I am doing permittivity measurements using the Arbitrary-Backed Reflection Method. (The one that requires a measurement with the sample and another without.)

I was wondering if anyone could point me to the literature that this model was based on. I can find the literature for the other models fine, but for this one I am having a hard time.

I was wondering if anyone could point me to the literature that this model was based on. I can find the literature for the other models fine, but for this one I am having a hard time.

Arthur R. Von Hippel in his 1950s book "Dielectric Materials and Applications" covers the short backed model. It is essentially the same as Agilent's implementation except he used tables to convert the measurements whereas Agilent does an iteration such that the permittivity is determined by minimizing the difference between the measured and calculated values of S11 with the sample backed by a short. The arbitrary backed model is a variation of this approach. Instead of a short, the backing is measured independently and then the iteration is done using this reflection instead of an assumed short. The advantage is that the short is a bad choice of backings for electrically thin samples. The arbitrary backed model was developed by IEEE I&M Distinguished Lecturer Phil Bartley. It has not been published because its basis is fundamental.