7. Analytically determine the expected low-frequency values of Z1, Z12, Z21, and Z2 and provide your...

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7. Analytically determine the expected low-frequency values of Z₁1, Z12, Z21, and Z₂2 and provide your derivation and results. Compare and comment on the accuracy of your measured results. Z₁1 Z12 Z21 Z22 (2) "z N = = 100 80 60 40 20 0 0 Zo Zo Zo Zo (1+S11)(1-S22) + S12S21 (1-S11)(1-S22) - S12S21 2 S12 (1 S₁1)(1-S22) - S12S21 2 S21 (1-S₁1)(1-S22) - S12S21 (1 S₁1)(1+S22) + S12S21 (1-S11)(1-S22) - S12S21 Z₁1 of the Impedance Matrix 100 Real part Imaginary part 300 200 Freq (MHz) Figure 8: Measured Z₁₁ of the II-circuit 400 V₁ S₁1V₁ + S12 V₂ V₂ = S21 V₁ + S22 V₂, (5) (6) (7) (8) 1. Start by using Eqs. 1 and 2 to derive the S-parameters of an arbitrary section of transmission line of length . (1) (2) 7. Analytically determine the expected low-frequency values of Z₁1, Z12, Z21, and Z₂2 and provide your derivation and results. Compare and comment on the accuracy of your measured results. Z₁1 Z12 Z21 Z22 (2) "z N = = 100 80 60 40 20 0 0 Zo Zo Zo Zo (1+S11)(1-S22) + S12S21 (1-S11)(1-S22) - S12S21 2 S12 (1 S₁1)(1-S22) - S12S21 2 S21 (1-S₁1)(1-S22) - S12S21 (1 S₁1)(1+S22) + S12S21 (1-S11)(1-S22) - S12S21 Z₁1 of the Impedance Matrix 100 Real part Imaginary part 300 200 Freq (MHz) Figure 8: Measured Z₁₁ of the II-circuit 400 V₁ S₁1V₁ + S12 V₂ V₂ = S21 V₁ + S22 V₂, (5) (6) (7) (8) 1. Start by using Eqs. 1 and 2 to derive the S-parameters of an arbitrary section of transmission line of length . (1) (2)