RF Sampling: How Oversampling Defrauds Physics
RF sampling converters can capture high frequency signals and large bandwidth signals; however, not every application can utilize signals that require very high speed sampling. In the case where the bandwidth or output frequency is not too high, there is still a great advantage of using the high sampling rate capability of the RF sampling converter. The sampling theorem states that the sampling rate must be at least twice the maximum bandwidth of the signal. Samples below this rate are called undersampling and cause aliasing. Samples above this rate are called oversampling. Oversampling offers some processing advantages that seem to disregard the laws of physics. One of the key measurement parameters of an analog-to-digital converter (ADC) is the signal-to-noise ratio (SNR). The SNR measures the relative level between the desired signal power and the total noise power in the first Nyquist zone. The bandwidth of the Nyquist zone equals the sampling rate divided by 2 (Fs/2). Remember, all signal and noise will return to the first Nyquist zone. This area actually represents the entire bandwidth of the device. One of the great benefits of oversampling is that the image components can be further separated in frequency space. This allows for easier analog filtering to eliminate interfering signals that can alias down into the captured bandwidth and reduce receiver sensitivity. Figure 1 shows two examples: a signal sampled at a rate close to the Nyquist rate and an oversampled signal. In an oversampled example, the analog anti-aliasing filter is easier to implement.
Figure 1: Effect of Filters on Nyquist Rate Sampling and Oversampling Oversampling can be improved without the theoretical quantization noise limit to improve the SNR performance of the device. This quantization noise is evenly distributed across the Nyquist bandwidth. By increasing the sampling rate, the same quantization noise is spread over a larger Nyquist bandwidth. The required signal remains unchanged. The combination of decimation and digital filtering reduces the noise bandwidth without affecting the desired signal. Note that decimation means oversampling because there must be other samples available for removal. In RF sampling ADCs, the extraction factor is more often mentioned than the oversampling rate; however, these parameters are actually equivalent. For example, to make a decimation factor of 2, you must make the signal's oversampling factor at least 2. In this example, the signal power remains unchanged, but the Nyquist bandwidth is halved. This eliminates half the noise power and increases the SNR of the ADC by 3dB. The first equation represents the ideal SNR due to quantization noise, where N is the number of bits in the converter. The second equation represents the SNR improvement associated with the decimation factor D.
According to the pure quantization noise analysis, the sampling rate increases by a factor of three each time (that is, four times the original value), which increases the resolution by one significant bit. In theory, a 12-bit data converter can achieve the SNR performance of a 14-bit converter by sampling at a rate that is 16 times the minimum Nyquist rate.
In practice, RF sampling data converters cannot achieve SNR performance comparable to the quantization noise limit due to other impairments associated with aperture jitter, clock jitter, and thermal noise; however, oversampling techniques can still provide nearly identical correlation SNR Improve the value. In many communications systems, this benefit is crucial.
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