fft for adc

12/6/13 5:10 PMChoose The Right FFT Window Function When Evaluating Precision ADCs

Page 1 of 8http://electronicdesign.com/print/analog/choose-right-fft-window-function-when-evaluating-precision-adcs

Related Articles

Understand Signal AnalysisIn The Time, Frequency,And Modulation DomainsThe Fundamentals OfSpectrum AnalysisFFT Brings SpectrumAnalysis To The Scope

print | close

Choose The Right FFT Window Function When EvaluatingChoose The Right FFT Window Function When EvaluatingPrecision ADCsPrecision ADCsElectronic DesignLuis Chioye

Luis Chioye, Contributing Technical ExpertTue, 2013-11-12 15:15

When evaluating the dynamic performance of precision analog-to-digital converters (ADCs) using fast Fourier transform(FFT) analysis, coherent sampling typically is used to accurately measure the noise and distortion spectral components inthe FFT. In applications where the coherent sampling criteria cannot be met, a window weighting function is applied tominimize spectral leakage. Designers should know how to select an optimal FFT windowing function when testing theperformance of precision ADCs using a single-tone signal.

On The Bench

The FFT analysis is a common method used to characterize an ADCs dynamic performance. This test method typicallyinvolves applying a pure, low-noise, low-distortion sinusoidal signal at the ADCs inputs. Samples are taken over a timeinterval and perform the ADC data FFT to quantify the noise and distortion spectral components in the frequency domain.

The FFT is an algorithm that quickly performs the discrete Fourier transform of thesampled time domain signal. The FFT requires a time domain record with a numberof samples (M) that is a power of 2. The FFT spectrum consists of M/2 discretefrequency bins with a range from dc to fS/2, and a bin width of fS/M, where fS isthe sampling frequency.

The FFT assumes the signal within the time record is repetitive (Fig. 1). If thesamples on the time record do not start and stop within the same value at the endpoints in the time domain frame, this is interpreted as a discontinuity in thewaveform.



The abrupt discontinuity at the records end points produces frequency components not present in the original signal,which introduces spectral leakage in the FFT. This can be understood by looking into the case where the sampled signal isa sinusoid (Fig. 2).



Coherent sampling ensures that an integral number of cycles of the input signal is included within the time frame. Whencoherent sampling is utilized, the resulting FFT displays only the frequencies corresponding to the input frequency and itsharmonics. The criterion for coherent sampling is given by:1

Mfi = JfS (1)

Where M is the number of samples in the data record, fi is the frequency of the input signal, J is an integer prime numberof cycles of the input waveform in the data record, and fS is the sampling frequency. To accomplish coherent sampling, theinput signal frequency and/or the sampling frequency is finely adjusted to meet the relation in Equation 1. Figure 3 showsillustrates an FFT of a sinusoidal signal using coherent sampling.



To precisely meet the coherent sampling criteria, the test setup requires a function generator that allows a fine adjustmentof the input signal frequency. Additionally, the function generator typically is phase-locked with the clock-signal generatorused to trigger the sampling of the ADC.

Windowing

In applications where the coherent sampling criteria cannot be met, a window weighting function can be applied to the timerecord to minimize spectral leakage. Windowing consists of multiplying the data in the time domain by a window function(Fig. 4).



Different window functions are available with different frequency response characteristics. Choosing an optimal windowfor a specific application requires knowledge of the signals involved, consideration of the frequency resolution, and thedynamic range requirements (Fig. 5).



In this application, a single-tone signal is used for dynamic testing of high-resolution ADCs. The optimal window functionrequires a high dynamic range to accurately resolve noise and distortion components in the frequency spectrum. Consideran ideal ADC, where the signal-to-noise ratio (SNR) is given as a function of the number of bits (N):

SNRIdeal = 6.02 N + 1.76 (dB) (2)

Using Equation 2, the SNR for an ideal 14-bit ADC yields 86 dB, and the SNR for a 16-bit ADC is 98 dB. The necessaryside lobe attenuation level should exceed the dynamic range of the ADC under test by some margin. The table listsparameters used to characterize the frequency response of a few windowing functions.

The Hann and Hamming windows do not offer enough side lobe attenuation to be used to test high-resolution ADCs. Thefour-term Blackman-Harris function has a side lobe rejection level that allows us to accurately test a 12-bit ADC converter.However, this window is not adequate to resolve the SNR of a 16-bit resolution ADC. The seven-term Blackman-Harrishas enough dynamic range to resolve the FFT spectral components of a 24-bit resolution ADC.

When using a single-tone sinusoidal signal, the SNR, with respect to the carrier, is calculated as the ratio of power of thetone signal (PSignal) to the power of the noise components in the spectrum (PNoise), excluding the harmonics of the signalas shown in:

SNRdB = 10log10(PSignal/PNoise) = PSignal(dB) PNoise(dB) (3)

For example, if the seven-term Blackman-Harris window is selected, the fundamental and its harmonics will spread across



the window main lobe width bins (7 side bins around the signal). Therefore, prior to performing the SNR calculation, youneed to remove these bins around the signals when calculating the noise power.

Processing loss is the reduction in SNR due to the signal spreading across the main lobe width. Because of this spreadingin the signal power, a gain correction factor must be used to accurately compute SNR. The processing loss assumes thefrequency of the test signal falls exactly in the middle of the frequency bin. Since the input frequency may not matchexactly the frequency bin in a non-coherent test setup, the scalloping loss is the perceived signal attenuation in the FFTwhen the signal frequency component falls exactly between bins. The worst-case processing loss is the sum of theprocessing loss and scalloping loss, and it provides a measure of the maximum SNR reduction due to the window functionand the worst-case frequency location.2

Conclusion

When evaluating the dynamic performance of precision ADCs using FFT analysis, coherent sampling provides the bestresults. In cases where coherent sampling cannot be achieved, a window function with low-side lobes is required to resolvethe noise and harmonic components in the frequency spectrum. For example, when using non-coherent sampling, the SNRand THD is estimated after applying an FFT window function and the processing loss correction factor.



References

1. Dominique Dallet and Jose Machado da Silva (2005), Dynamic characterization of analogue-to-digital converters,Dordrecht, the Netherlands: Springer, Chapter 4, pp. 86-88

2. Bores Signal Processing, FFT Window Functions: Limits on FFT Analysis, http://www.bores.com

3. Frederick J. Harris, On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform, Proceedingsof the IEEE, vol 66, pp. 51-83, January 1978

4. For more information about ADCs, visit www.ti.com/adc-ca

5. Need a trusted source to quickly find reference designs for your system design? TI Precision Designsis a library ofcomplete board- and system-level circuits designed to help engineers quickly evaluate and customize their systems whileexpanding their analog knowledge base: www.ti.com/precisiondesigns-ca.

Luis F. Chioye is an applications engineer with TIs Precision Analog group, where he is responsible for precision dataconverters. He received his BS in electrical engineering from the University of Arizona, Tucson, and his MS in electricalengineering from Walden University/NTU School of Engineering and Applied Science, Minneapolis, Minn. He can bereached at [email protected].

Source URL: http://electronicdesign.com/analog/choose-right-fft-window-function-when-evaluating-precision-adcs

fft for adc

Documents