Solve for er from propagation constant

Hello All,

I am implementing a TRL calibration, as a results i am solving for the propagation constant of my transmission lines. Solving for α+iβ... isn't β = 2π / λ where λ is the wavelength of the transmission line --> λ / √(er).

With some test data, I can see my TRL calibration indeed returns the corrected response, but Im not sure if my gamma is scaled or if I am computing er correctly.

Above is my TRL setup in simulation in order to test my code.

that results in transmission lines with gamma:

the calculated Gamma at 10 GHz = 0.0023 + 0.6415i. Alpha seems to match up well with what line calc predicts, but i have not been able to convert Beta to an effective dielectric.

Thanks for the help,
Sami

Aside from the fact that your DUT has an open connection in it, everything looks correct (assuming your substrate is non-magnetic).

The e_r is the k_eff given in linecalc, 3.006.

The question was: how do I solve for er (keff) if i know the propagation (gamma) constant for a microstrip line? When i perform the real measurement I want to solve for eff and ultimately Zo of the line.

γ = α + jβ, so you want to extract β = Im{γ}

β = ω/v_Φ, so you want to solve v_Φ = ω/Im{γ} for each radial frequency ω = 2πf

Lastly, √(e_r) = c/v_Φ, so finally, you have: e_r = (c*Im{γ}/(2πf))2

So, out of frustration i worked backwards with my keff ADS number.

(√(3) * 2πf ) / c = imag(γ) = 362.76 Rad/m (10 GHz)

If i take my beta (0.6415), divide by the length of my "line" standard, 1.766e-3 m, i get really close 363.257.

Seems too good to be true, seems too coincidental. Perhaps, the TRL algorithm solves for βl directly? Hence needing to divide by l?

Thanks,
Sami