Temperature Dependence of Resonances in Metamaterials

Metamaterials are increasingly being proposed for many different microwave applications. Metamaterials are highly resonant structures and metamaterial device design is based on the resonance frequency for both civilian and military applications. These applications are often in a high-temperature environment. In this paper, we have performed an experimental study of the shift in resonance frequency of selected metamaterials (split-ring resonators and thin wires) in the 25°C -400°C range using FR4 and low-temperature co-fired ceramic substrates. We have provided a theoretical explanation for the observed shift in resonance frequency by calculating the shift in frequency resulting from the temperature dependence of the substrate permittivity and electrical conductivity of the metal, as well as thermal expansion of the metallo-dielectric structures comprising the metamaterial. The measured downward shift of the resonance frequency with increasing temperature agrees very well with full-wave finite-element simulation. It is found that the change of permittivity of the substrate is the primary effect, while the thermal expansion of the metallic structure is a secondary effect. The reducing resonance strength is due to the decrease in electrical conductivity with rising temperature. This study can be applied to other metamaterial metallo-dielectric structures or other planar microwave resonators printed on dielectric substrates.