# Tunable Bandpass Filtering in Coupled Nanodrums Enabled by 1:1 Internal Resonance

## TL;DR

Researchers developed a new way to tune high-frequency nanoelectromechanical systems using internal resonance, allowing for precise control of bandpass filters.

## Contribution

The study introduces a gate-programmable tuning strategy for NEMS using 1:1 internal resonance, enabling high-frequency and wide-range reconfigurable bandpass filtering.

## Key findings

- Theoretical analysis shows up to 200% programmability in frequency tuning using 2D materials like MoS2.
- A three-drum system achieves a 21.79 kHz bandwidth, nearly four times wider than a two-drum system under the same conditions.
- Fine bandwidth control is achieved with mV-level bias mismatch, enabling sensitive trimming of the passband.

## Abstract

In recent years, microelectromechanical systems (MEMS) filters exploiting structural nonlinearity and coupled resonance have enabled programmable passband shaping beyond traditional single-peak designs, yet they still face low operating frequencies and limited electrical tuning range. Here, leveraging 1:1 internal resonance, we propose a gate-programmable tuning strategy for two-dimensional (2D) material-based nanoelectromechanical systems (NEMS), enabling high-frequency operation and wide-range reconfigurability. Benefiting from the high resonant frequency and wide electrostatic tunability of 2D materials such as MoS2, our theoretical analysis indicates wide-range programmability up to f/f0≈200%. Sweeping Vg1=Vg2 from 9 to 16 V while maintaining ≈1:1 frequency matching shifts the passband upward quasi-linearly at 4.4~MHz/V. In contrast, with the coupling strength nearly unchanged, mV-level bias mismatch perturbs the frequency ratio by 10−5, enabling highly sensitive bandwidth trimming from 3.18 to 5.20 kHz, supporting a two-step strategy of coarse center-frequency tuning followed by fine bandwidth control. To broaden the bandwidth, we further analyze a three-drum case: with Vg1=Vg2=Vg3=16 V, the bandwidth reaches 21.79 kHz with a 5056.05 dB/MHz transition slope and 0.95 dB ripple, which is nearly 4 times wider than the two drum case with the same gate voltage. This study shows that 1:1 internal resonance can be used to tune the bandpass response of NEMS resonators. All results are obtained from theoretical modeling and numerical simulations.