In linear, passive, time‑invariant and non‑magnetized electromagnetic media (reciprocal media), the transfer relation between two points or ports is symmetric: the response (field, voltage or scattering parameter) measured at point B due to a source at A equals the corresponding response at A when the same source is placed at B, under the same loading and excitation conditions.

Principle

Source and observation points can be interchanged without changing the measured linear transfer in reciprocal systems; S21 = S12 and Green's functions are symmetric under the reciprocity conditions.

Demonstration

Illustrative measurement → Two matched antennas in a reciprocal medium are connected to a network analyser to measure S21. Recognition → Replace transmitter and receiver positions and repeat measurement. Action → Compare S21 and S12 under the same matching and excitation. Consequence → Measured S21 ≈ S12 (within measurement error), allowing one direction's measurement to substitute for the other.

Misapplication

Assuming reciprocity in systems containing magnetized materials (biased ferrites), active devices that inject power or time‑varying elements, or in nonlinear components; these break the symmetry and invalidate interchangeability assumptions.

Consequence

Reciprocity reduces measurement burden and simplifies antenna and network design by guaranteeing symmetric transmission between ports in passive linear systems; it constrains admissible network responses and simplifies modelling.

Reversal

Reciprocity fails for non‑reciprocal media or components (magneto‑optic materials, biased ferrites, circulators), for active/time‑varying circuits, or when system conditions (matching, loading, bias) differ between source placements.

Boundary

Applies when the system is linear, passive, time‑invariant, and reciprocal (no magnetic bias or gyrotropy); ports must be equivalently defined and matched. Does not apply to nonlinear, active, time‑variant, or magnetically biased systems.

Semantic Tension

Reciprocity versus intentional isolation — designers rely on reciprocity for symmetry and measurement, but practical devices often require nonreciprocity (isolation, routing), which must be produced by breaking reciprocity intentionally.

Synthesis

Reciprocity is a structural symmetry of passive linear EM systems that both simplifies analysis and constrains design: achieving asymmetric behaviors (isolation, one‑way transfer) requires explicit nonreciprocal elements or time‑variance.