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In gate-based dispersive sensing, the response of a resonator attached to a
quantum dot gate is detected by a reflected radio-frequency signal. This
enables fast readout of spin qubits and tune up of arrays of quantum dots, but
comes at the expense of increased susceptibility to crosstalk, as the resonator
can amplify spurious signals and induce fluctuations in the quantum dot
potential. We attach tank circuits with superconducting NbN inductors and
internal quality factors $Q_{\mathrm{i}}$>1000 to the interdot barrier gate of
silicon double quantum dot devices. Measuring the interdot transition in
transport, we quantify radio-frequency crosstalk that results in a ring-up of
the resonator when neighbouring plunger gates are driven with frequency
components matching the resonator frequency. This effect complicates qubit
operation and scales with the loaded quality factor of the resonator, the
mutual capacitance between device gate electrodes, and with the inverse of the
parasitic capacitance to ground. Setting qubit frequencies below the resonator
frequency is expected to substantially suppress this type of crosstalk.