Self-similar solution of distributed linear and nonlinear networks

The method of "self-similar solution of partial differential equations" is introduced and applied to the distributed RGC network. For linear networks convolution integrals,
V(x,t) = V_{\delta} \times V_{source}
and
V(x,t) = V_{\delta'} \times I_{source}
are obtained where
V_\delta
and
V_\delta'
are, respectively, the responses to the
\delta
function voltage and current sources found and from the self-similar analysis, and
V_source
and
I_{source} \propto \partial V_{source}/\partial x
are arbitrary voltage and current sources. For certain sources, these integrals have been performed and the results will be presented. The technique is also successfully applied to nonlinear networks which are useful in modeling various microelectronic circuit components.