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Digital Electronics
simply as eight-bit resolution. If such a converter has a full-scale analogue input range of 10 V, it can
resolve a 40 mV change in input.
12.9.2 Accuracy
The accuracy specification describes the maximum sum of all errors, both from analogue sources
(mainly the comparator and the ladder resistors) and from the digital sources (quantization error) of
the A/D converter. These errors mainly include the gain error, the offset error and the quantization
error. The accuracy describes the actual analogue input and full-scale weighted equivalent of the output
code corresponding to the actual analogue input. The accuracy specification is rarely provided on the
datasheets, and quite often several sources of errors are listed separately.
12.9.3 Gain and Offset Errors
The gain error is the difference between the actual full-scale transition voltage and the ideal full-scale
transition voltage. It is expressed either as a percentage of the full-scale range (% of FSR) or in LSBs.
The offset error is the error at analogue zero for an A/D converter operating in bipolar mode. It is
measured in % of FSR or in LSBs.
12.9.4 Gain and Offset Drifts
The gain drift is the change in the full-scale transition voltage measured over the entire operating
temperature range. It is expressed in full scale per degree Celsius or ppm of full scale per degree
Celsius or LSBs. The offset drift is the change with temperature in the analogue zero for an A/D
converter operating in bipolar mode. It is generally expressed in ppm of full scale per degree Celsius
or LSBs.
12.9.5 Sampling Frequency and Aliasing Phenomenon
If the rate at which the analogue signal to be digitized is sampled is at least twice the highest
frequency in the analogue signal, which is what is embodied in the Shannon–Nyquist sampling theorem,
then the analogue signal can be faithfully reproduced from its quantized values by using a suitable
interpolation algorithm. The accuracy of the reproduced signal is, however, limited by the quantization
error (discussed in Section 12.9.6). If the sampling rate is inadequate, i.e. if it is less than the Nyquist
rate, then the reproduced signal is not a faithful reproduction of the original signal and these spurious
signals, called aliases, are produced. The frequency of an aliased signal is the difference between the
signal frequency and the sampling frequency. For example, if sampled at a 1.5 kHz rate, a 2 kHz sine
wave would be reconstructed as a 500 Hz sine wave. This problem is called aliasing and, in order to
avoid it, the analogue input signal is low-pass filtered to remove all frequency components above half
the sampling rate. This filter, called an anti-aliasing filter, is used in all practical A/D converters.
12.9.6 Quantization Error
The quantization error is inherent to the digitizing process. For a given analogue input voltage range
it can be reduced by increasing the number of digitized levels. An A/D converter having an n-bit
Digital Electronics
simply as eight-bit resolution. If such a converter has a full-scale analogue input range of 10 V, it can
resolve a 40 mV change in input.
12.9.2 Accuracy
The accuracy specification describes the maximum sum of all errors, both from analogue sources
(mainly the comparator and the ladder resistors) and from the digital sources (quantization error) of
the A/D converter. These errors mainly include the gain error, the offset error and the quantization
error. The accuracy describes the actual analogue input and full-scale weighted equivalent of the output
code corresponding to the actual analogue input. The accuracy specification is rarely provided on the
datasheets, and quite often several sources of errors are listed separately.
12.9.3 Gain and Offset Errors
The gain error is the difference between the actual full-scale transition voltage and the ideal full-scale
transition voltage. It is expressed either as a percentage of the full-scale range (% of FSR) or in LSBs.
The offset error is the error at analogue zero for an A/D converter operating in bipolar mode. It is
measured in % of FSR or in LSBs.
12.9.4 Gain and Offset Drifts
The gain drift is the change in the full-scale transition voltage measured over the entire operating
temperature range. It is expressed in full scale per degree Celsius or ppm of full scale per degree
Celsius or LSBs. The offset drift is the change with temperature in the analogue zero for an A/D
converter operating in bipolar mode. It is generally expressed in ppm of full scale per degree Celsius
or LSBs.
12.9.5 Sampling Frequency and Aliasing Phenomenon
If the rate at which the analogue signal to be digitized is sampled is at least twice the highest
frequency in the analogue signal, which is what is embodied in the Shannon–Nyquist sampling theorem,
then the analogue signal can be faithfully reproduced from its quantized values by using a suitable
interpolation algorithm. The accuracy of the reproduced signal is, however, limited by the quantization
error (discussed in Section 12.9.6). If the sampling rate is inadequate, i.e. if it is less than the Nyquist
rate, then the reproduced signal is not a faithful reproduction of the original signal and these spurious
signals, called aliases, are produced. The frequency of an aliased signal is the difference between the
signal frequency and the sampling frequency. For example, if sampled at a 1.5 kHz rate, a 2 kHz sine
wave would be reconstructed as a 500 Hz sine wave. This problem is called aliasing and, in order to
avoid it, the analogue input signal is low-pass filtered to remove all frequency components above half
the sampling rate. This filter, called an anti-aliasing filter, is used in all practical A/D converters.
12.9.6 Quantization Error
The quantization error is inherent to the digitizing process. For a given analogue input voltage range
it can be reduced by increasing the number of digitized levels. An A/D converter having an n-bit