Realizability and synthesis for infinite grids of positive resistances

A semi-infinite resistive grid can be characterized from its boundary conditions by a certain function
F(z)
of the complex variable
z
. We establish herein both pole-zero and pole-residue realizability conditions that insure that
F(z)
does represent a resistive grid. We also show how that grid can be synthesized from a realizable
F(z)
. These results are established for both two-dimensional and three-dimensional grids.