Determining the Broadwall Dimension

To a large extent, the performance of a waveguide is determined by a, its broadwall dimension. Ideally, this dimension would be determined through mechanical measurement, but for sub-THz waveguides, it is not possible to measure the broadwall dimension in this way. The very small internal dimensions leave much of the length inaccessible to mechanical measurement methods. However, an estimate for an effective value of a can be determined by other means.

The electrical length, l_e, of a 2-port device can be derived from its unwrapped transmission phase response, φ, using Equation 3:

where λ_g is the guide wavelength at the measurement frequency, calculated using:

where λ is the free space wavelength. The lengths of the waveguide sections were also determined mechanically, acting here as the known values of length for each waveguide section. As found in a similar investigation,⁹ the results of the electrical length calculation are particularly sensitive to the assumed value of a used in the equation.⁴ Use of the nominal value of a can give electrical length results that vary significantly from the mechanical length. Therefore, to perform an effective calculation of the electrical length, estimates of a for each section were obtained using a minimization technique. The electrical lengths of the sections were calculated using Equations (3) and (4), using a value of a that minimizes the difference between the electrical and mechanical results.

Figure 8 Mechanical and derived electrical lengths of the Flann sections.

The outcome from this process gave a value of a = 378 μm for both the 1 in. and 2 in. sections. For the WM-380 waveguide, the nominal value for a is 380 μm. This value of a is well within the expected tolerance of this dimension, which is expected to be around 10 μm for this waveguide size. The determinations of the electrical lengths of the sections using this estimate for a are plotted in Figure 8 along with the mechanical measurements of the two sections. The mean values of the electrical results agree with the mechanical results to within 10 μm. These results further indicate the successful manufacture of these THz waveguides.

CONCLUSION

Waveguide sections for the WM-380-band have been developed by Flann Microwave. They feature a seamless design and they have been benchmarked through the analysis of electrical measurements conducted at NPL. When compared with sections manufactured by VDI, the current industry standard and with modeled results, the measured results showed very good performance. These outcomes show great promise for this design technique to be applied to straights, bends and twists for waveguide component operation up to 1.1 THz. These components are now in development.

ACKNOWLEDGMENTS

The authors would like to thank Jeffrey Hesler of VDI for his cooperation with this work. This work was supported by the U.K. Government’s Department for Science, Innovation & Technology (DSIT) through the National Measurement System program.

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