  The electrical and optical properties of ordered passive arrays, constituted
of inductive and capacitive components, are usually deduced from Kirchhoff's
rules. Under the assumption of periodic boundary conditions, comparable results
may be obtained via an approach employing transfer matrices. In particular,
resonances in the dielectric spectrum are demonstrated to occur if all
eigenvalues of the transfer matrix of the entire array are unity. The latter
condition, which is shown to be equivalent to the habitual definition of a
resonance in impedance for an array between electrodes, allows for a convenient
and accurate determination of the resonance frequencies, and may thus be used
as a tool for the design of materials with a specific dielectric response. For
the opposite case of linear arrays in a large network, where periodic boundary
condition do not apply, several asymptotic properties are derived. Throughout
the article, the derived analytic results are compared to numerical models,
based on either Exact Numerical Renormalisation or the spectral method.
