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

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

Hi Patricio, thanks for your reply. This is not really experiment related. I am just trying to understand the calculations. I understand your point about the symmetry of the network. How does that change the calculations?

Thanks!

Paul