  Thin-film superconducting transmission lines play important roles in many
signal transmission and detection systems, including qubit coupling and
read-out schemes, electron spin resonance systems, parametric amplifiers, and
various ultra high sensitivity detectors. Here we present a rigorous method for
computing the electromagnetic behaviour of superconducting microstrip
transmission lines and coplanar waveguides. Our method is based on conformal
mapping, and is suitable for both homogeneous superconductors and
proximity-coupled multilayers. We also present an effective conductivity
approximation of multilayers, thereby allowing the multilayers to be analysed
using existing electromagnetic design software. We compute the numerical
results for Al-Ti bilayers and discuss the validity of our full computation and
homogeneous approximation.
