ECE 6130 – S-Parameters Text Section 4.3 Describe and Compute S-Parameters Examples: Chapter 4, Problems 10,11 S-Parameters: Recall – Scattering Matrix (S-parameters) Where Sij = Vi- / Vj+ when Vk+ = 0 for k≠j 1) Terminate all ports except j with matched load. 2) Drive port j with Vj+ 3) Measure reflected voltage Vi- on port i. EXAMPLE: 3dB attenuator Find S11: Z2 = 50 ohms; Zin(port 1) = 8.56 + (141.8 || (8.56 + 50) ) = 50 ohms V1- = 0 (no reflection) S11 = V1- / V1+ =0 Find S22: Circuit is symmetric. S22 = S11 Find S12: S12 = V2- / V1+ when port 2 is terminated ⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡=⎥⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎢⎣⎡+++−−−NNNNNNVVVSSSSSSVVV211211121121Since S11 =0, we know that V1- = 0 when port 2 is terminated, and V2+ = 0 (by definition) Then V2- = V2 = Vmiddle (8.56 / (8.56 + 50)) Vmiddle = V1 (8.56 || 141.8) / (8.56 + 8.56 || 141.8 ) Return Loss RL = -20 log(Sii) dB Insertion Loss TL = -20 log(Sij) dB
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