with.Using the voltage parameter to construct a recursion model， this paper studies electrical characteristics，

including the node voltage，branch current and equivalent resistor etc.，a type of the complex n-order ladder shaped

resistor network，which has an external load on an arbitrary node and a random resistor on the right boundary.By　

means of the network analysis， this paper establishes the difference equation model of the voltage，and the equation

model of the boundary compatible with the constraint conditions.After then，explicit expressions of the common solution

and the particular solution are derived， from which the formulae of voltages of arbitrary nodes，branch currents，

and the equivalent resistors are also obtained.All the formulae obtained here have multi-functions and universality，

and many special cases.