Frequency Synchronization Circuit Model for Analog Vector-Matrix Multiplication in the Frequency Domain
Abstract
This work introduces a frequency synchronization circuit model for analog vector-matrix multiplication in the frequency domain. The frequency synchronization is implemented by coupling oscillators through all-to-all connections. Each oscillator is implemented using complementary cross-coupled transconductance pairs and RC high-pass filters. In this work, the frequency synchronization is achieved not only using oscillators alone but also through a configuration in which oscillators and resonator models (i.e., MEMS/NEMS resonators) are combined. While addressing the frequency synchronization of all the coupled oscillators, a partial synchronization is also discussed by controlling the coupling strength of a selected subset of oscillators. This frequency synchronization analysis focuses on the small-signal analysis using analog circuit and resonator models, thereby enabling an understanding of the synchronized frequency defined by the parameters of the analog circuit and resonator models.
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BibTeX
@misc{lee2026frequency,
title = {{Frequency Synchronization Circuit Model for Analog Vector-Matrix Multiplication in the Frequency Domain}},
author = {Taeju Lee and Scott T. Habermehl and Timothy W. Caplice and Michael L. Roukes and Philip X. -L. Feng and Kenneth L. Shepard},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27765},
eprint = {2608.27765},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27765},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Frequency Synchronization Circuit Model for Analog Vector-Matrix Multiplication in the Frequency Domain
AU - Taeju Lee
AU - Scott T. Habermehl
AU - Timothy W. Caplice
AU - Michael L. Roukes
AU - Philip X. -L. Feng
AU - Kenneth L. Shepard
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.27765
UR - https://arxiv.org/abs/2608.27765
AB - This work introduces a frequency synchronization circuit model for analog vector-matrix multiplication in the frequency domain. The frequency synchronization is implemented by coupling oscillators through all-to-all connections. Each oscillator is implemented using complementary cross-coupled transconductance pairs and RC high-pass filters. In this work, the frequency synchronization is achieved not only using oscillators alone but also through a configuration in which oscillators and resonator models (i.e., MEMS/NEMS resonators) are combined. While addressing the frequency synchronization of all the coupled oscillators, a partial synchronization is also discussed by controlling the coupling strength of a selected subset of oscillators. This frequency synchronization analysis focuses on the small-signal analysis using analog circuit and resonator models, thereby enabling an understanding of the synchronized frequency defined by the parameters of the analog circuit and resonator models.
ER -