Definition
A network is reciprocal if the transmission coefficient between any two ports is identical regardless of which port is the source and which is the receiver:
Reciprocal: Sᵢⱼ = Sⱼᵢ for all i, j [S] = [S]ᵀ (transpose of S-matrix equals itself = symmetric matrix) Example (2-port reciprocal filter): S21 = S12 (forward IL = reverse IL — both measure the same thing!) S11 ≠ S22 (input match ≠ output match, unless also symmetric)
Why Passive Components Are Reciprocal
All passive components built from conductors, dielectrics, and capacitance/inductance without applied magnetic bias are reciprocal. This is a consequence of electromagnetic reciprocity (Lorentz reciprocity theorem) for materials with symmetric permittivity and permeability tensors.
Non-Reciprocal Devices
| Device | Why Non-Reciprocal | S12 vs S21 |
|---|---|---|
| Amplifier (LNA, PA) | Active device provides power gain one way | S21 >> S12 (isolation = S21−S12) |
| Ferrite circulator | Magnetized ferrite breaks EM reciprocity | S21 ≠ S12 by design |
| Ferrite isolator | Terminated circulator | S21 ≈ 0 dB, S12 < −20 dB |
| RF switch (asymmetric) | Sometimes due to active control element | S21 ≈ S12 for passive switches |
Verification in RF View
Load device .s2p → select S21 and S12 overlaid on same chart If S21 = S12 (traces coincide): reciprocal device (passive filter, cable, attenuator) If S21 ≠ S12 (traces different): non-reciprocal (amplifier, isolator, circulator) Reciprocity test: |S21_dB − S12_dB| < 0.1 dB → reciprocal to within measurement noise
RF View Reciprocity Check: Overlay S21 and S12 on the same chart — identical traces confirm reciprocity. Any difference immediately flags an active or magnetized component. Free on Android.