The resonant frequency of a superconducting planar resonator is depend
ent on the material properties and thicknesses of the superconductors,
the dielectric (substrate), and the buffer layers. In this article, w
e compute the first and second derivatives with respect to temperature
of a wave velocity ratio (with respect to free space) for various com
binations of material properties. The dependence of resonant frequency
on the dielectric constant and thicknesses of the substrate and buffe
r layers is discussed. An example of YBCO thin films on rutile with sa
pphire buffer layers was computed. From this example, it may be conclu
ded that, if a turning point can be realized at T = 60 K and the tempe
rature controlled to better than 0.1 mK, then frequency standards with
stabilities of parts in 10(15) should be attainable. (C) 1997 America
n Institute of Physics.