  Continued fractions are classical representations of complex objects (for
example, real numbers) as sums and inverses of simpler objects (for example,
integers). The analogy in linear circuit theory is a chain of series/parallel
one-ports: the port behavior is a continued fraction containing the port
behaviors of its elements. Truncating a continued fraction is a classical
method of approximation, which corresponds to deleting the circuit elements
furthest from the port. We apply this idea to chains of series/parallel
one-ports composed of arbitrary nonlinear relations. This gives a model
reduction method which automatically preserves properties such as incremental
positivity. The Scaled Relative Graph (SRG) gives a graphical representation of
the original and truncated port behaviors. The difference of these SRGs gives a
bound on the approximation error, which is shown to be competitive with
existing methods.
