MCP6271R Microchip Technology Inc., MCP6271R Datasheet - Page 26

• Manufacturer Part Number: MCP6271R
• Description: 170 ?a, 2 Mhz Rail-to-rail Op Amp
• Manufacturer: Microchip Technology Inc.

The Number Of Bits vs LSB Errors
By Bonnie C. Baker, Microchip Technology Inc.
What do the Least Significant Bits (LSB) specifications mean
when you are looking at Analog-to-Digital converters (ADC)?
A fellow engineer told me that a 12-bit converter, from X
manufacturer, had just seven usable bits. So, essentially the
12-bit converter was only a 7-bit converter. He based this
conclusion on the device’s offset and gain specifications. The
maximum specifications were:
At first glance, I thought he was right. From the list above, the
worst specification is gain error (± 5 LSB). Applying simple
mathematics, 12 bits minus 5 bits of resolution is equal to 7
bits, right? Why would an ADC manufacturer introduce such a
device? The gain-error specification motivates me to purchase a
lower-cost, 8-bit converter, but that doesn’t seem right. Well, as it
turns out, it wasn’t right.
Let’s start out by looking at the definition of LSB. Think of a
serial 12-bit converter, it produces a string of 12 ones or zeros.
Typically, the converter’s first transmitted digital bit is the Most
Significant Bit (MSB) (or LSB + 11). Some converters transmit
the LSB first. We will assume that the MSB is first in this
discussion (shown in Figure 1). The second bit is MSB-1 (or
LSB+10), the third bit is MSB-2 (or LSB+9), etc. At the end of
this string of bits, the converter finally transmits as MSB-11 (or
LSB).
Figure 1: The data from this serial ADC clocks MSB out first and
LSB last.
The terminology, LSB, is very specific. It describes the last
position in the digital stream. It also represents a fraction of the
full-scale input range. For a 12-bit converter, the LSB value is
equivalent to the analog full-scale input range, divided by 2
4,096. If I put this in terms of real numbers, I have an LSB size
of 1 mV with a 12-bit converter that has full-scale input range of
4.096V. However, the most instructive definition of LSB is that it
can represent one code out of the 4096 codes possible.
24
Analog and Interface Guide – Volume 2
DOUT
CLK
CS
Analog-to-Digital Converters
offset error = ± 3 LSB,
gain error = ± 5 LSB,
1
2
(LSB + 11)
3
MSB
11
D
4
10
D
5
D
9
6
D
8
7
D
7
8
D
6
9
D
10 11 12 13 14
5
D
4
D
3
D
2
(MSB + 11)
D
1
LSB
15
D
0
12
or
Going back to the specifications and translating them into a
12-bit converter that has an input full-scale range of 4.096V:
These specifications actually claim that the converter can have
(worst case) an 8 mV (or 8 code) error introduced through the
conversion process. This is not to say that the error occurs at
the LSB, LSB-1, LSB-2, LSB-3, LSB-4, LSB-5, LSB-6 and LSB-7
positions in the output-bit stream of the converter. The errors
can be up to eight times one LSB, or 8 mV. Precisely stated, the
transfer function of the converter could have up to eight codes
missing out of 4,096 codes. These codes will be missing at the
lower or upper range of the codes. For instance, a converter with
an error of +8 LSB ((+3 LSB offset error) + (+5 LSB gain error))
will produce possible output codes of zero to 4,088. The lost
codes are from 4088 up to 4,095. This is a small, incremental
error of 0.2% at full-scale. In contrast, a converter with an error
of -3 LSB ((-3 LSB offset error) – (-5 LSB gain error)) will produce
codes from three up to 4,095. The gain error in this situation
produces an accuracy problem, not a loss of codes. The lost
codes are 0, 1 and 2. Both of these examples illustrate the worst
possible scenario. Typically, the offset errors and gain errors do
not track this closely in actual converters.
The real-life performance enhancements, due to incremental
improvements in an ADC’s offset or gain specifications, are
negligible to non-existent. To some designers this seems like
a bold assumption, if precision is one of the design objectives.
It is easy to implement digital calibration algorithms with your
firmware. However, more importantly, the front-end amplification/
signal conditioning section of the circuit typically produces higher
errors than the converter itself.
This discussion puts a new light on the conclusions reached
at the beginning of this article. In fact, the 12-bit converter,
as specified above, has an accuracy of approximately 11.997
bits. The good news is that a microprocessor or microcontroller
can remove this offset and gain error with a simple calibration
algorithm.
offset error = ± 3LSB = ± 3 mV,
gain error = ± 5LSB = ± 5 mV,