Single Split-Ring Resonator Design

Key Takeaways

• The metamaterials that are commonly used as miniaturized antennas and RF lenses follow subwavelength thin wires or split ring resonator design. The electric and magnetic dipoles generated in the wires and rings due to electromagnetic field interactions enable special properties in metamaterials.

• Split-ring resonators (SRRs) consist of two concentric metallic rings in a circular or square shape, etched on the dielectric substrate. They have splits or gaps at opposite ends. 

• The equivalent circuit of the single split resonator consists of inductance (L) and capacitance (C). The resonant frequency depends on the LC values and is given by: 

The artificially fabricated, low-dimensional structural inhomogeneities in metamaterials offer exceptional properties that are different from constituent materials. The electric and magnetic dipoles generated in the wires and rings due to electromagnetic field interactions enable special negative material properties in metamaterials, including electric permittivity, magnetic permeability, and refractive index. 

Due to these negative material properties, the electromagnetic wave propagation through metamaterials showcases new responses. The unique characteristics of metamaterials make them useful for building miniaturized antennas, RF lenses, and fast signaling channels between points. The metamaterials that are commonly used in communication systems follow subwavelength thin wires or split-ring resonator design. 

Split-Ring Resonators

Split-ring resonators (SRRs) consist of two concentric metallic rings in a circular or square shape, etched on the dielectric substrate. They have splits or gaps at opposite ends. The splits are the structural inhomogeneities that help the SRRs support resonant wavelengths much greater than the diameter of the rings. 

The capacitance formed by the splits in the rings is large in value. As the capacitance is inversely proportional to the resonant frequency, a large capacitance helps the resonator exhibit resonance at frequencies considerably greater than its dimension. The resonant wavelength is much higher than the dimension of the SRR, and therefore, quality improves. It can be summarized that the geometry of the SRR, its resonant frequency, and related properties are interdependent. 

Characteristics of SRRs

SRRs have the advantage of having low radiative losses. They have negative effective permeability at frequencies closer to the resonant frequency and have been used to make left-handed media with the negative refractive index. 

When a uniform, time-varying magnetic field is applied perpendicular to the rings, current loops at resonance are generated. The large capacitance from the splits completes the closed-loop for current circulation and the SRR behaves like an LC resonator. The current circulation and large capacitance supported by the resonance phenomenon reduces the electric size of the resonator. 

For smaller sizes and higher frequencies, the different dimensions and inter-element spacing between rings are implemented in SRRs. The variety of SRRs include nested split-rings, rod split-rings, spiral split-rings, deformed split-rings, and single split-rings. 

Equations to Know For Single Split-Ring Resonator Design

Double SRRs are in-demand in microwave and RF applications. They can be considered an advanced design of single SRRs. Even though the design equation and equivalent circuits of single and double split-rings are different, there are some similarities in their structures—most importantly, their split-ring geometry. 

The dimensions of the single split-ring structure include inner radius (R), height (h), thickness (w), and gap width (g). The equivalent circuit of the single split resonator consists of inductance (L) and capacitance (C). 

Resonant Frequency

The resonant frequency depends on the LC values and is given by: 

The shape of the split rings plays an important role in the properties of SRRs. Under a similar footprint, the frequency shift is different for circular, square, and hexagonal SRRs. The same shape effect is also seen on the equivalent L and C values, which are dependent on the dimensions of the split-rings. A variation of L and C can be made by modifying the SRR structure. 

Inductance 

For a single split-ring resonator, the inductance is dependent on the constructional parameters and is expressed as:

where  is the permeability of free space.

Capacitance

The two capacitances—gap capacitance and surface capacitance—can be given by equations (3) and (4), respectively:

where  is the permittivity of free space.

The total capacitance of the resonator is equal to

From the above equations, it is understood that by adjusting the length, width, radius, and height of single split-ring structures, we can create filters, oscillators, or mixers from SRRs that work perfectly at the specified resonant frequency.  

When it comes to RF applications, circuits such as demodulators, synthesizers, and mixers require filters and oscillators. Split-ring resonator design is suitable to be used in such circuits, due to its electrical properties and smaller foot-print. The capability to modify the resonant frequency by altering the structure is the biggest advantage of split-ring resonators. 

Consider a split-ring resonator if your application requires you to tune the resonant frequency. By optimizing split-ring resonator design, you can customize the resonant frequency of any application by simply adjusting the structure of the split-ring.