Passive Networks and Their S-Matrix Constraints
A passive network dissipates no power (at most converts RF to heat — always less output than input). This constrains the S-matrix:
Passive (lossy or lossless):
Power dissipated = P_in − P_out = Σ|aᵢ|² − Σ|bᵢ|² ≥ 0
[S]†[S] ≤ [I] (S-matrix is sub-unitary or unitary)
Lossless passive (ideal filter, T-line):
[S]†[S] = [I] (unitary: no dissipation)
Example: |S₁₁|² + |S₂₁|² = 1 (all power either reflected or transmitted)
Reciprocal passive (filters, cables, lumped elements):
[S] = [S]ᵀ (symmetric matrix)
Sᵢⱼ = Sⱼᵢ for all i,j
Active Networks – Violating Passive Constraints
Active amplifier:
|S₂₁|² > 1 (gain > 0 dB → output power > input power)
Power comes from DC bias supply
Active amplifier is non-reciprocal:
|S₂₁| >> |S₁₂| (forward gain ≫ reverse isolation)
[S] ≠ [S]ᵀ (not symmetric)
Ferrite circulator/isolator:
Non-reciprocal passive: S₂₁ ≠ S₁₂ (directional property)
Power from magnetic bias — "passive" but not reciprocal
Practical S-Parameter Checks for Device Classification
| Device | Passive? | Reciprocal? | Check |
|---|---|---|---|
| SAW filter | Yes | Yes | S12=S21, |S11|²+|S21|²≤1 |
| RF attenuator | Yes (lossy) | Yes | S12=S21, |S11|²+|S21|²<1 |
| LNA | No (gain) | No | |S21|>>|S12|, S12≠S21 |
| Ferrite isolator | Yes | No | S21≈0 dB, S12≪0 dB |
| RF switch (ON) | Yes | Yes | S21=S12, low loss |
Why Reciprocity Matters
Reciprocal networks have S21=S12, meaning the device behaves identically whether you transmit signal from port 1 to port 2 or port 2 to port 1. Non-reciprocal devices (amplifiers, circulators) are directional — essential for amplifier chains (signal flows one way) and duplexer systems (TX power cannot leak into RX path).
RF View: Verify reciprocity by selecting S21 and S12 in RF View and checking if they overlay. Any difference indicates an active or non-reciprocal device in your measurement path.