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The resonant frequency of a superconducting planar resonator is dependent on the material properties and thicknesses of the superconductors, the dielectric ͑substrate͒, and the buffer layers. In this article, we compute the first and second derivatives with respect to temperature of a wave velocity ratio ͑with respect to free space͒ for various combinations of material properties. The dependence of resonant frequency on the dielectric constant and thicknesses of the substrate and buffer layersdoi:10.1063/1.1148325 fatcat:ypad4wj65jbvdenquyrsjherqu