When to Convert from S to Z or Y
S-parameters are ideal for high-frequency measurements (matched ports). Z and Y parameters become useful when: combining networks that share ports, using SPICE models that require Z/Y, or performing noise analysis where Z-parameters relate directly to noise voltage and current sources.
S → Z Conversion (2-Port)
Δ_S = (1 − S11)(1 − S22) − S12·S21 Z11 = Z₀·(1 + S11)(1 − S22) + S12·S21) / Δ_S Z12 = Z₀·2·S12 / Δ_S Z21 = Z₀·2·S21 / Δ_S Z22 = Z₀·(1 − S11)(1 + S22) + S12·S21) / Δ_S For reciprocal network: Z12 = Z21 (and S12 = S21) For symmetric network: Z11 = Z22 (and S11 = S22)
S → Y Conversion (2-Port)
Δ_S = (1 + S11)(1 + S22) − S12·S21 Y11 = (1/Z₀) · (1 − S11)(1 + S22) + S12·S21) / Δ_S Y12 = (1/Z₀) · (−2·S12) / Δ_S Y21 = (1/Z₀) · (−2·S21) / Δ_S Y22 = (1/Z₀) · (1 + S11)(1 − S22) + S12·S21) / Δ_S
Reverse: Z → S Conversion
S11 = ((Z11−Z₀)(Z22+Z₀) − Z12·Z21) / ((Z11+Z₀)(Z22+Z₀) − Z12·Z21) S21 = 2·Z₀·Z21 / ((Z11+Z₀)(Z22+Z₀) − Z12·Z21) [similar for S12, S22 by symmetry]
Practical Application Example
Two parallel-connected two-ports (Y-matrices add): Network A and Network B connected in shunt: [Y_total] = [Y_A] + [Y_B] Convert back: [S_total] from [Y_total] This is used for: modeling parallel feedback networks, combining simulation results from different sources.
RF View S11→Z Calculator: RF View's Utilities tab converts S11 (magnitude + angle) to complex impedance Z = R + jX using the 1-port formula. For full 2-port conversion, use EDA tools or Python scikit-rf. Free on Android.