It is easy to see that the MDKC of Figure 3.6(a) will be MD-passive if the inductances and , and consequently the port resistances and of the MDWDF in Figure 3.6(b) are non-negative. From (3.54), this gives a constraint on , the space step/time step ratio, namely that we must have
It is important to mention, however, that the instances of the MDWDF, sampled at every grid point as in Figure 3.7 are not connected port-wise, as must be true for a traditional lumped WD-network. The output wave at the bottom port at spatial location is sign-inverted and then sent as input to the same port, at location at the next time step. Thus the realization of Figure 3.7 can not be analyzed directly as a chain of lumped elements; passivity follows from the multidimensional representations shown in Figure 3.6.