In this work we study the localization properties of the disordered classical dual transmission lines, when the values of capacitances {C-j} and inductances {4} fluctuate in phase in the form C-j= C-0+b sin(2 pi x(j)) and L-j= L-0+b sin(2 pi x(j)), where b is the fluctuation amplitude. {x(j)} is a disordered long-range correlated sequence obtained using the Fourier filtering method which depends on the correlation exponent alpha. To obtain the transition point in the thermodynamic limit, we study the critical behavior of the participation number D. To do so, we calculate the linear relationship between In(D) versus In(N), the relative fluctuation eta(D) and the Binder cumulant BD. The critical value obtained with these three methods is totally coincident between them. In addition, we calculate the critical behavior of the normalized localization length Lambda(b) as a function of the system size N. With these data we build the phase diagram (b,alpha) which separates the extended states from the localized states. A final result of our work is the disappearance of the conduction bands when we introduce a finite number of impurities in random sites. This process can serve as a mechanism of secure communication, since a little alteration of the original sequence of capacitances and inductances, can destroy the band of extended states. (C) 2013 Elsevier BY. All rights reserved.