You have heard the term “LSB” (Least Significant Bit) many times in electronics. It is often considered in relation to either the Vref or the Full Scale (FS) of an ADC or DAC, and this can sometimes lead to confusion for readers.
So, this article will help in understanding the definition of “LSB.”.
When an ADC (Analog-to-Digital Converters) converts voltage to digital form, one digital code consists of a range of voltage. This voltage range that is equivalent to a single code is called an LSB ,or least significant bit.
LSB is the smallest level that an ADC can convert (smallest voltage increment the ADC can detect.), or the smallest increment a DAC can output.
An ADC needs a voltage reference to convert an analog signal to digital. Depending on the number of bits it has, it divides the voltage reference into small counts.
Example:
If this is an 8-bit ADC, the count will look like 1, 2, 3, … up to 256.
1 count is 1 LSB and is defined as:
LSB = Vref / 2^N
Where:
- N is the number of bits.
The Full Scale (FS) is calculated using the formula:
- FS = Vref - 1 × LSB, or
- FS = Vref × ((2^N - 1) / 2^N)
Example: Calculate LSB for a -5 to +5 volt input range with a 16bit A/D converter.
FS Range = 10 Volts (-5V to +5V),
16bit resolution = 65,536 bits
LSB = 10/65536 = 0.0001525 volts/bit (153 µVolts/bit)
ADC Conversion Errors Measured in LSB
In ADCs, conversion errors are often expressed in terms of LSB (Least Significant Bit).
If an ADC has a ±2 LSB error , it means the digital output can deviate by up to 2 counts from the ideal value due to internal inaccuracies.
For example, if an 8-bit AD converter has 0.0V to 5.0V conversion range and a conversion error of ±2 LSB, the AD conversion range of a 2.5V input,
LSB = 5v/ 256 = 0.0195V
Ideal digital value for 2.5V input (AD converter is error-free) = Digital Value= Vin/ LSB
2.5/ 0.0195 =128⇒0x80 (hex)
With ±2 LSB error , The output could be anywhere from:
128−2=126⇒0x7E
128+2=130⇒0x82
So, the ADC might output 0x7E to 0x82 for a 2.5V input, even though the ideal value is 0x80 .