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Oversample on Purpose

By Jon Titus, Contributing Writer -- Design News, October 20, 2008

Suppose you have an 8-bit (1 part in 256) ADC with a 0 to 10V input range that lets you resolve an unknown voltage to within 0.0391V. If you have a noise-free input signal at, say, 1.985V, the ADC produces an 8-bit value, 00110011₂ or 51₁₀, which represents the span from 1.97 to 2.01V. If you require more resolution, you can gain “extra” bits by oversampling your signal at a rate given by the formula:

f_oversample = f_Nyquist * 4ⁿ

Where n = the additional bits of resolution you want. If you need two additional bits of resolution, you must sample at 16 times the Nyquist frequency. Need three additional bits? Sample at 64 times the Nyquist frequency. Keep in mind adding useful resolution requires an ADC with the characteristics of the total resolution you need. Don't expect to turn a 10-bit ADC into a 16-bit device unless the 10-bit device can meet 16-bit specs.

But simply oversampling the 1.985V signal does not extend resolution because you would simply obtain the same value again and again. So, you add some white noise to the signal — which seems counterintuitive — and oversample. The added noise can range from just more than ±1 LSB (±0.0391 for the 8-bit ADC) to perhaps several times ±0.0391. The addition of the random noise produces ADC outputs spread across several ADC steps, as shown in the figure, below left. Now when the ADC samples the noisy unknown signal you see values between 49 and 52.

To obtain three additional bits of resolution for the 8-bit ADC, you sample the noisy signal 64 times faster and add the 64 8-bit binary values. That addition yields a 14-bit result (2⁸ * 2⁶ = 2¹⁴). Delete the three LSBs and you have an 11-bit result. Deleting these three bits results in a binary division by eight, which arises from 2ⁿ, where n equals the number of “extra” bits you specified in the equation, left. During these 64 A-to-D conversions, the unknown signal must remain stable. If you plan to measure a slowly changing voltage, it may remain constant enough on its own during the measurement period. Varying signals may require an accurate sample-and-hold amplifier in front of the ADC.

The nearby diagram, left, shows a 1.985V signal without noise and with added noise generated by the Data Analysis Tools in Microsoft Excel. In this test, quantizing and averaging 64 samples yielded an 11-bit binary value equivalent to 1.982V. A 256 sample produced the same value.

The oversampling technique simply reduces an ADC's quantization error or quantization noise by spreading it over a wider bandwidth. Lowering measurement errors requires faster sampling as the trade-off. And the ADC must be more accurate than the measurement uncertainties inherent in the system.

Useful Links

1. “Oversampling,” Wikipedia: http://rbi.ims.ca/5728-513.

2. “Sampling, Oversampling, Imaging and Aliasing,” Lavry Engineering: http://rbi.ims.ca/5728-514.

3. “Enhancing ADC Resolution by Oversampling,” AVR121. Atmel: http://rbi.ims.ca/5728-515.

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