Why S-Parameters Cannot Be Directly Added
Unlike dB values (which add for simple series losses), S-parameters are complex wave quantities. You cannot simply multiply |S21_A| × |S21_B| for the total S21 of two cascaded networks because of impedance interactions at the junction. The correct method is ABCD matrix multiplication.
Cascade Procedure: ABCD Method
Step 1: Convert each S-parameter set to ABCD matrix: A = (1+S11)(1−S22)/(2S21) + S12·S21/(2S21) ... (full formula for bilateral network) Simplified for 50Ω system: A = (S11 + S22 + 1 − S12·S21) / (2·S21) × ... (Z₀-normalized) Step 2: Multiply ABCD matrices: [ABCD_total] = [ABCD₁] × [ABCD₂] × [ABCD₃] × ... Step 3: Convert back to S-parameters: S11 = (A + B/Z₀ − C·Z₀ − D)/(A + B/Z₀ + C·Z₀ + D) S21 = 2/(A + B/Z₀ + C·Z₀ + D)
Numerical Example: LNA + Filter Cascade
LNA at 1.8 GHz:
S11=0.1∠−150°, S21=8.0∠45°, S12=0.03∠10°, S22=0.15∠−120°
Filter at 1.8 GHz (passband):
S11=0.15∠170°, S21=0.8∠−30°, S12=0.8∠−30°, S22=0.15∠170°
After ABCD cascade multiplication:
Total S21 ≈ S21_LNA × S21_filter / (1 − S22_LNA × S11_filter)
≈ 8.0 × 0.8 / (1 − 0.15 × 0.15) (simplified for well-matched)
≈ 6.4 / 0.978 = 6.54 → 16.3 dB
Note: 18 dB + (−1.9 dB) ≠ 16.3 dB — interaction term is significant!
Without cascade correction: 15.1 dB (incorrect by 1.2 dB)
Quick Method: RF View Circuit Simulator
RF View handles all ABCD mathematics automatically:
- Load LNA as S2P block → Load filter as S2P block
- Place filter block after LNA in the chain
- Simulate → RF View computes exact cascaded S-parameters
- No manual ABCD conversion needed
RF View Cascade Simulation: Load multiple S2P blocks in sequence — RF View automatically cascades them using exact ABCD multiplication. Handles all port impedance interactions. Free on Android.