  Superconducting quantum circuits must be designed carefully to avoid
dissipation from coupling to external control circuitry. Here we introduce the
concept of current transformation to quantify coupling to the environment. We
test this theory with an experimentally-determined impedance transformation of
$\sim 10^5$ and find quantitative agreement better than a factor of 2 between
this transformation and the reduced lifetime of a phase qubit coupled to a
tunable transformer. Higher-order corrections from quantum fluctuations are
also calculated with this theory, but found not to limit the qubit lifetime. We
also illustrate how this simple connection between current and impedance
transformation can be used to rule out dissipation sources in experimental
qubit systems.
