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Calculating Reflection and Transmission Coeff's from S Parms

Question asked by DoctorT on Apr 8, 2010
Latest reply on Jan 6, 2011 by Dr_joel
Probably another rookie question, but can anyone help me to understand the proper calculation of the Reflection and Transmission coefficients?

Taking the values for PTFE in a 10 cm beadless airline from the HP Product Note #8510-3:
S11 = 0.422
S21 = 0.906
I calculate K = ((S11^2 - S21^2)=1)/(2*S11) = 0.423
This leads to G = K + SQRT(K^2 -1) = 0.423 + j0.906. The magnitude of this vector is 1.0.
Similarly T = ((S11 +S21) -G)/(1-(S11 +S21)*G) = 0.907 + j0.422. The magnitude of the Transmission vector is again 1.0.

Either I am mis-applying the equations or don't have the correct physical interpretation of the Transmission and Reflection coefficients. I would have expected both to be less than unity, and from the value of S11<S21, would have expected to see a larger value for the magnitude of T than G.

Similarly when measuring our 30 cm beadless airline: G = 0.137 + j0.991, T = 0.9997 + j0.024; both with vector magnitude 1.0. Again, I would have expected to see a primarily transmissive response with a small bit of reflection.

So, am I miscalculating G and T somehow, or misinterpreting their physical significance? Or both? Most publications focus on derived parameters, such as e' and u' for materials. I don't find a lot of information about the transmission and reflection parameters.

Thanks from the rookie!

Edited by: iandoubleyou on Apr 24, 2012 11:34 AM