  We present a design and implementation of frequency-tunable superconducting
resonator. The resonance frequency tunability is achieved by flux-coupling a
superconducting LC-loop to a current-biased feedline; the resulting screening
current leads to a change of the kinetic inductance and shift in the resonance
frequency. The thin film aluminum resonator consists of an interdigitated
capacitor and thin line inductors forming a closed superconducting loop. The
magnetic flux from the nearby current feedline induces Meissner shielding
currents in the resonator loop leading to change in the kinetic part of the
total inductance of the resonator. We demonstarte continuous frequency tuning
within 160 MHz around the resonant frequency of 2.7 GHz. We show that: (1)
frequency upconversion is achieved when kHz AC modulation signal is
superimposed onto the DC bias resulting in sidebands to the resonator tone; (2)
three-wave mixing is attained by parametrically pumping the nonlinear kinetic
inductance using a strong RF pump signal in the feedline. The simple
architecture is amenable to large array multiplexing and on-chip integration
with other circuit components. The concept could be applied in flux
magnetometers, upconverters, and parametric amplifiers operating above 4 Kelvin
cryogenic temperatures when alternative high critical temperature material with
high kinetic inductance is used.
