Figure 3

Result of step 1. Behavior of the Lorenzian function as a function of frequency, fitted to experimentally measured TE110 (left and right figures of the top figure) and a TE210 (left and right figures of the bottom figure) resonance in an air filled aluminium pipe of 128.5 mm internal diameter. Resonant frequencies and quality factors are extracted from a Lorentzian fit the transmission measurement. Complex resonant frequencies in (6) are calculated as \(\omega_{0} = f_{0}^{\mathrm{TEm}10} + i\frac{f_{0}^{\mathrm{TEm}10}}{2Q_{0}^{\mathrm{TEm}10}}\), which form input to the combined transverse resonant open ended coaxial waveguide functional. The top and bottom figures on the right side show the relative difference between the measured data and the Lorenzian function.