antimetric
The converse of symmetric in electrical network theory, especially filter theory. A network where the input and output image impedances are the dual, or inverse, of each other as opposed to symmetric networks where they are equal.
antimetric: mismatched impedance by design
An antimetric network is a two-port electrical network in which the image impedances seen at the input and output ports are reciprocals of each other, rather than equal. If the input image impedance is Z, the output image impedance will be 1/Z (in normalized units) or k/Z where k is a scaling constant. This property makes antimetric networks fundamentally different from symmetric networks, which present identical image impedances at both ports.
Antimetric construction appears most commonly in filter design, particularly in the synthesis of lattice filters and bridge networks. A classic example is the antimetric T-section filter, where series and shunt elements are configured so that the network transforms impedance in a predictable way. This impedance transformation is often deliberate: the network acts as an impedance converter or matching device in addition to performing frequency selectivity. The mathematical relationship between input and output impedances makes antimetric networks useful for cascading stages with different characteristic impedances.
Why the construction matters
Antimetric filters require careful calculation of component values because the impedance transformation must be precise. Unlike symmetric networks, where identical construction at both ends simplifies analysis, antimetric designs demand that series and shunt branches be deliberately unequal. This asymmetry is not a tolerance issue but a deliberate feature. The network will not function as intended if treated as symmetric.
In practice, antimetric networks are less commonly encountered than symmetric or cascaded symmetric designs, partly because symmetric networks are easier to analyze and because modern filter synthesis often relies on direct numerical optimization. However, antimetric networks remain important in specialized applications: impedance transformation, certain types of equalizers, and frequency-dependent impedance matching where the transformation ratio itself carries information or function.
The term reflects the strict terminology of network theory. Metric refers to measurement and comparison; symmetric networks have matching metrics at both ports, while antimetric networks have metrics that are opposites or reciprocals. Care is needed not to confuse antimetric with unbalanced or asymmetric in the colloquial sense: an antimetric network can be perfectly balanced electrically while remaining antimetric in its image impedance property.