  We develop a two-dimensional (2D) Superconducting Quantum Interference Filter
(SQIF) array based on recently introduced high-linearity tri-junction
bi-SQUIDs. Our bi-SQUID SQIF array design is based on a tight integration of
individual bi- SQUID cells sharing inductances with adjacent cells. We provide
extensive computer simulations, analysis and experimental measurements, in
which we explore the phase dynamics and linearity of the array voltage
response. The non-uniformity in inductances of the bi-SQUIDs produces a
pronounced zero-field single antipeak in the voltage response. The anti-peak
linearity and size can be optimized by varying the critical current of the
additional junction of each bi-SQUID. The layout implementation of the tight 2D
array integration leads to a distinct geometrical diamond shape formed by the
merged dual bi-SQUID cells. Different size 2D arrays are fabricated using
standard HYPRES niobium 4.5 kA/cm2 fabrication process. The measured linearity,
power gain, and noise properties will be analyzed for different array sizes and
the results will be compared with circuit simulations. We will discuss a design
approach for the electrically small magnetic field antenna and low-noise
amplifiers with high bandwidth based on these 2D bi-SQUID SQIF arrays. The
results from this work will be used to design chips densely and completely
covered in bi-SQUIDs that has optimized parameters such as linearity and power
gain.
