Dynamic Testing of A/D Converters Using the Multiple Coherence Function

The multiple coherence function is utilized to dynamically test an arbitrary number of A/D converters that all sample the same signal. Based on the multiple-channel coherent removal method that has been popularized by Bendat and Piersol, the residual spectrum for each A/D converter under test is determined by removing the portion of the signal that can linearly be predicted by the remaining channels. Following accepted practice, the multiple coherence function is calculated from cross-spectral densities by using the Welch periodogram method. The acquisition channel of each A/D converter is modeled using an equivalent noise source model. The residual spectrum of any particular channel, which is expressed in terms of the equivalent noise sources, is determined to be the converter noise of the particular channel plus the parallel combination of the converter noise of the remaining channels. The resulting set of equations can iteratively be solved, yielding the converter noise of every channel under test. Broadband test signals are recommended so that close-to-unity coherence is achieved throughout the frequency band. When sine waves are used, the requirement for a sine wave of high spectral purity is eliminated, similar to the requirement for sidelobe suppression that uses data windowing or coherent sampling (acquiring an integer number of oscillations). Since the method confirms both synchronization and resolution, it is well suited to simultaneously test sampled multiple-channel data acquisition cards. Testing results with white noise and sine-wave signals that use an eight-channel 24-bit data acquisition card, which is synchronized with a four-channel, 16-bit data acquisition card, are presented and compared to the signal-to-noise-and-distortion ratio (SINAD) testing procedure. This procedure estimates converter noise by removing all harmonic content that can linearly be predicted by the remaining channels. With sine waves of sufficient amplitude, the removed harmonic content includes harmonic distortion that was created in the A/D converter process. For broadband test signals and small-amplitude sine waves, harmonic distortion that is created in the A/D converter process is negligible compared to the converter noise.