What Is Resonance?

Resonance is the phenomenon in which a system driven by a periodic force responds with disproportionately large amplitude when the driving frequency approaches one of the system's natural frequencies. It arises wherever energy can move back and forth between two storage mechanisms with little loss, such as inductance and capacitance in an electrical circuit, mass and compliance in a mechanical oscillator, or magnetic moment and applied field in a spin system. The sharpness of the response is quantified by the quality factor Q, defined as 2π times the ratio of the energy stored in the system to the energy it dissipates per cycle of oscillation, and it determines both the amplification at resonance and the bandwidth over which the effect is significant.

Because the same mathematics describes oscillators in every physical domain, resonance appears across electrical engineering, magnetism, optics, acoustics, and power systems. Some forms are exploited as measurement tools, and others, notably in power networks, are hazards to be predicted and suppressed. In optics the effect appears as resonance light scattering, the sharp enhancement of elastic scattering that occurs when the illuminating wavelength falls near an absorption band of the scatterer, a signature used to detect aggregation of nanoparticles and biomolecules.

Nuclear Magnetic Resonance

Nuclear magnetic resonance occurs when nuclei with non-zero spin, placed in a static magnetic field, absorb radio frequency energy at the Larmor frequency, which is the product of the field strength and the nuclear gyromagnetic ratio. For the hydrogen nucleus that ratio is about 42.58 MHz per tesla, so a 14 tesla magnet puts proton resonance near 600 MHz. Small shifts in the resonance frequency caused by the local electronic environment, called chemical shifts, and the couplings between neighboring nuclei make NMR spectroscopy the primary method for determining molecular structure in solution. Higher field strength improves both spectral resolution and sensitivity, which is why user facilities such as the NMR and MRI program at the National High Magnetic Field Laboratory operate magnets well beyond commercial ratings. Spatial encoding of the same signal with magnetic field gradients produces magnetic resonance imaging.

Electron, Ferromagnetic, and Antiferromagnetic Resonance

Electron paramagnetic resonance, also called electron spin resonance, is the analogous effect for unpaired electron spins. The electron gyromagnetic ratio is roughly 660 times larger than that of the proton, placing resonance near 28 GHz per tesla and putting typical experiments in the microwave X band. The technique detects radicals, transition metal centers, and defect states, and facilities such as the magnetic resonance laboratory at Pacific Northwest National Laboratory apply it to catalysis and materials chemistry. In ferromagnets the individual spins precess collectively, and ferromagnetic resonance depends on sample shape through demagnetizing fields as well as on magnetocrystalline anisotropy, which makes it a standard method for measuring anisotropy constants and magnetic damping. Antiferromagnetic resonance involves two coupled sublattices, and the strong exchange field pushes its frequencies into the hundreds of gigahertz or the terahertz range, a property that motivates interest in antiferromagnetic spintronic devices.

Ferroresonance in Power Systems

Ferroresonance is a nonlinear resonance that occurs when a saturable iron-cored inductance, typically a transformer winding, is connected in series with a capacitance such as a cable, a grading capacitor, or line-to-ground capacitance. Because the inductance varies with flux, the circuit has no single resonant frequency: it can jump abruptly between operating states and settle into sustained fundamental, subharmonic, or chaotic oscillation. As surveyed in a review of ferroresonance in power distribution grids, the resulting overvoltages can approach or exceed twice rated peak voltage and persist indefinitely, damaging voltage transformers, surge arresters, and insulation. Mitigation relies on damping resistors, switching sequences that avoid single-phase energization, and careful circuit analysis during design.

Stochastic Resonance

Stochastic resonance is the counterintuitive result that adding noise to a nonlinear system can improve its response to a weak periodic signal. In a bistable system the noise drives transitions between states, and when the mean transition rate matches the signal period the output signal-to-noise ratio reaches a maximum at a non-zero noise intensity, a behavior analyzed in work on stochastic resonance for non-equilibrium systems. The effect has been identified in sensory neurons, climate models, superconducting quantum interference devices, and threshold detectors.

Applications

Resonance has applications in a wide range of disciplines, including:

• Magnetic resonance imaging and clinical diagnostics
• Molecular structure determination by NMR spectroscopy
• Materials characterization through electron and ferromagnetic resonance
• Filter, oscillator, and antenna design in radio frequency engineering
• Power system protection against ferroresonant overvoltage
• Weak-signal detection in noisy sensors and instrumentation