Electrically tunable terahertz filter based on single split-ring resonators integrated with graphene

We present a compact, electrically reconfigurable terahertz (THz) filter based on a single split-ring resonator (SRR) bridged by gate-tuned graphene ribbons. By varying the graphene Fermi level from 0 to 1.5 eV, we continuously modulate the SRR's gap capacitance and realize a reversible blue-shift of the LC resonance from 1.19 to 2.50 THz (, 109% relative tuning). Full-wave simulations predict modulation depths above 98% at zero bias and exceeding 94% across the entire tuning range, with Δf≈1.30THz depth at both the low- and high-voltage extremes. The resonance quality factor evolves from at 0 eV into a critically damped broadband state ( for 0.05-0.4 eV), before recovering to at 1.5 eV. Group-delay measurements reveal gate-programmable dispersion, enabling both slow-light operation (slow-light ) and a flat, low-latency response in the critically damped regime. An equivalent RLC circuit model-parametrized by simulated S-parameters-captures the frequency shift and insertion loss within 2% error, confirming that gap-capacitance modulation and bias-dependent graphene absorption govern device performance. Field analysis further shows a smooth transition from a capacitive LC mode to a conductive-bridge resonance, underpinning the device's ultra-broad tuning range and voltage-controllable Q-factor. Our single-element design sets a new benchmark, to our knowledge, for dynamically tunable THz filters and is immediately applicable to 6G transceivers, hyperspectral imagers, and adaptive sensing platforms requiring high spectral agility and rapid electronic control.