# A Novel High-Precision Imaging Radar for Quality Inspection of Building Insulation Layers
## 3 Radar System Design
### Ultra-Wideband High-Bunching Antenna Design
#### 3.3.2 Ultra-Wideband High-Bunching Antenna  
The ultra-wideband high-bunching antenna consists of an ultra-wideband planar sinusoidal antenna radiation oscillator, reflecting plate, feed strip line, and lens, and the input and output interfaces can adopt an SMA coaxial interface, as shown in Figure 5.  
The radiation oscillator is a sinusoidal antenna similar to the sinusoidal asymptotic log-periodic structure, and this type of antenna can meet the requirements of wideband. In order to make the antenna oscillator and the transceiver match well, a ring micro-strip line structure is adopted. Based on the working center frequency, two balanced feed terminals with a phase difference of 180 degrees are connected to the center of the two oscillator arms. The basic component of a sinusoidal antenna is the sinusoidal curve, seen in Figure 6, and its antenna structure belongs to the frequency-independent log-periodic or quasi-log-periodic structure, which can be obtained by rotating the basic sinusoidal curve appropriately, and the basic sinusoidal curve is determined by two parameters, the scale factor \(\tau\) and the angle \(\alpha\), and the sinusoidal curve is formed by a series of unit group segments connected together, and the \(p\)-th unit group segment can be defined by the following equation [34],  
\[\phi(r)=(-1)^{p}\cdot\alpha_{p}\cdot\sin\left[\frac{\pi\cdot\ln\left(\frac{r}{ R_{p}}\right)}{\ln\left(\tau_{p}\right)}\right]\quad R_{p+1}\leq r\leq R_{p} \tag{7}\]  
where r and \(\alpha\) are the polar coordinates of the curve, r represents the distance from the pole, and \(p\) is the number of the segments of different unit groups, which increases from the outer unit to the inner unit of the curve. The radial distance of the pth unit is denoted by \(R_{p}\), which can be described by the following formula,  
\[R_{p}=\tau_{p-1}\cdot R_{p-1} \tag{8}\]  
The following two curves are obtained by rotating the basic sinusoidal curve around the coordinate origin by an angle \(\delta\) counterclockwise and clockwise, respectively,  
\[\phi(r)=(-1)^{p}\cdot\alpha_{p}\cdot\sin\left[\frac{\pi\cdot\ln\left(\frac{r }{R_{p}}\right)}{\ln\left(\tau_{p}\right)}\right]\pm\delta\quad R_{p+1}\leq r \leq R_{p} \tag{9}\]  
Figure 5: Ultra-wideband high-bunching antenna structure. The range of the area jointly enclosed by the two curves described by the above equation is called an arm of the sinusoidal antenna. In order to make the antenna performance meet its requirements, the antenna parameters are transformed for modeling simulation and the electrical model is as shown in Figure 7.  
The standing wave ratio (SWR) curve of the antenna radiation oscillator obtained from Ansys Student is as shown in Figure 8. It can be seen from the SWR curve that the optimized model can achieve a standing wave ratio of less than 3 in the 6-12 GHz range, which can meet the matching requirements of the system. Here, a standing wave ratio of less than 3 means that the voltage reflection is less than 50%, which is a commonly used practical threshold for evaluating antenna performance. The plane pattern of the antenna is shown in Figure 9. It can be seen that the pattern of each typical frequency point is similar in shape, and they are all one-sided spherical radiation patterns with good directivity. Figure 6: Schematic diagram of a sinusoidal antenna [34]. The basic sinusoidal curve is determined by two parameters, the scale factor \(\tau\) and the angle \(\alpha\), and two curves on the right side are obtained by rotating the basic sinusoidal curve at the left side around the coordinate origin by an angle \(\delta\). Figure 7: Simulation model of an antenna oscillator. Two balanced feed terminals with a phase difference of 180 degrees are connected to the center of the two oscillator arms. The lens has the characteristics of enhancing radiation directivity [35]. This section presents a design procedure for the dielectric lens. The lens geometry is shown below. It is made up of two parts, a hemisphere and a cylinder.