  We generalize solid-state tight-binding techniques for the spectral analysis
of large superconducting circuits. We find that tight-binding states can be
better suited for approximating the low-energy excitations than charge-basis
states, as illustrated for the interesting example of the current-mirror
circuit. The use of tight binding can dramatically lower the Hilbert space
dimension required for convergence to the true spectrum, and allows for the
accurate simulation of larger circuits that are out of reach of charge basis
diagonalization.
