# Calculate Zo and gamma

This calculator calculates Zo and γ from Zsc and Zoc of a line section of known length.

 Inputs: Real /magnitude Imaginary / angle Short circuit a+jb r,θ(°) r,θ(ᶜ) S11 Real,Imaginary S11 ρ,θ(°) S11 ρ,θ(ᶜ) S11 ρ(dB),θ(°) S11 ρ(dB),θ(ᶜ) Open circuit a+jb r,θ(°) r,θ(ᶜ) S11 Real,Imaginary S11 ρ,θ(°) S11 ρ,θ(ᶜ) S11 ρ(dB),θ(°) S11 ρ(dB),θ(ᶜ) Line length (m) k Frequency (MHz) Results: Zo (Ω) γ (Note 1) MLL (dB/m) VF

The calculator does not do a lot of error checking, if you enter nonsense, it will probably produce nonsense.

Beware: randomly chosen spot values expose the result to effects of measurement noise, be mindful of measurement noise.

Note 1: The solution for γ involves the log of a complex number $$r \angle \theta$$ which is one of the many possible values $$ln(r) + j \left(\theta + 2 \pi k \right)$$ for non-negative integer k. Conveniently, the real part α is simply $$ln(r)$$ and the real part of γ is the matched line attenuation in Np/m which can be scaled to dB/m. The value given is the kth solution.

Example 1 is from a sweep of a RG6 CCS cable, data @ 1.87MHz extracted from the saved .s1p files.

Example 2 is from a sweep of speaker twin, data @ 40.53MHz extracted from the saved .s1p files.

Example 3 is from a sweep of Commscope C4510404 RG-11 CCS, data @ 3.6MHz extracted from the saved .s1p files.