Analysis of time delay difference due to parametric mismatch in matched filter channels

Abstract

SUMMARYThis paper presents an analysis of the time delay difference between the outputs of two matched filter channels, in the presence of parametric mismatch. A theorem for computing the cross-correlation value between two signals is developed. From the cross-correlation theorem, expressions are developed that estimate the effect of parametric mismatch in the differential time delay (DTD) for filters of arbitrary type and order and input signals of arbitrary form. The accuracy of these expressions is simulated and then demonstrated experimentally using a carefully designed setup. Filter design considerations that attempt to minimize spurious DTD in high-precision time delay estimation systems are presented.

Matched dual-channel front-end preamplifier for differential time delay measurements

“…Following the developments in [6], the time domain waveforms were acquired and the cross-correlation operation was performed on them to estimate the DTD. For each frequency value, 20 cycles of the output waveforms were acquired with a time resolution of 1 × 10 6 points per cycle.…”

“…For instance, the data used to evaluate three different architectures [1][2][3], with the physical setup described in [7], was collected using a first-order lowpass filter (f c ¼ 300Hz) preamplifier with off-the-shelf 5% tolerance components. According to [6], this produces ideally a worst-case 26 ms DTD at low frequencies. Further refinements using 1% tolerance resistors and 2% tolerance capacitors, reduced the worst-case DTD to 7.9 ms.…”

“…Several miniature systems based on integrated circuits (ICs) have been proposed in the literature [1][2][3][4][5]. As shown in [6], the parametric mismatch of the front-end filters introduces a frequency dependent differential time delay (DTD) that can mask the intrinsic DTD of the signals, introducing a frequency dependent error to the spatial localisation accuracy. For instance, the data used to evaluate three different architectures [1][2][3], with the physical setup described in [7], was collected using a first-order lowpass filter (f c ¼ 300Hz) preamplifier with off-the-shelf 5% tolerance components.…”

Analysis of mismatch impact on image rejection ratio for passive polyphase filters

“…4 However, only an IRR of 20 dB is obtained if, due to temperature and process variations, there is a change of 20% in passive components. 5 In the same way, mismatch seriously limits the passive filter performance, 6 as it does in active filters based on balanced structures.…”