Implementing NRW Extraction Routine on Waveguides at Extremely High Frequencies (EHF band) : A simulation Based Approach
A Transmission-Reflection technique such as Nicolson-Ross-Weir (NRW) is used for predicting the electromagnetic properties of engineered materials in order to understand the electrical dynamics of such materials for use in fabricating RF circuits. This method involves placing a sample of the unknown material inside the cross section of a standard rectangular waveguide and measuring the S-Parameters by allowing the TE10 dominant mode to propagate.
For this example, a standard WR-10 waveguide 1-inch extension is designed with an inner cross section of 2.54 * 1.27 mm and an outer cross section of 3.54*2.27 mm as shown in Fig 1. The inner walls of the waveguide on are Copper coated. The simulation is performed using Feko’s FEM solver for computing the S-parameters. The frequency range is chosen at the W-band between 75-85 GHz and the simulated S-Parameters for the empty waveguide is shown in Fig 2.
Fig 1. Schematic of the W-band waveguide with dimensions in mm.
Fig 2. Simulated S-Parameters of an empty waveguide extension.
The next step after validating the correctness of the simulated s-parameters of an empty waveguide extension is to set up the forward problem where one can add any known sample inside the cross section of the waveguide and simulate for the S-Parameters. Use the NRW extraction routine on the simulated S-Parameters to check if the extracted value of the dielectric properties matches with the input. This solves the forward problem. In this example, the sample used has a dielectric constant of 2.1 and loss tangent of 0 with a thickness of 0.5 mm placed in the cross section for the simulation to obtain the S-parameters.
The procedure of NRW begins with defining intermediate quantities I1 and I2 using the reflection coefficient (S11) and the transmission coefficient (S21) from the waveguide simulation with the sample in the cross section. I1 and I2 are computed as in (1) and (2), respectively.
The propagation factor and the reflection coefficient at the interface between the free space and sample material can be determined by solving (1) and (2).
The sign ambiguity of P is resolved by using the choice of x for which 
.
For a rectangular waveguide with TE10 mode incident, the wavenumber is defined as (6), where a is the width of the guide. The propagation constant is defined as 
is the thickness of the sample.
Using (5) and (6) in the definition of the propagation constant, the electromagnetic properties of the sample can be extracted as in (7) and (8).
The above routine is valid for a homogenous material and the predicted properties from the S-Parameters aid in understanding the behavior of the unknown sample. The extraction procedure outlined above is solved using Altair Compose to solve the forward problem and predict the dielectric constant of the sample in the waveguide. Fig 3 shows the extracted dielectric constant from the simulated data using the NRW routine and it is close to the input dielectric constant of 2.1 thereby validating the forward problem.
Fig 3. Extracted dielectric constant from the simulated S-Parameters of the known sample.
Comments
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Very interesting. Please could you upload the cfx file for the FEM simulation? Thanks
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Claudio Curcio said:
Very interesting. Please could you upload the cfx file for the FEM simulation? Thanks
Please find below the cfx file.
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