Quantifying the Maximum Phase-Distortion Error Introduced by Signal Samplers

Quantifying the errors introduced by signal sampler imperfections is of interest to people who are doing frequency domain measurements. The phase-distortion introduced by the sampler is hard to quantify and is usually neglected. In this article upper bounds for this phase-distortion error are derived which are based upon simple assumptions, namely that the sampler weighting function is strictly positive, that it is limited in time and that the function has only one local maximum. The theoretical limits are applied in order to specify the accuracy of a calibration procedure for broadband sampling oscilloscopes. Introduction Signal samplers are a very important part of waveform digitizers. Quantifying the errors introduced by the signal sampler imperfections is necessary in order to specify these instruments. A measurement error which is hard to quantify and which is of particular interest to people who are doing frequency domain measurements is the phase-distortion introduced by the signal sampler. In this paper upper bounds for a signal sampler phase-distortion error are derived which are based upon simple assumptions. First, it is assumed that the sampler is linear such that it is completely characterized by a weighting function p(t). Note that p(t) describes the mathematical relationship between the input signal x(t) and the sampled value q at sampling instant T by means of the following relationship: . (1) In practice, it is often impossible to measure p(t) directly. Some assumptions concerning the shape of p(t) can be made, however, resulting in upper bounds for the phase-distortion error. First, an upper bound is calculated based upon the assumption that p(t) is strictly positive and is limited in q T ( ) p t T – ( )x t ( ) t d ∞ – ∞ ∫ =