can be seen in Fig. \[fig:mschema\](c), a cryogenic circulator was used at the mixing chamber plate to separate the input signal from the signal reflected by the cavity. The circulator had an insertion loss of $0.35\ \textrm{dB}$. Finally, the connection between the PCB of the sample holder and the on-chip cavity input/output line was done with two aluminum wire bonds $25\ \mu\textrm{m}$ in diameter and roughly $2\ \textrm{mm}$ in length. These wire bonds cause impedance mismatch and as a result some reflection occurs at each end of the wire bond. The power which reaches the on-chip resonator cavity will be reduced due to this reflection, and the reduction in power can be expressed as an equivalent attenuation of $$10\cdot \log_{10}\left(\left[1 - \frac{|Z_w - 50\ \Omega|}{Z_w + 50\ \Omega}\right]^2\right)\ [\textrm{dB}],$$ where $Z_w \simeq \sqrt{\frac{L_w}{C_w}}$ is the wave impedance of the wire-bond connection, $L_w$ and $C_w$ are the inductance and the capacitance of the wire bond connection. The estimate of the inductance of each wire is $1.9\ \textrm{nH}$, and the capacitance of the wire is of the order of $25\ \textrm{fF}$. These values give $Z_w = 137\ \Omega$ for the two wire bonds, resulting in $10.8\ \textrm{dB}$ for the attenuation of the 