Current-voltage characteristic of a non linear resistor network

Experimental I(V) characteristics of a lattice are reported. Each bond of the lattice is a non linear resistor characterized by a threshold 03C5g for the potential drop below which it becomes an insulator. If the thresholds are randomly distributed, the current I flowing through the lattice is a quadratic function of the voltage V, as predicted by Roux and Herrmann. J. Physique 48 (1987) 1609-1611 OCTOBRE 1987, Classification Physics Abstracts 05.40 05.50 Recent studies of non linear two dimensional electrical networks have extended the range of application of problems of percolation type [1,2] . The interest is motivated in part by the analogy [3] between such electrical networks and mechanical or hydrodynamical two dimensional random media [4,5] . Recently, Roux and Herrmann [6] have calculated the currentvoltage characteristic I(V) of an electrical network where each bond is a non linear resistor characterized by a threshold value vg for the the potential drop below which it becomes an insulator. If the thresholds vg are randomly distributed, the current I flowing through the lattice of such bonds is a non linear function of the voltage V. The quadratic dependence observed then comes from the increasing number of passing bonds with applied voltage. In this note, the numerical results of reference [6] are illustrated by experimental measurements of the I( q characteristic of a non linear resistor network. Two dimensional square lattices tilted by 45° of m x n Zener diodes with m,n29 have been realized (Fig.l). The diodes are chosen among 7 different populations of 100 diodes and randomly distributed as the bonds of the network. A resistor (r=1000 0) is mounted in series with each diode. Figure 2 shows the I(V) characteristic of each of the seven kinds of diodes in series with r. The current is very small below the threshold vg and above vg it increases with an asymptotic resistance of 1000 il. The threshold values vg spread between 1V and 3V. The voltage across the network is measured as a function of the total bias current I. The I( V) characteristic of a 10 x 24 network is shown in the insert of figure 3. Below Vg = 20V, there is almost no current in the network. In an intermediate range of voltages, the curve is parabolic. It becomes linear at high voltage. This behavior can ° be seen in figure 3 where Ln I is plotted as a function of Ln (V Vg) : the slope of the curve changes from 2 at moderate voltages to 1 at high voltages. Fig.l.On each link of the square lattice shown are distributed at random a Zener diode in the forward direction and a lkfl resistance mounted in series. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198700480100160900