  We propose a new quantization method for superconducting electronic circuits
involving a Josephson junction device coupled to a linear microwave
environment. The method is based on an exact impedance synthesis of the
microwave environment considered as a blackbox with impedance function Z(s).
The synthesized circuit captures dissipative dynamics of the system with
resistors coupled to the reactive part of the circuit in a non-trivial way. We
quantize the circuit and compute relaxation rates following previous formalisms
for lumped element circuit quantization. Up to the errors in the fit our method
gives an exact description of the system and its losses.
