AN118: Improving ADC Resolution by ... - Silicon Labs

1 Rev. 7/13 Copyright 2013 by Silicon LaboratoriesAN118AN118 Improving ADC Resolution BY OVERSAMPLING AND AVERAGING1. IntroductionMany applications require measurements using ananalog-to-digital converter (ADC). Suchapplications will have Resolution requirementsbased in the signal s dynamic range, the smallestchange in a parameter that must be measured, andthe signal-to-noise ratio (SNR). For this reason,many systems employ a higher Resolution off-chipADC. However, there are techniques that can beused to achieve higher Resolution measurementsand SNR.

2 This application note describes utilizingoversampling and averaging to increase theresolution and SNR of analog-to-digitalconversions. Oversampling and averaging canincrease the Resolution of a measurement withoutresorting to the cost and complexity of usingexpensive off-chip application note discusses how to increase theresolution of analog-to-digital (ADC) measure-ments by oversampling and averaging. Addition-ally, more in-depth analysis of ADC noise, types ofADC noise optimal for oversampling techniques,and example code utilizing oversampling and aver-aging is provided in appendices A, B, and Crespectively at the end of this Key Points Oversampling and averaging can be used to increase measurement Resolution , eliminating the need to resort to expensive, off-chip ADCs.

3 Oversampling and averaging will improve the SNR and measurement Resolution at the cost of increased CPU utilization and reduced throughput. Oversampling and averaging will improve signal-to-noise ratio for white Sources of Data Converter NoiseNoise in ADC conversions can be introduced frommany sources. Examples include: thermal noise,shot noise, variations in voltage supply, variation inthe reference voltage, phase noise due to samplingclock jitter, and noise due to quantization error. Thenoise caused by quantization error is commonlyreferred to as quantization noise.

4 Noise power fromthese sources can vary. Many techniques that maybe utilized to reduce noise, such as thoughtfulboard layout and bypass capacitance on the refer-ence voltage signal trace. However, ADCs willalways have quantization noise, thus the best SNRof a data converter of a given number of bits isdefined by the quantization noise with no oversam-pling. Under the correct conditions, oversamplingand averaging will reduce noise and improve then-bitADCx(t)Input SignalSampleFrequency (fs)e[n] (Noise)x[n]x[n]+e[n]OSRLow-PassFilterDow nsampleOversample and Average(Software Accumulate and Dump)(n+w) bitOutput DataFigure 1.

5 Oversampling and Averaging to Increase Measurement Resolution By w BitsAN1182 Rev. This will effectively increase the number ofbits of a measurement s Resolution . Such a systemis shown in Figure 1 on page 1, and can be imple-mented with Silicon Lab s on-chip ADC and a soft-ware routine that takes a set of samples andaverages (filters) them for the the Resolution of an ADC MeasurementMany applications measure a large dynamic rangeof values, yet require fine Resolution to measuresmall changes in a parameter.

6 For example, anADC may measure a large temperature range, yetstill require the system to respond to changes ofless than one degree. Such a system could require ameasurement Resolution of 16 bits. Rather thanresorting to an expensive, off-chip 16-bit ADC,oversampling and averaging using Silicon Lab son-chip, 12-bit ADC can measure a parameter with16 bits of applications will use an ADC to analyze asignal with higher frequency components. Such asystem will also benefit from oversampling andaveraging. The required sampling frequency inaccordance with the Nyquist Theorem is theNyquist Frequency: Sampling frequencies (fs) above fn is oversam-pling, and will increase the Resolution of a measure-ment.

7 Please see Appendix A for a discussion ofhow this the Oversampling Requirements To Increase ResolutionTo increase the effective number of bits (ENOB),the signal is oversampled, or sampled by the ADCat a rate that is higher than the system s requiredsampling rate, fs. The required sampling rate maybe determined by how often a system requires aparameter be measured (output word rate), or itmay be the Nyquist frequency, each additional bit of Resolution , the signalmust be oversampled by a factor of four:A derivation of Equation 2 is presented inAppendix a system is using a 12-bit ADC to output atemperature value once every second (1 Hz).

8 Toincrease the Resolution of the measurement to 16-bits, we calculate the oversampling frequency asfollows:Thus, if we oversample the temperature sensor atfs=256 Hz, we will collect enough samples withinthe required sampling period to average them andcan now use 16-bits of the output data for a 16-bitmeasurement. To do so, we accumulate (add 256consecutive samples together), then divide the totalby 16 (or right shift the total by 4-bits). Such a pro-cess is commonly referred to as decimation. Thisfn2fm =where fm is the highest frequency compo-nent of interest in the input signalEquation 1.

9 Nyquist Frequencyfos4wfs =where w is the number of additional bits ofresolution desired, fs is the original sam-pling frequency requirement, and fos is theoversampling frequencyEquation 2. Oversampling Frequency To Add Measurement Resolutionfos441Hz 256Hz==AN118 Rev. in 16-bits of useful data. Such an operationis referred to as accumulate and dump. Once wecalculate the result of 256 samples (in this exam-ple), we store or process the data and begin collect-ing data for the next output : The memory location used to accumulate theoversampled data and perform the divide musthave enough bytes to prevent overflow and trunca-tion example of such oversampling and averaging isprovided in Appendix C.

10 In this example, SiliconLab s on-chip temperature sensor is sampled usingthe on-chip 12-bit ADC to make a 16-bit measure-ment. For a more formal discussion of how over-sampling affects noise and increases Resolution ,please see Appendix the Oversampling Requirements To Increase SNRThe theoretical limit of the SNR of an ADC mea-surement is based on the quantization noise due tothe quantization error inherent in the analog-to-dig-ital conversion process when there is no oversam-pling and averaging. Because quantization errordepends on the number of bits of Resolution of theADC (see Equation 5), the best case SNR is calcu-lated as a function of the Effective Number of Bitsof a data conversion as follows:Note Equation 3 is valid for a full-scale input.