and is virtually impossible
to measure in the application, it can be misleading and will not be used.
Consistency with previous Freescale documents can be achieved by replacing
references to Offset Error with Zero-Scale Error and Gain Error with the
difference between of Zero Scale Errors and Full-Scale Errors.
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Differential Non-Linearity (DNL)
Differential Non-Linearity (DNL)
Differential Non-Linearity (DNL) is the maximum of the differences in the each
conversion’s Current Code Width (CCW) and the Ideal Code Width (ICW). DNL
is the most critical of the measures of an ADC’s performance for many control
applications since it represents the ADC’s ability to relate a small change in
input voltage to the correct change in code conversion. DNL is defined as:
Code DNL = CCW – ICW
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DNL = Max (Code DNL)
Some literature defines DNL using the Adjusted Code Width (ACW), which
means Zero- and Full-Scale Error have been adjusted for. For relatively
accurate ADC’s, the difference with respect to DNL is negligible, but using the
ACW complicates defining and testing DNL. Additionally, this definition is only
valid if the application has trim capability.
Differential Non-Linearity
Conversion
Missing Code
Conversion
Non-Monotonicity
Conversion
$7
$7
$7
DNL = +0.25
$6
$5
$6
DNL = 0.0
$5
$4
$4
$3
$3
$2
$2
$1
$1
DNL = -0.25
$0
VREFL 1
2
3
4
5
6
7V
REFH
Input Voltage in LSB
$6
DNL = -1.0
$5
DNL = +1.5
$4
$3
Code $3 is
missing
$2
Code $2 is
converted after $3
$1
$0
VREFL 1
2
3
4
5
6
7V
REFH
$0
VREFL 1
Input Voltage in LSB
2
3
4
5
6
7V
REFH
Input Voltage in LSB
Figure 3. Differential Non-Linearity, Missing Codes, and Non-Monotonicity Graphs
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Related to DNL are two critical figures of merit used in defining ADC operation.
These are:
•
Missing Codes — An ADC has missing codes if an infinitesimally small
change in voltage causes a change in result of two codes, with the
intermediate code never being set. A DNL of –1.0 LSB indicates the
ADC has missing codes (DNL measured by this definition cannot be less
than –1.0 LSB).
•
Monotonicity — An ADC is monotonic if it continually increases
conversion result with an increasing voltage (and vice versa). A nonmonotonic ADC may give a lower conversion result for a higher input
voltage, which may also mean that the same conversion may result from
two separate voltage ranges. Often, the transfer function will completely
miss the lower code until after the higher code is converted (on an
increasing input voltage).
Some literature suggests that a DNL of greater than 1.0 LSB may indicate nonmonotonicity. Non-monotonicity is usually accompanied by large, positive DNL
(>1.0 LSB), although a non-monotonic situation can be coincident with a DNL
of less than 1.0 LSB.
Integral Non-Linearity (INL)
Integral Non-Linearity
Conversion
$7
$6
$5
$4
Adjusted Transfer
Function (Dashed)
Ideal Transfer
Function (dotted)
INL = 0.0
$3
$2
INL = +0.50
$1
INL = +0.25
$0
VREFL 1
2
3
4
5
6
Integral Non-Linearity (INL) is defined as the
sum from the first to the current conversion
(integral) of the non-linearity at each code
(Code DNL). For example, if the sum of the
DNL up to a particular point is 1LSB, it means
the total of the code widths to that point is
1LSB greater than the sum of the ideal code
widths. Therefore, the current point will
convert one code lower than the ideal
conversion.
7V
REFH
In more fundamental terms, INL represents
the curvature in the Actual Transfer Function
relative to a baseline transfer function, or the
difference between the current and the ideal transition voltages. There are
three primary definitions of INL in common use. They all have the same
fundamental definition except they are measured against different transfer
functions. This fundamental definition is:
Input Voltage in LSB
Code INL = V(Current Transition) – V(Baseline Transition)
INL = Max(Code INL)
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Integral Non-Linearity (INL)
The three primary definitions are:
1. INL, Adjusted INL, or Endpoint INL — The current transition voltage is
compared to the corresponding transition voltage on the Adjusted
Transfer Function. This is a useful indicator of the best the ADC can do
if the endpoint non-linearities (Zero- and Full-Scale Errors) are
measured and trimmed out.
2. Unadjusted INL — The current transition voltage is compared to the
corresponding transition voltage on the Ideal Transfer Function. This is
a measure of the total error except for Quantization Error.
3. Best-Fit INL — The current transition voltage is compared to the
corresponding transition voltage on the Best-Fit Transfer Function. This
will usually give a balanced positive and negative error across the entire
curve so the results look very optimistic, but since it is difficult to obtain
the Best-Fit Transfer Function in application, it is not a very useful
measure. Unfortunately, this is what many evaluation packages
(hardware and software) measure.
Total Unadjusted Error
ETUE = -1.5
Conversion
Code Error
Conversion
$7
$7
$6
$6
$5
$5
$4
$4
$3
$3
$2
Ideal Straight Line
Transfer Function
$1
ETUE = 1.75
4
5
6
7V
REFH
Input Voltage in LSB
Code Error
= $1 or $2
Ideal
Transfer
Function
$2
$1
Code Error = $2
VREFL 1
2
3
4
5
6
7V
REFH
Input Voltage in LSB
Figure 4. Total Unadjusted and Code Error Graphs
There are some related definitions to Total Unadjusted Error that vary slightly
in definition. These are:
• Total Error is the same as Total Unadjusted Error, but the term is
misused in several ADC references and is therefore misleading. The
less ambiguous term Total Unadjusted Error is preferred.
• Total Adjusted Error is the difference between the Actual and Adjusted
Straight-Line Transfer Function, accounting for INL plus Quantization
Error. This term is redundant and potentially confusing with respect to
Total Unadjusted Error and will not be used.
• Code Error is the error between the ideal code and the current code.
This is the only figure of merit that measures by the quantized output
instead of voltage. The code error is the Total Unadjusted in LSB,
rounded to the nearest integer.
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Power Supply Noise Error
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Power Supply Noise Error (ENS) is the difference in conversion caused by
power supply noise (on the VDDAD; ADC power or VSSAD; ADC ground pins).
Power Supply Noise Errors are caused by:
•
Comparator Power Supply Rejection Ratio (PSRR) — This ratio
defines the ability of the comparator to reject power supply noise
(relative to the inputs) when making a differential comparison between
the inputs. PSRR is commonly measured in decibels (db). A comparator
with a PSRR of 60 db will interpret 1-V power supply noise the same as
1 mV of differential input voltage.
•
Power Supply Decoupling Ratio (PSDR) — This ratio defines how
much of the power supply noise is coupled onto the inputs (either
reference or input). A decoupling ratio of 24 db indicates that 16 mV of
power supply noise will cause 1 mV of input or reference noise.
•
Differential Power Supply Decoupling Ratio (DPSDR) — This ratio
defines how much of the power supply noise is coupled onto the
differential between the inputs. The most common way of reducing
Power Supply Noise Error is by decoupling the reference and input
equally (since it is impossible to reduce coupling altogether). A
differential decoupling ratio of 30 db means that 32 mV of power supply
noise will be interpreted as 1 mV of differential input noise.
Power Supply Noise Error is ultimately inherent in any ADC design. It is
reduced in the design phase by the use of differential, cascaded circuits
(increases PSRR), reducing parasitics (increase PSDR), and matching
parasitics on the input and reference paths (increases DPSDR). However,
these techniques are not perfect. The end user can apply the following
techniques to reduce Power Supply Noise Error:
•
Analog Power Supply Bypassing — The ADC power supply must be
bypassed to its ground as close to the MCU pins as possible. The
preferred method is with a high-frequency capacitor (0.01 µF or 0.1 µF)
near the MCU and a larger capacitor near the power supply’s source.
Resistive impedance must be minimum, and chokes should never be
used.
•
Digital Power Supply Bypassing — The input channel for the ADC
often is selected on a multi-purpose I/O pin. In this case, there is
considerable coupling to the digital power supply. Additionally, most
ADC’s integrated into microcontrollers are built on the same silicon
substrate as the digital circuits, which means ground noise will be
coupled. For these reasons, the same bypassing techniques are
recommended for the digital power supplies as the analog supplies.
•
Elimination of Noise Sources — The best way to eliminate Power
Supply Noise Error is to eliminate Power Supply Noise. Critical ADC
conversions must be conducted when the rest of the system is as quiet
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Input to Reference Differential Noise Error
as possible. Most importantly, no Output Drivers on the microcontroller
should be activated during the ADC conversion. The preferred mode for
ADC conversions is in WAIT mode.
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Input to Reference Differential Noise Error
Input to Reference Differential Noise Error, or Input Noise Error (ENIN), is the
error due to noise, or short-term deviation from the DC-average, on the input
(VIN) or either reference (VREFH or VREFL) relative to the other. Input Noise
Error is caused by:
• Reference Coupling Ratio — This defines the amount of noise that is
injected onto one reference (i.e., VREFH) that will be coupled onto the
other reference (i.e., VREFL). The higher the coupling ratio, the closer the
references are to each other. If the coupling ratio is low, then between
half and all of this noise will be differential to the input signal, depending
on which reference the input is more closely coupled to and which
reference the input voltage is closer to. The external (board-level)
network of capacitors and parasitic impedances connected between the
references and noise sources usually defines this ratio.
• Differential Coupling Ratio — This defines the amount of noise that is
injected onto either the input or either reference that will be coupled onto
the other. The higher the coupling ratio, the less differential noise will be
seen between the input and the reference. This ratio primarily depends
on the decoupling or filtering method that is used on the input.
• Input Coupling Ratio — This defines the amount of noise that is
generated from a given noise source that is injected onto the input or
reference. This depends on the layout and parasitics on the external
board as well as the internal circuit.
• EMC — Conducted or Radiated noise can be picked up by the input or
reference signals even in otherwise good printed circuit board layouts.
This pick-up is usually dependent on the impedance of the input or
reference source. It commonly affects the input more than the reference
since the reference is usually much lower impedance.
Input to Reference Differential Noise is primarily externally controllable through
good PC board layout and decoupling. Internally, shielding and isolation from
switching signals and clock feed-through reduction techniques are usually
employed to reduce internal sources. External methods of reducing Input Noise
include:
• Reference Bypassing — The high and low references (VREFH and
VREFL) should be bypassed to each other similar to the method used on
VDDAD and VSSAD (high-frequency capacitor near pins, low frequency
capacitor near source, low resistive impedance and no choke). This
increases the Reference Coupling Ratio, reducing differential noise.
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•
•
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•
Input Bypassing — Placement of a capacitor from the input to the
reference increases the Differential Coupling Ratio, reducing the
amount of differential noise. The size of the capacitor should be as large
as possible, allowing for the required dV/dt of the input given the analog
source impedance and the function of the signal.
Star Routing — The references and analog power supplies should be
star-routed so that all loads see an equal impedance to the source, and
there is little coupling from one load to another that is not common to all
loads.
Input Shielding — Placing shields (preferably a double shield using first
one of the references and then VSSAD) between the inputs and all other
signals (including supplies) can increase differential coupling and
reduce input coupling. This also reduces EMC issues.
Noise Error Mechanism
Regardless of the type of noise (Power Supply Noise or Input to Reference
Differential Noise), the error mechanism is the same. While the DC-average of
most noise is zero (primarily due to the power supply which sources the
reference or input), the short-term average is non-zero as shown in Figure 5.
The amount of error depends on the magnitude and decay rate of the noise
relative to the width of the sample or compare window.
Input Noise
Noise Error
Long-term DC-average
Running DC-average
Sample/Compare Window
Figure 5. Noise Error Graph
Figure 5 is a simplification of the true mechanism meant for illustrative
purposes. In reality, phase error due to parasitic impedances in the noisecoupling path, analog source impedance, and the gain and slew rate of the
comparator will tend to shift the sensitivity either towards the beginning of the
sample/compare window (in the cases of phase shift and comparator gain) or
end of the sample window (in the case of analog source impedance). The
general mechanism is the same in all cases.
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Synchronous Noise Offset Error
Synchronous Noise Offset Error
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The worst particular type of noise with regards to ADC performance is
synchronous noise, or noise that occurs with the same signature at the same
relative time in the ADC conversion process on repetitive conversions. One
common example of such noise is the microcontroller’s bus clock noise, if the
ADC is synchronous to the bus. Other examples include I/O drivers controlling
other board-level functions that in turn control the analog input.
In the case of synchronous noise, the same noise error, see Figure 5, occurs
with each conversion. This can appear to be an offset error, instead of the
variable errors typically associated with noise. In some cases, this could
appear as a gain error, if the noise coupling is dependent on the voltage
difference between the input and one of the supplies or references.
Changing the ADC conversion time relative to the synchronous noise can
reduce Synchronous Noise Offset (after all other noise reduction techniques
have been used). This is most practical if the noise source is low frequency. If
the noise source is the microcontroller bus clock (or based thereupon) and the
ADC is synchronous to the bus, the only option is to operate in Wait mode.
Reducing Random Noise Error
Random noise has the same signature as shown above, but has a random
timing relationship with respect to the ADC conversion process. Noise of this
type includes single events (very slow switching signals), EMC events, line
noise, and white noise. A similar form of noise includes asynchronous noise,
such as communication devices running asynchronous to the ADC clock such
as SPI’s. The magnitude of the noise error (as described in Figure 5) of this
type must have a uniform distribution across ADC samples (either truly random
or white) or it is at least partially synchronous.
Random noise can be divided into the following types relative to the ADC
conversion cycle (the entire cycle must be considered, not just the individual
sample/compare windows):
• Single Event, Returns to Zero in Less than 1 Conversion Cycle —
Since the noise error on subsequent conversions is 0LSB, the effective
noise error can be reduced to less than 1⁄4LSB by sampling four times for
every 1LSB of noise error. This is the type of noise expected from
occasional I/O switching or other low-frequency switching events.
• Single Event, Returns to Zero in X Conversion Cycles — For an
unknown return-to-zero waveform to be reduced to 1⁄4LSB, the input
must be sampled 4*X times for every 1LSB of noise error. If the
waveform is predictable, the maximum noise error (therefore, the
number of cycles required to average it out) can be reduced. This type
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•
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•
of noise includes line noise and DC-bias shifts due to regulator load
changes, display drivers, etc.
High Frequency Events (Random Frequency) — Random Frequency
noise that is at more than 1⁄4 the ADC conversion cycle frequency can be
averaged out in the same manner as low frequency nose (four samples
for every 1LSB of noise for 1⁄4LSB error). White noise and other
background noise are of this type.
High Frequency Event (Single Frequency) — Any single-frequency
noise at higher than 1⁄4 the ADC conversion cycle frequency will beat with
the ADC frequency, causing aliasing to occur at the beat frequency.
Removing this aliasing error requires that four samples (for every 1LSB
of noise) be taken at uniform intervals of at least twice the beat
frequency. Higher levels of over-sampling may be necessary if the beat
frequency is not known precisely. This type of noise, which includes
asynchronous clock switching or higher frequency communication
devices such as CAN, does not fit the uniform-distribution requirement
necessary for accurate noise reduction.
Input Leakage Offset Error (EINO)
There is an additional source of input error that is often overlooked but can be
extremely significant. Leakage on the Analog input pin or on the PC board can
cause a voltage drop across the resistive portion of the Analog Input Source.
Many circuits (especially battery voltage and temperature detection circuits)
use high value resistive voltage dividers to create the analog reference.
Usually, a capacitor is placed on the input so the Analog AC Source Impedance
(ZAIN) is reduced so the ADC will be able to acquire the signal properly.
However, the Analog DC Source Resistance (RAIN) is still potentially very high
(perhaps 100 kΩ).
Leakage on the analog inputs (IIN) is usually specified at a maximum of 1 µA.
Typical numbers vary from 5 nA (older process at room temperature) to 500 nA
(newer process at hot temperature). This leakage on all processes increases
exponentially with temperature. Added to this is PC board resistance (RB),
which can be as low as 1 MΩ but is usually around 10 MΩ. Given this, the Input
Leakage Offset Error is:
EINO = (IIN + VIN/RB)*RAIN / 1LSB
This error can be on the order of 10’s of LSB if the Analog DC Source
Resistance is high (example, 1 µA*100k/2.5 mV = 40 LSB). There is no way of
perfectly trimming this error especially since it is temperature dependent. The
user can set up a parallel input with the same Analog Source Impedance and
similar, but fixed, VIN to get a rough idea of the error, but since the input leakage
is variable from pad to pad this method will not be perfect.
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Acquisition Error (EAQ)
The best way to eliminate this error is to reduce the Analog DC Source
Resistance and any form of leakage within the customer’s control (PC Board
leakage). An active circuit (op-amp) that buffers the Input Voltage (VIN) can
reduce Analog DC Source Resistance, but the problem may just shift to the
input of the active circuit.
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Acquisition Error (EAQ)
Acquisition Error is the error due to the inability of the acquisition circuits to fully
charge the input of the ADC in the time allotted. The Acquisition Error will
depend on the type of acquisition circuit the ADC uses:
• Fixed Acquisition Time Sample and Hold Acquisition — This type of
circuit opens the input of the ADC to the Analog Input for a fixed period
of time, usually some number of conversion clock cycles. In these cases,
the Analog AC Source Impedance is critical since it will have to be less
than a specified amount in order for the input to charge in the given time.
Many ADC’s from Freescale use this architecture.
• Fixed Acquisition Time Sample and Hold with Buffered Input
Acquisition — This type of circuit is similar to the Fixed Acquisition
Time architecture only for the first few cycles of the acquisition period,
an op-amp buffers the input so that the ADC charges much faster.
During the last few cycles of the acquisition period, the buffer is disabled
and the Analog Input Source charges the ADC input the rest of the way.
This architecture is nominally faster than the other for a given source
impedance, but if the offset in the op-amp is high then the total charge
time (from the input-offset voltage to the correct input voltage) may still
be dependant on the AC source impedance. Most remaining Freescale
ADC’s use this architecture.
• Variable Acquisition Time Sample and Hold Acquisition — This type
of circuit uses a variable period — either software controlled or
controlled through a programmable timer — for the acquisition phase. In
this manner, high Analog Source Impedance can be compatible with the
ADC, at the expense of acquisition time. Since the time is variable, then
in cases where there is low Analog Source Impedance the acquisition
time can be as fast as possible. Many competitors use this form of
acquisition.
• Continuous Acquisition — This type of circuit continually applies the
input voltage to the ADC’s comparator input. Few 10b ADC architectures
are compatible with this method (full-RDAC SAR architectures can use
this type of acquisition but are usually limited to about 7b of accuracy).
The Acquisition Error is related to the difference between the required
Acquisition time and the allowed acquisition time.
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Acquisition Time (Sample and Hold) and Error Calculations
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A number of steps are required during an analog-to-digital conversion. When
an analog-to-digital conversion begins, one channel select switch is closed,
allowing the sample and hold capacitor (CAIN) to charge. The channel select
switch is then opened. The charge applied to the sample and hold capacitor is
then converted into a digital representation by the successive approximation
register. A conversion complete flag will be set and an optional interrupt can be
generated.
RAS
INPUT PIN
VAIN
+
—
CAS
INPUT PIN
INPUT PIN
CHANNEL
SELECT 0
RAIN2
CHANNEL
SELECT 1
RAIN3
.
..
INPUT PIN
ATD SAR
ENGINE
RAIN1
CHANNEL
SELECT 2
RAINn
CHANNEL
SELECT n
CAIN
Figure 6. Resistor and Capacitor Placement
Proper sampling is dependent on the following factors:
•
Analog Source Impedance — This is the resistive (or real, in the case
of high frequencies) portion of the network driving the analog input
voltage VAIN.
•
Analog Source Capacitance (CAS) — This is the filtering capacitance
on the analog input, which (if large enough) may help the analog source
network charge the ATD input in the case of high RAS.
•
ATD Input Resistance (RAIN) — This is the internal resistance of the
ATD circuit in the path between the external ATD input and the ATD
sample and hold circuit. This resistance varies with temperature,
voltage, and process variation but a worst case number is necessary to
compute worst case sample error.
•
ATD Input Capacitance (CAIN) — This is the internal capacitance of the
ATD sample and hold circuit. This capacitance varies with temperature,
voltage, and process variation but a worst case number is necessary to
compute worst case sample error.
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Acquisition Time (Sample and Hold) and Error Calculations
•
ATD Conversion Clock Frequency (fATDCLK) — This is the frequency
of the clock input to the ATD. It clocks the counter for the successive
approximation register and times the sample and hold and conversion
sequencing. This clock is normally driven from the MCU’s bus clock and
may employ a clock prescaler. This frequency will determine the width
of the sample window and the time for the conversion. In these
examples, we will use 14 ATDCLK cycles for the total conversion.
•
Input Sample Frequency (fSAMP) — This is the frequency that a given
input channel is sampled.
•
Delta-Input Sample Voltage (∆VSAMP) — This is the difference
between the current input voltage (intended for conversion) and the
previously sampled voltage (which may be from a different channel).
•
Delta-Analog Input Voltage (∆VAIN) — This is the difference between
the current input voltage and the input voltage during the last conversion
on a given channel.
In cases where there is no external filtering capacitance (CAS), the sampling
error is determined by the number of time constants of charging and the change
in input voltage relative to the resolution of the ATD:
# of time constants (τ) = (14 / fATDCLK) / ((RAS + RAIN) * CAIN)
sampling error in LSB (ES) = 2N * (∆VSAMP / (VREFH – VREFL)) * e−τ
The maximum sampling error (assuming maximum change on the input
voltage) will be:
ES = (3.6/3.6) * e–(14/((7 k + 10 k) * 50 p * 2 M)) * 1024 = 0.271 LSB
In the case where an external filtering capacitance is applied, the sampling
error can be reduced based on the size of the source capacitor (CAS) relative
to the analog input capacitance (CAIN). Ignoring the analog source impedance
(RAS), CAS will charge CAIN to a value of:
ES = 2N * (∆VSAMP / (VREFH – VREFL)) * (CAIN / (CAIN + CAS))
In the case of a 0.1 µF CAS, a worst case sampling error of 0.5 LSB is achieved
regardless of RAS. However, in the case of repeated conversions at a rate of
fSAMP, RAS must re-charge CAS. This recharge is continuous and controlled
only by RAS (not RAIN), and reduces the overall sampling error to:
ES = 2N * {(∆VAIN / (VREFH – VREFL)) * e−(1 / (fSAMP * RAS * CAS )
+ (∆VSAMP / (VREFH – VREFL)) * Min[(CAIN / (CAIN + CAS)),
e−(1 / (fATDCLK * (RAS + RAIN) * CAIN )]}
This is a worst case sampling error which does not account for RAS recharging
the combination of CAS and CAIN during the sample window. It does illustrate
that high values of RAS (>10 kΩ) are possible if a large CAS is used and
sufficient time to recharge CAS is provided between samples. In order to
achieve accuracy specified under the worst case conditions of maximum
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∆VSAMP and minimum CAS, RAS must be less than the maximum value of
10 kΩ. The maximum value of 10 kΩ for RAS is to ensure low sampling error in
the worst case condition of maximum ∆VSAMP and minimum CAS.
Summary of Specification Parameters
Freescale Semiconductor, Inc...
The following terms and simplified definitions will be used to describe
Motorola’s future ADC’s:
•
Zero-Scale Voltage (VZS) — The voltage at the bottom end of the input
range (equal to VREFL), measured in Volts.
•
Full-Scale Voltage (VFS) — The voltage at the upper end of the input
range (equal to VREFH), measured in Volts.
•
Least Significant Bit (LSB) — An ideal code width, or the valid input
range divided by the number of possible codes.
•
Resolution (N) — The number of bits in the output conversion; defines
the number of possible codes.
•
Quantization Error (EQ) — The error between the Ideal Transfer
Function and the Ideal Straight Line Transfer Function as a result of the
quantization of the output, measured in LSB.
•
Differential Non-Linearity (DNL) — The error between the current
code width and the ideal code width, measured in LSB.
•
Integral Non-Linearity (INL) — The error between the actual and the
corresponding Adjusted Transfer Function transition voltages,
measured in LSB.
•
Zero-Scale Error (EZS) — The error between the actual and ideal first
transition voltages, measured in LSB.
•
Full-Scale Error (EFS) — The error between the actual and ideal last
transition voltages, measured in LSB.
•
(Alternatively to EFS) Gain Error (EG) — The error between the voltage
range the Actual Transfer Function covers from first to last transition and
that of the Ideal Transfer Function, measured in LSB.
•
Total Unadjusted Error (ETUE) — The error between the Actual
Transfer Function and the Ideal Straight-Line Transfer Function,
measured in LSB.
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Common ADC Terminology
Common ADC Terminology
The following words are often used to describe ADC performance:
•
•
Freescale Semiconductor, Inc...
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Absolute Error — Total Unadjusted Error.
Actual Transfer Function — The conversion code vs. input voltage
curve.
Adjusted Code Width (ACW) — The amount of the input range (in
Volts) that the ADC would convert to each code assuming a perfectly
linear transfer function between the first and last transition voltages.
Adjusted Gain Error — Gain Error.
Adjusted Integral Non-Linearity — Integral Non-Linearity.
Adjusted Offset Error — Offset Error.
Adjusted Straight-Line Transfer Function — The straight line
between the minimum voltage plus Zero-Scale Error and the maximum
voltage minus Full-Scale Error.
Adjusted Transfer Function — The ideal conversion code vs. input
voltage curve assuming perfect linearity between the first and last
transition voltages.
Analog AC Source Impedance (ZAIN) — The real portion of the Analog
Input Source Impedance at the Acquisition Frequency; determines how
fast the Analog Input Source can charge the ADC input.
Analog DC Source Resistance (RAIN) — The real portion of the
Analog Input Source Impedance at DC; determines the voltage drop
from the true source to the analog input given the input leakage.
Best-Fit Transfer Function — The transfer function for which the
average error between it and the actual transfer function is minimum.
Board Resistance (RB) — The resistance (leakage) on the Analog
Input due to the printed circuit board.
Code — The digital output of the ADC.
Code DNL — The DNL at a particular conversion.
Code Error — The error between the current conversion and the ideal
conversion.
Conversion — The single point transfer function between VIN and the
output code.
Conversion Code Width (CCW) — The difference between the
voltages at which the conversion transitions to and from the specified
code.
Differential Non-Linearity (DNL) — The difference between the
Current Code Width and the Ideal Code Width.
Endpoint INL — Integral Non-Linearity.
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•
•
•
•
Freescale Semiconductor, Inc...
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Full-Scale Conversion — The maximum code output by the ADC,
typically $3FF for a 10b ADC.
Full-Scale Error (EFS) — The difference between the ideal last
transition and the actual last transition voltages.
Full-Scale Offset — Full-Scale Error.
Full-Scale Voltage (VFS) — The maximum of the input voltage range,
typically equal to VREFH.
Gain Error (EG) — The difference in the ideal ADC slope and the slope
of the ADC transfer function, measured as the difference in the number
of Ideal Code Widths from the first to last conversion between the ideal
transfer function and the actual.
Ideal Code Width (ICW) — The amount of the input range (in Volts) that
an ideal ADC would convert to each code.
Ideal Straight-Line Transfer Function — The straight line from the
minimum to the maximum voltage.
Ideal Transfer Function — The ideal conversion code vs. input voltage
curve assuming perfect linearity across the input voltage range.
Input Leakage (IIN) — The leakage into the pad (not ADC), usually due
to ESD circuits.
Integral Non-Linearity (INL) — The sum of the individual Code DNL,
except for the Zero-Scale Error, up to the current code, or the difference
between the current transition and the corresponding transition on the
Adjusted Transfer Function.
Least Significant Bit (LSB) — A unit of voltage equal to the valid input
range divided by the number of possible output codes. The bit has the
smallest value.
Most Significant Bit (MSB) — The bit having the largest value. Its value
will be 1⁄2 of full scale.
Offset Error (EO) — The difference between the actual and ideal first
transition voltages.
Quantization Error (EQ) — The error between the Straight-Line
Transfer Function and corresponding Transfer Function as a result of
Quantization; only included in Total Unadjusted Error.
Resolution — The number of bits in the output code of the ADC, this
term has no real bearing on the performance of the ADC except that all
performance parameters are measured against the theoretical best ADC
of equal resolution.
Straight-Line Transfer Function — The code vs. input voltage that
would define an ADC with an infinite number of codes.
Total Error — Total Unadjusted Error.
Total Adjusted Error — The difference between the Actual Transfer
Function and the Adjusted Straight-Line Transfer Function; includes INL
and EQ.
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Conclusion
•
•
•
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•
•
•
•
•
•
•
•
•
Total Unadjusted Error (ETUE) — The difference between the Actual
Transfer Function and the Ideal Straight-Line Transfer Function;
includes all forms of error.
Transfer Function — The code vs. voltage relationship that defines the
ADC output vs. input function.
Transition Voltage (or Point) — The voltage at which the ADC output
changes from one code to another.
Unadjusted INL — The sum of the Code DNL up to the current
conversion, or the difference between the current transition and the
corresponding transition on the Ideal Transfer Curve.
Uncompensated Quantization — Technique in which the ideal transfer
function’s first transition voltage is at 1LSB.
VIN — The input voltage to the ADC.
VREFL — The low-voltage reference to the ADC analog circuitry,
typically (but not always) equal to VSSAD.
VREFH — The high-voltage reference to the ADC analog circuitry,
typically allowed to go lower than VDDAD while maintaining a minimum
voltage difference between it and VREFL.
Zero-Scale Conversion — The minimum code output by the ADC,
typically $000 for a 10b ADC.
Zero-Scale Error (EZS) — The difference between the first transition
and the ideal first transition voltages.
Zero-Scale Voltage (VZS) — The minimum of the input voltage range,
typically equal to VREFL.
½LSB Compensated Quantization — Technique in which the ideal
transfer function’s first transition voltage is shifted to cause the first
transition voltage at 1⁄2LSB instead of 1LSB.
Conclusion
Once a user has a good working knowledge of the various terminology used to
describe the specifications and characteristics of analog-to-digital converters,
he can select a converter to best suite the requirements of the system. A good
understanding of the terms used to specify the converter can help the user sort
out the most important design parameters for his system and enable him to get
the best cost and performance trade-offs for the design.
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