Measuring volterra kernels of analog-to-digital converters using a stepped three-tone scan

The Volterra theory can be used to mathematically model nonlinear dynamic components such as analog-to-digital converters (ADCs). This paper describes how frequency-domain Volterra kernels of an ADC are determined from measurements. The elements of the Volterra theory are given, and practical issues are considered, such as methods for signal conditioning and finding the appropriate test signals scenario and suitable sampling frequency. The results show that, for the used pipeline ADC, the frequency dependence is significantly stronger for second-order difference products than for sum products and the linear frequency dependence was not as pronounced as that of the second-order Volterra kernel. It is suggested that the Volterra kernels have the symmetry properties of a specific box model, namely, the parallel Hammerstein system.