Precision Measurement System of High-Frequency Signal Based on Equivalent-Time Sampling

Abstract

A high frequency periodic signal measurement system based on equivalent sampling method is developed. A high-speed sampling voltage tracking circuit, the core component of the system, is described in detail. The circuit can transform the amplitude corresponding to different phase points of the signal undertest into the equivalent DC level through successive approximation of multiple periods. The measurement system designed in this paper completes digital sampling with high accuracy only by connecting the low-cost voltage tracking circuit to the existing commercial instruments, such as two-channel waveform generator and high-precision digital multimeter, which makes the method easy to be generalized. The special structure of the sampling tracking circuit greatly reduces the influence of random noise and time jitter on the measurement results. The experimental results show that the non-linearity error of the system is as low as 0.002%, the bandwidth can reach 200 MHz, and the uncertainty of measuring the RMS of AC voltage with peak value of ±1 V and frequency of 10 kHz, 100 kHz and 1 MHz can reach 2.8 × 10−4 V, 4.6 × 10−4 V and 2.0 × 10−4 V (k = 2), respectively.

Minimal Required Resolution to Capture the 3D Shape of the Human Back—A Practical Approach

“…The Nyquist theorem only holds true for a perfect signal, and thus, in practice, an oversampling with respect to the minimal required resolution is required. In the literature, an oversampling of at least five times the required sampling frequency is recommended for similar practical applications [ 31 , 32 , 33 , 34 , 35 ]. This level of oversampling leads to a required sampling frequency ten times higher than the highest frequency of interest.…”

“…With a cut-off frequency of 0.05 mm −1 , the error remains small (0.13 mm). Applying a five- Some studies propose a practical oversampling of five times (×5) for similar applications [31][32][33][34][35]. With this, the required sampling frequency is 1 mm −1 , which translates to one sampling point every millimeter (oversampling of at least five times leads to a frequency that is ten times higher).…”