Consider again the Timoshenko system of (5.17) and (5.18). We can scale the variables just as for the transmission line (see §3.7). That is, we can write


The constant proportional terms on the righthand side appear antisymmetrically, and can be interpreted as a lossless gyrator coupling. We can now write down a MDKC for the scaled system of equations; it is shown, along with element values in Figure 5.5. Its MDWD counterpart is pictured in Figure 5.6. Here, we have used the coordinate transformation defined in (3.18) with step sizes . We have used for the oneport time inductors.
An MDWD network can obviously also be designed to operate on alternating grids, just as in the case of the (1+1)D transmission line.A comment is necessary regarding the gyrator in Figure 5.6. In order to deal with the delayfree loop which arises from the placement of a gyrator between two series junctions, we have set the corresponding ports of the series junctions on either side of the gyrator to be reflectionfree. This, however, means that the two port resistances of the gyrator are not, in general, equal to the gyrator constant, which, in this case, will be . In terms of wave variables, the signal flow diagram of the gyrator will not be of the simple form of (2.26), but takes the more general form of (2.25) mentioned in §2.3.4. It is of course also possible to set only one of the ports connected to the gyrator to be reflectionfree, (say ), and then the other port resistance to be , in which case the general gyrator form degenerates to a pair of scalings.
As for the parameters and , an optimal choice can be shown to be