A photograph of the measurement setup is presented in Fig. 5.10. The samples and connectors were cleaned carefully with isopropanol (IPA) before testing. A two-tier calibration technique was used to characterise the HPCIW. The first-tier Short-Open-Load-Thru (SOLT) calibration was performed using a 2.4mm mechanical calibration kit to place the reference planes to the ends of the coaxial cables. The second-tier calibration used TRL calibration [149] to shift the reference plane from the input port of the end launch connectors to the middle of thru line as shown in Fig. 5.7.
The raw measurement data after first-tier SOLT calibration are shown in Fig. 5.11. From Fig. 5.11(a), a transmission window that matches the simulation results can be clearly observed, with a frequency range which also agrees
First-tier SOLT Calibration Reference Plane
Fig. 5.10 Measurement Setup. SOLT calibration was applied to set the reference plane to the ends of the 2.4 mm coaxial cables. Clamps were used to squeeze out the air gaps between the metal plates and the photonic crystal layer as much as possible.
with the theoretical analysis based on the dispersion relation. The measured return losses are also about 10 dB for the thru and DUT, agreeing with the simulation results shown in Fig. 5.8. A reduction of transmission slightly above the upper bound of the guided band is observed which corresponds to the transmission gap between even mode (I) and even mode (II) as revealed by previous numerical studies. The q-factor of this transmission gap is slightly lower than the simulation results, which is probably caused by the relatively high practical transmission line loss. Compared Fig. 5.8 with Fig. 5.11, the measured S21 difference between the thru and DUT is much more obvious than that of the simulation results, which indicates the insertion losses of the measurement results are higher than that of the simulation results. Factors that increase the loss, such as residual air gaps between different layers, surface roughness, oxidation of copper, residual burnt dielectric powders, and fabrication errors, are not considered in the simulation, which contribute to the difference between the simulated and measured results.
(a)
The measured propagation loss of the fabricated HPCIWs, shown in Fig. 5.12, is obtained by using TRL calibration method [149]. A guided band ranging from 28.75 GHz to 37.41 GHz is observed, which corresponds to the even mode (I) shown in Fig. 5.2 and Fig. 5.3. A narrow frequency range of negative propagation loss around 32.79 GHz is observed. It is likely that this ripple is caused by the transition waveguides and photonic crystal structures were not placed at precisely the same position from one measurement to another.
An additional method comparing the maximum available gain (𝐺£c¾) [138] of the thru and DUT was used as a reference to the TRL calibration method. It is called as the GMAX method in this chapter. The maximum available gain is defined as: 𝐺£c¾ = 10 log•K 1 𝐾 + 𝐾y− 1 𝑆y• 𝑆•y , where 𝐾 =1 − 𝑆•• y− 𝑆yy y+ ∆ y 2 𝑆y•𝑆•y ,
and ∆= 𝑆••𝑆yy− 𝑆•y𝑆y•.Then, the propagation loss using GMAX method is given by
𝛼 dB cm =𝐺£c¾} (dB) − 𝐺£c¾Á (dB) −Δ𝑙 (cm) , where, 𝐺£c¾} and 𝐺
£c¾Á are the maximum available gains of thru and DUT, respectively, and Δ𝑙 is the difference of length between them. The thru and
Fig. 5.12 Propagation loss of the proposed HPCIW. The simulation result outside the guided band is less accurate since it doesn’t fulfill the required of multiline calibration method.
the DUT is compared intentionally because the s-parameters between them are more consistent than the line, which indicates the misplacements of components in the waveguide are smaller. It should be noted that the GMAX method used here is more accurate than the cut-back method [150] which only compares the output power of two waveguides with different length, especially when the impedance of the waveguide is not matched with the feeding network. It is because both insertion loss and return loss are considered in the GMAX method, while the cut-back method only takes into account insertion loss. The propagation loss calculated by using the GMAX method is also presented in Fig. 5.12 using the red solid curve. Good agreement between the TRL calibration method and GMAX method inside the guided band was achieved, and the negative propagation losses around 32.79 GHz are avoided with the GMAX method. From the red solid curve, It can be seen that at the lower and upper bounds of the guided band, the propagation loss is seen to increase, which agrees with the lower and upper limit of the dispersion curve of the even mode (I). The transmission window slightly above 37.41 GHz supports the propagation of the even mode (II), which is outside the guided band of interest. According to the GMAX method, the measured propagation loss of the HE10 mode is below 0.69 dB/cm over the frequency range from 28.75 GHz to 37.41 GHz, with a minimum loss of 0.07 dB/cm at 32.66 GHz.
In Fig. 5.12, the simulated loss calculated by using the GMAX method is also included. From 28.75 GHz to 37.41 GHz, the measured propagation losses are higher than simulated results on average. The difference in the propagation loss between the simulation and the measurement results is smaller in the centre of the guided band than that at the edge of the guided band. It is because the confinement of the wave by the photonic crystal structure is stronger in the band centre than that at the band edge, and consequently the EM wave in the band centre is less affected by the oxidized copper and defects in the cladding, resulting in a lower loss. Based on Fig. 5.5, the zero group-velocity dispersion points happens at 0.457𝑎, which is 33.4 GHz when 𝑎 = 4.106 mm in the real situation.
5.5 Concluding remarks
This chapter presents a novel hollow photonic crystal integrated waveguide (HPCIW) which combines the advantages of substrate integrated waveguide and photonic crystal waveguide. The design concept is experimentally verified at Ka-band with a good agreement with theoretical analyses. The
proposed HPCIW supports single-HE10-mode propagation under even-field excitation conditions. It achieves a bandwidth of 26% centred at 0.453 c a, and a zero GVD point at 0.457 c a. The measured propagation loss of the fabricated waveguide is less than 0.69 dB/cm from 28.75 GHz to 37.41 GHz, with a minimum loss of 0.07 dB/cm at 32.66 GHz. A zero GVD point is founded at 33.4 GHz according to the dispersion relation. The design presented in this chapter can easily be scaled to other bands, such as THz and optical frequencies, by properly changing the lattice constant of the photonic crystal and choosing a suitable high permittivity host material.