## 3 Results and Discussion  
The simulated results of the proposed transition exhibit wide impedance bandwidth and low insertion loss. For experimental verification, a back-to-back microstrip-to-waveguide is designed and fabricated. Figure 9 shows the photograph of the fabricated prototype. All components of the transition are processed in blocks and then assembled with screws. The metal parts are made of aluminum, and the substrate part uses single-layer Roger RT/Duroid 5880. Agilent network analyzer N5245A and a pair of frequency expansion components are used to measure the S-parameters of the back-to-back transition. The measured and simulated results are shown in Figure 10a, where the length of the microstrip line is 10 cm. The measured results show that a reflection coefficient below \(-15\) dB can be obtained in the entire W-band. Meanwhile, it can be observed that there is a good agreement between the simulated and measured reflection coefficients. The measured transmission coefficient is lower than the simulated one, especially in the higher frequency band. The deviation between transmission coefficients can be attributed to two aspects. On the one hand, the loss tangent of Ro 5880 provided by the manufacturer is measured at 10 GHz, which may not be accurate in W-band. The design experience indicates that the loss tangent rises with frequency. Thus, the loss tangent at W-band will be higher than the nominal one. On the other hand, the conductor loss cannot be ignored because the metal components are not gold-plated. To estimate the insertion loss of the proposed transition, the second back-to-back transition with the 12 cm length of the microstrip line is fabricated and measured. Figure 10b shows the measured insertion losses with different lengths of the microstrip line. After calculation, the average loss of the microstrip line is about 0.28 dB/cm in W-band. The calculated insertion loss of a single transition is shown in Figure 10b, with an average value of about 1.2 dB. The calculated insert loss for a single transition has a relatively high value due to the fact that the conductor loss is not eliminated. Figure 8: The simulated S-parameters with different widths of groove. Figure 9: The designed back-to-back transition. (**a**) Photograph of the fabricated prototype. (**b**) Test scenario. A performance comparison of our work and some up-to-date transitions are summarized in Table 2. To achieve wide bandwidth, the transition in [8] with multi-stage ridge and transition in [11] with long antipodal slot line are designed, which results in a large size. The metal pins in [11] and additional branch waveguide in [17] increase the fabricated complexity. In [19], a microstrip-to-waveguide is designed on quartz substrate by using a quasi-Yagi antenna. However, the stub arrays and indented waveguide are required to suppress the rectangular cavity resonances, which makes whole structure more complex. The transition in [21] is similar to our work. However, the bandwidth and insertion loss of transition using common probe are not so satisfactory. This comparison verifies the advantages of the proposed transition in terms of bandwidth, compactness, and complexity. The insertion loss of the proposed transition is relatively high, but it may be improved by plating gold on the waveguide surface. Figure 10: The results of the proposed back-to-back transition. (**a**) Simulated and measured S-parameters. (**b**) The loss of transition with different lengths of microstrip line and the calculated insertion loss of single transition.