  Designing superconducting electronic devices involves a careful study of all
the elements in the circuit, including the superconducting bias leads, however,
the effect of the bias current leads on the performance of the device have not
been previously addressed. In this work, we introduce a theoretical model for
two-dimensional superconducting quantum interference device (SQUID) arrays
capable of simulating the response of devices with different bias current
configurations. First, we compare uniformly biased and centre biased SQUID
arrays by investigating the voltage versus magnetic flux response, maximum
transfer function and voltage modulation depth. Then, we calculate the
time-averaged fluxoid distributions for 1D and 2D centre biased arrays.
Finally, we study the performance of the two bias current configurations
depending on array size, screening parameter, thermal noise strength and
kinetic self-inductance fraction. Our calculations reveal: (i) centre biased 1D
parallel SQUID arrays present an unusual voltage response caused by the
asymmetric fluxoid distribution; (ii) the optimal transfer function of centre
biased arrays strongly depends on the number of junctions in parallel; (iii)
the performance of centre biased arrays approaches the uniform biased ones when
the number of junctions in series exceeds those in parallel; (iv) while the
screening parameter and the thermal noise strength clearly affect the device
performance, the kinetic self-inductance fraction seems to play only a
secondary role.
