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[Part 1 explains the basics of data sampling and shows how to use undersampling and antialiasing filters. Part 3 examines distortion and noise in practical ADCs.]
ADC and DAC Static Transfer Functions and DC Errors
The most important thing to remember about both DACs and ADCs is that either the input or output is digital, and therefore the signal is quantized. That is, an N-bit word represents one of 2N possible states, and therefore an N-bit DAC (with a fixed reference) can have only 2N possible analog outputs, and an N-bit ADC can have only 2N possible digital outputs. The analog signals will generally be voltages or currents.
The resolution of data converters may be expressed in several different ways, including the weight of the least significant bit (LSB), parts per million of full scale (ppm FS), millivolts (mV). Different devices (even from the same manufacturer) will be specified differently, so converter users must learn to translate between the different types of specifications if they are to successfully compare devices. The size of the least significant bit for various resolutions is shown in Figure 2-7.
(Click to enlarge)
Figure 2-7: Quantization—The Size of a Least Significant Bit (LSB).
Before we can consider the various architectures used in data converters, it is necessary to consider the performance to be expected, and the specifications that are important. The following sections will consider the definition of errors and specifications used for data converters. This is important in understanding the strengths and weaknesses of different ADC/DAC architectures.
The first applications of data converters were in measurement and control where the exact timing of the conversion was usually unimportant, and the data rate was slow. In such applications, the dc specifications of converters are important, but timing and ac specifications are not. Today many, if not most, converters are used in sampling and reconstruction systems where ac specifications are critical (and dc ones may not be). These will be considered in the next part of this section.
Figure 2-8 shows the ideal transfer characteristics for a 3-bit unipolar DAC, and Figure 2-9 a 3-bit unipolar ADC. In a DAC, both the input and the output are quantized, and the graph consists of eight points. While it is reasonable to discuss the line through these points, it is very important to remember that the actual transfer characteristic is not a line, but a number of discrete points.
Figure 2-8: Transfer Function for Ideal 3-Bit DAC.
Figure 2-9: Transfer Function for Ideal 3-Bit ADC.
The input to an ADC is analog and is not quantized, but its output is quantized. The transfer characteristic therefore consists of eight horizontal steps (when considering the offset, gain, and linearity of an ADC we consider the line joining the midpoints of these steps).
In both cases, digital full scale (all 1s) corresponds to 1 LSB below the analog full scale (the reference, or some multiple thereof). This is because, as mentioned above, the digital code represents the normalized ratio of the analog signal to the reference.
The (ideal) ADC transitions take place at 1/2 LSB above zero, and thereafter every LSB, until 1-1/2 LSB below analog full scale. Since the analog input to an ADC can take any value, but the digital output is quantized, there may be a difference of up to 1/2 LSB between the actual analog input and the exact value of the digital output. This is known as the quantization error or quantization uncertainty as shown in Figure 2-9. In ac (sampling) applications this quantization error gives rise to quantization noise, which will be discussed in the next section.
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