Antimetric electrical network

The term is often encountered in filter theory, but it applies to general electrical network analysis.

Antimetric is the diametrical opposite of symmetric; it does not merely mean "asymmetric" (i.e., "lacking symmetry").

However, the network resulting from the application of Bartlett's bisection theorem[2] applied to the first T-section in each network, as shown in figure 3, are neither physically symmetric nor antimetric but retain their electrical symmetric (in the first case) and antimetric (in the second case) properties.

[3] The conditions for symmetry and antimetry can be stated in terms of two-port parameters.

For instance, a low-pass Butterworth filter implemented as a ladder network with an even number of elements will be antimetric.

Figure 1. Examples of symmetry and antimetry: both networks are low-pass filters but one is symmetric (left) and the other is antimetric (right). For a symmetric ladder the 1st element is equal to the n th, the 2nd equal to the ( n -1)th and so on. For an antimetric ladder, the 1st element is the dual of the n th and so on.
Figure 2. Adding another T-section to the ladders of figure 1
Figure 3. Examples of symmetric (top) and antimetric (bottom) networks which do not exhibit topological symmetry nor antimetry.