# A Wideband Dielectric Waveguide-Based 160-GHz Radar Target Generator
## 3 Components
### Dielectric Waveguide  
The dielectric waveguide is often used in the mm-wave range [12; 13; 14] due to several advantageous characteristics. It is a low loss waveguide compared to metallic waveguides or microstrip lines. The fabrication of dielectric waveguides, usually made of flexible plastics, is comparatively simple and low cost. The fundamental mode in the rectangular dielectric waveguide is the HE\({}_{11}\) mode [15] as shown in Figure 2. For this mode, field components exist both inside and outside the dielectric material. The field distribution and the phase constant \(\beta_{g}\) depend on the cross-section of the waveguide, the permittivity  
Figure 1: System concept of the radar target generator. of the material, and the frequency. By increasing the permittivity or the size of the waveguide, the field components inside the material and the phase constant increase. This results in additional dielectric losses, less flexibility, but also less radiation losses. For the design process this should be taken into account to achieve a maximum range and compactness for the RTG. A further aspect in the design process is the dispersion of the dielectric waveguide. With increasing frequency, the field components inside the waveguide and the phase constant also increase. This results in a frequency dependent group velocity \(v_{\mathrm{gr}}\) as shown in Figure 3 which affects the radar response of an FMCW radar. In comparison to the free-space propagation of the wave, the measured delay \(\tau\) for a target in distance \(R\) is given with  
\[\tau(f)=\frac{2R}{v_{\mathrm{gr}}(f)}. \tag{1}\]  
Due to the frequency dependent group delay, a target peak is broadened over a range usually covering several range cells. This effect increases with the bandwidth and the target distance since the delay time \(\tau\) is proportional to \(R\). A simulated range spectrum for the RTG and in free space for a target distance of 2 m and a bandwidth of 20 GHz is shown in Figure 4. Since the power is distributed over the range, the SNR also decreases. Due to the lower group velocity in the waveguide compared to free-space propagation, the electrical length \(L_{\mathrm{el}}\) is larger than the mechanical length \(L_{\mathrm{mech}}\) and the target is shifted by an extension factor \(l_{\mathrm{s}}=\frac{L_{\mathrm{el}}}{L_{\mathrm{mech}}}=1.57\) to larger distances. Figure 3: Group velocity \(v_{\mathrm{gr}}\) over frequency for a rectangular dielectric waveguide with permittivity \(\epsilon_{r}=2.25\). The cross-sectional area is 1295 \(\upmu\)m \(\times\) 648 \(\upmu\)m.  
Figure 2: E-field distribution of the fundamental HE\({}_{11}\) mode in a dielectric waveguide with polarization in \(y\)-direction [12] (© IEEE 2017). In this work, the manufactured dielectric waveguide is a good compromise taking into account loss mechanisms and dispersion. The desired cross-sectional area of the rectangular dielectric waveguide is \(1295\,\mathrm{\SIUnitSymbolMicro m}\times 648\,\mathrm{\SIUnitSymbolMicro m}\) and is made of high-density polyethylene (HDPE, \(\varepsilon_{r,\mathrm{HDPE}}=2.25\), \(\tan\delta=3.1\times 10^{-4}\) at \(160\,\mathrm{GHz}\)). Since HDPE is a thermoplastic material, the waveguide is manufactured using an extrusion process. This allows the waveguide to be manufactured in almost any length required for the RTG. The cross-section of the extruded waveguide is shown in Figure 5.  
The measured dimensions are \(1180\,\mathrm{\SIUnitSymbolMicro m}\times 510\,\mathrm{\SIUnitSymbolMicro m}\) and therefore smaller than specified. Furthermore, the rectangular cross-section of the waveguide has rounded corners and through-like indents. The deviations from the design result in a slight shift of the properties to higher frequencies. The measured attenuation of the manufactured waveguide is shown in Figure 5. For frequencies below \(150\,\mathrm{GHz}\) the attenuation is larger than \(7.5\,\mathrm{dB/m}\).