Digital Electronics: Principles, Devices and Applications

Data Conversion Circuits – D/A and A/D Converters 497output can only identify 2 n output codes while there are an infinite number of analogue input valuesadjacent to the LSB of the A/D converter that are assigned the same output code. For instance, if weare digitizing an analogue signal with a peak value of 7 V using three bits, then all analogue voltagesequal to or greater than 5.5 V and less than or equal to 6.5 V will be represented by the same outputcode, i.e. 110 (if the output coding is in straight binary form). The error is ±0.5Vor±1/2 LSB, asa one-LSB change in the output corresponds to an analogue change of 1 V in this case. The ±1/2LSB limit to resolution is known as the fundamental quantization error. Expressed as a percentage, thequantization error in an eight-bit converter is one part in 255 or 0.4 %.12.9.7 NonlinearityThe nonlinearity specification [also referred to as the integral nonlinearity (INL) by somemanufacturers] of an A/D converter describes its departure from a linear transfer curve. The nonlinearityerror does not include gain, offset and quantization errors. It is expressed as a percentage of full scaleor in LSBs.12.9.8 Differential NonlinearityThis indicates the worst-case difference between the actual analogue voltage change and the idealone-LSB voltage change. The DNL specification is as important as the INL specification, as anA/D converter having a good INL specification may have a poor-quality transfer curve if the DNLspecification is poor. DNL is also expressed as a percentage of full scale or in LSBs. DNL in factexplains the smoothness of the transfer characteristics and is thus of great importance to the user.Figure 12.27 shows the transfer curve for a three-bit A/D converter with a 7 V full-scale range,1/4-LSB INL and one-LSB DNL. Figure 12.28 shows the same for a7Vfull-scale range, one-LSBINL and 1/4-LSB DNL. Although the former has a much better INL specification, the latter, witha better DNL specification, has a much better and smoother curve and may thus be preferred. Toohigh a value of DNL may even grossly degrade the converter resolution. In a four-bit converter111110OutputDigital1011000110100011LSB DNL0000 1 2 3 4 5 6 7 8Analog Input (V)Figure 12.27Transfer characteristics of a three-bit A/D converter (INL = one LSB, DNL = 1LSB).