  We report the efficient coupling of a $50\,\Omega$ microwave circuit to a
high impedance conductor. We use an impedance transformer consisting of a
$\lambda/4$ co-planar resonator whose inner conductor contains an array of
superconducting quantum interference devices (SQUIDs), providing the resonator
with 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 noise
power emitted by a dc biased high resistance tunnel junction connected to the
resonator. We demonstrate matching to impedances in the $15$ to
$35\,\mathrm{k}\Omega$ range with bandwidths above $100\,\mathrm{MHz}$ around a
resonant frequency tunable in the $4$ to $6\,\mathrm{GHz}$ range.
