M1AFS600-PQ208 Datasheet, PDF (118/334 Pages) Microsemi Corporation – Fusion Family of Mixed Signal FPGAs

Device Architecture
This process results in a binary approximation of VIN. Generally, there is a fixed interval T, the sampling
period, between the samples. The inverse of the sampling period is often referred to as the sampling
frequency f_S = 1 / T. The combined effect is illustrated in Figure 2-82.
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Figure 2-82 • Conversion Example
Figure 2-82 demonstrates that if the signal changes faster than the sampling rate can accommodate, or if
the actual value of VIN falls between counts in the result, this information is lost during the conversion.
There are several techniques that can be used to address these issues.
First, the sampling rate must be chosen to provide enough samples to adequately represent the input
signal. Based on the Nyquist-Shannon Sampling Theorem, the minimum sampling rate must be at least
twice the frequency of the highest frequency component in the target signal (Nyquist Frequency). For
example, to recreate the frequency content of an audio signal with up to 22 KHz bandwidth, the user
must sample it at a minimum of 44 ksps. However, as shown in Figure 2-82, significant post-processing
of the data is required to interpolate the value of the waveform during the time between each sample.
Similarly, to re-create the amplitude variation of a signal, the signal must be sampled with adequate
resolution. Continuing with the audio example, the dynamic range of the human ear (the ratio of the
amplitude of the threshold of hearing to the threshold of pain) is generally accepted to be 135 dB, and the
dynamic range of a typical symphony orchestra performance is around 85 dB. Most commercial
recording media provide about 96 dB of dynamic range using 16-bit sample resolution. But 16-bit fidelity
does not necessarily mean that you need a 16-bit ADC. As long as the input is sampled at or above the
Nyquist Frequency, post-processing techniques can be used to interpolate intermediate values and
reconstruct the original input signal to within desired tolerances.
If sophisticated digital signal processing (DSP) capabilities are available, the best results are obtained by
implementing a reconstruction filter, which is used to interpolate many intermediate values with higher
resolution than the original data. Interpolating many intermediate values increases the effective number
of samples, and higher resolution increases the effective number of bits in the sample. In many cases,
however, it is not cost-effective or necessary to implement such a sophisticated reconstruction algorithm.
For applications that do not require extremely fine reproduction of the input signal, alternative methods
can enhance digital sampling results with relatively simple post-processing. The details of such
techniques are out of the scope of this chapter; refer to the Improving ADC Results through
Oversampling and Post-Processing of Data white paper for more information.
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