We report the efficient coupling of a $50\,\Omega$ microwave circuit to ahigh impedance conductor. We use an impedance transformer consisting of a$\lambda/4$ co-planar resonator whose inner conductor contains an array ofsuperconducting quantum interference devices (SQUIDs), providing the resonatorwith a large and tunable lineic inductance $\mathcal{L}\sim 80 \mu_0$,resulting in a large characteristic impedance $Z_C\sim 1\,\mathrm{k}\Omega$.The impedance matching efficiency is characterized by measuring the shot noisepower emitted by a dc biased high resistance tunnel junction connected to theresonator. We demonstrate matching to impedances in the $15$ to$35\,\mathrm{k}\Omega$ range with bandwidths above $100\,\mathrm{MHz}$ around aresonant frequency tunable in the $4$ to $6\,\mathrm{GHz}$ range.
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