ABCs of ADCs - Analog-to-Digital Converter Basics (PDF)

Quantization Error111Digital Output1101011000110100011 LSBERROR0000 V REFV REF3V REFV REF4 3V REF2 5V REF4 7V REFV REF8 88 8Input (V)1 LSB0The Magnitude of the Error Ranges from Zero to 1 LSB7Continuing with the simple example of a 3-bit ADC, an ADC input of zero produces an output code ofzero (000). As the input voltage increases towards V REF /8, the error also increases because the inputis no longer zero, but the output code remains at zero because a range of input voltages isrepresented by a single output code. When the input reaches V REF /8, the output code changes from000 to 001, where the output exactly represents the input voltage and the error reduces to zero. Asthe input voltage increases past V REF /8, the error again increases until the input voltage reachesV REF /4, where the error again drops to zero. This process continues through the entire input rangeand the error plot is a saw tooth, as shown here.The maximum error we have here is 1 LSB. This 0 to 1 LSB range is known as the “quantizationuncertainty” because there are a range of analog input values that could have caused any given codeand we are uncertain at to exactly what the input voltage was that caused a given code. Themaximum quantization uncertainty is also known as the “quantization error”. This error results fromthe finite resolution of the ADC. That is, the ADC can only resolve the input into 2 n discrete values.Each output code represents a range of input values. This range of values is a quanta, to which weassign the symbol q.The converter resolution, then, is 2 n . So, for an 8 Volt reference (with a unity gain factor), a 3-bitconverter resolves the input into V REF /8 = 8V/8 = 1 Volt steps. Quantization error, then, is a round offerror.But an error of 0 to 1 LSB is not as desirable as is an error of ± 1 / 2 LSB, so we introduce an offset intothe A/D converter to force an error range of ± 1 / 2 LSB.ABCs of ADCs - Rev 3, June 2006Authored by: Nicholas “Nick” Gray7Copyright © 2003, 2004, 2006 National SemiconductorCorporationAll rights reserved