# A Wideband Dielectric Waveguide-Based 160-GHz Radar Target Generator
## 4 Link Budget  
The maximum distance to be emulated with the RTG is at least 10 m. This means that the received power with the RTG is within the dynamic range of the radar. In the following, the link budgets for free-space propagation and for the RTG are derived and compared.  
The received power \(P_{r}\) of a radar for free-space propagation is determined by the radar equation. For a monostatic radar system with antenna gain \(G\) and an extended target with reflectivity \(|\Gamma|\) in the distance \(R\), the radar equation is given by  
\[\frac{P_{r}}{P_{t}}=\frac{G^{2}\lambda_{0}^{2}}{(4\pi)^{2}(2R)^{2}}\,|\Gamma|^ {2}, \tag{3}\]  
where \(P_{t}\) is the transmit power and \(\lambda_{0}\) is the free-space wavelength.  
For the RTG the received power depends on the losses of the dielectric waveguide (\(a_{\text{dwg}}\)), the rectangular waveguide (\(a_{\text{wg}}\)), and the coupling transition (\(a_{t}\)). Neglecting the rectangular waveguide length (\(<5\) cm), the modified radar equation for a target with reflectivity \(r\) in the distance \(L\) is given by  
\[\frac{P_{r}}{P_{t}}=\left(\frac{r}{a_{t}a_{\text{wg}}\cdot a_{\text{dwg}}L} \right)^{2}. \tag{4}\]  
Since the group velocity in the dielectric waveguide is smaller than the speed of light in air, the electrical length \(L_{\text{el}}\) must be used in (4). However, the attenuation in the dielectric waveguide was determined for the mechanical length. Taking the definition of the extension factor \(l_{s}\) into account, (4) becomes  
\[\frac{P_{r}}{P_{t}}=\left(\frac{r}{a_{t}a_{\text{wg}}\cdot a_{\text{dwg}}\frac {L_{\text{el}}}{l_{s}}}\right)^{2}. \tag{5}\]  
The ratio \(P_{r}/P_{t}\) for the free-space propagation and the RTG over distance is shown in Figure 10 for water (a) and palm oil (b). The used parameters are shown in Table 1 and corresponds to the measured values in Section 3. In the case of water as reflective medium, more power is received with the RTG than with a free-space radiating radar up to a distance of 8.69 m. The received power of the  
Figure 9: Cross-section of the Rohacell holder with the dielectric waveguide (**a**) and the simulated and measured insertion loss (**b**).  
RTG decreases linearly due to the linear attenuation of the waveguide, whereas the receive power for a radar with free-space propagation decreases logarithmically. The received power of the RTG with a simulated palm oil medium is below the power of a free-space radiating radar from a distance of 8.41 m.  
For a power ratio \(P_{r}/P_{t}=-71\) dB, the minimum required distance of 10 m is met. The ratio of the RTG at the maximum distance is only 6 dB below the power ratio of a radar with free-space radiation. Consequently, the requirement is normally fulfilled. In order to completely emulate the physical behavior of a level sensor scenery with respect to range and received power, a commercially available attenuator in the rectangular waveguide section could be used. Thus, the received power difference between free-space propagation and the RTG can be compensated in the range below 8 m.  
For a radar under test without a rectangular waveguide interface, the RTG can be extended with a horn antenna. The maximum distance is reduced by approximately 3.5 m due to additional free-space losses between the radar sensor and the RTG.