Generalized Mathematical Model of Electric Firing Circuits and its Analysis

In this paper we analyze the universal mathematical model of the electric firing circuit representing its constituent parts in the form of quadrupoles connected to each other. By means of this model we analyze the state of the electric firing circuit effected by the four most frequently encountered factors: direct current, alternating current, exponential effect, generalized effect. We have calculated the transmission coefficients for current and voltage for this circuit based on which we have determined the dependence for current distribution between the electric detonators in the circuit and the probabilities of their activation. The maximum possible number of simultaneously initiated electric detonators is determined. A numerical example of calculation is given. Practical recommendations on the design of blasting devices, on the optimal electromagnetic compatibility of the electric firing circuit, as well as on increasing the safety and reliability of blasting operations are given.