DSP Tricks: A/D converter testing techniques and finding missing codes in ADCs
Digital signal processing techniques are often useful in testing of A/D converters. Here are two schemes for measuring converter performance; first, a technique using the Fast Fourier Transform (FFT) to estimate overall converter noise, and second, a histogram analysis scheme to detect missing converter output codes.
Estimating A/D Quantization Noise
with the FFT
The combination A/D converter quantization noise, missing bits, harmonic distortion, and other nonlinearities can be characterized by analyzing the spectral content of the converter's output.
Converter performance degradation caused by these nonlinearities is not difficult to recognize because they show up as spurious spectral components and increased background noise levels in the A/D converter's output samples.
We can use the FFT to compute the spectrum of an A/D converter's output samples, but we have to minimize FFT spectral leakage to improve the sensitivity of our spectral measurements. Traditional time-domain windowing, however, provides insufficient FFT leakage reduction for high performance A/D converter testing.
|Figure 13"22 Ideal A/D converter output when the input is an analog 8fs/128 Hz sinusoid: (a) output time samples; (b) spectral magnitude in dB.|
The trick to circumventing this FFT leakage problem is to use an sinusoidal analog input voltage whose frequency is an integer fraction of the A/D converter's clock frequency as shown in Figure 13"22(a) above. That frequency is mfs/N, where m is an integer, fs is the clock frequency (sample rate), and N is the FFT size.
Figure 13"22(a) shows the x(n) time domain output of an ideal A/D converter when its analog input is a sinewave having exactly eight cycles over N = 128 converter output samples.
In this case, the input frequency normalized to the sample rate fs is 8fs/128 Hz. Recall that the expression mfs/N defines the analysis frequencies, or bin centers, of the discrete Fourier Transform (DFT), and a DFT input sinusoid whose frequency is at a bin center causes no spectral leakage.
The first half of a 128-point FFT of x(n) is shown in the logarithmic plot in Figure 13"22(b) above where the input tone lies exactly at the m = 8 bin center and FFT leakage has been sufficiently reduced. Specifically, if the sample rate were 1 MHz, then the A/D's input analog tone would have to be exactly 8(106/128) = 62.5 kHz.
In order to implement this scheme we need to ensure that the analog test generator be synchronized, exactly, with the A/D converter's clock frequency of fs Hz. Achieving this synchronization is why this A/D converter testing procedure is referred to as coherent sampling.
That is, the analog signal generator and the A/D clock generator providing fs must not drift in frequency relative to each other—they must remain coherent. (We must take care here from a semantic viewpoint because the quadrature sampling schemes are also sometimes called coherent sampling, and they are unrelated to this A/D converter testing procedure.)
|Figure 13"23 Seven-cycle sinusoidal A/D converter output.|
As it turns out, some values of m are more advantageous than others. Notice in Figure 13"22(a), that when m = 8, only nine different amplitude values are output by the A/D converter. Those values are repeated over and over. As shown in Figure 13"23 above, when m = 7 we exercise many more than nine different A/D output values.