# Design of Miniaturized Dual-Band Microstrip Antenna for WLAN Application
## 3 Design of Miniaturized Dual-Band Broadband Printed Antennas
### The Structural Analysis of the Antenna  
According to the working principle of the monopole antenna, using the principle of mirror image, the ground plane can be introduced to reduce the length of the half-wave dipole antenna by half, which is equivalent to 1/4 wavelength of the monopole antenna. Then, the resonant frequency of printed monopole antenna is expressed as:  
\[f=\frac{c}{4L\sqrt{\varepsilon_{r}}} \tag{1}\]  
where \(c\) is the speed of light, \(L\) is the resonant path length of the radiator, and \(\varepsilon_{r}\) is the relative dielectric constant of the dielectric-slab. The antenna adopts a 50 \(\Omega\) microstrip to feed, and the width of the microstrip feeder can be obtained by the following equation:  
Figure 3: Antenna structure chart.  
When \(w/h>1\),  
\[Z_{0}=Z_{f}2\pi\sqrt{\varepsilon_{eff}}\ln(8\frac{h}{w}+\frac{w}{4h}) \tag{2}\]  
\[\varepsilon_{eff}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2}[(1+12 \frac{h}{w})^{\frac{-1}{2}}+0.04(1-\frac{w}{h})^{2}] \tag{3}\]  
When \(w/h<1\),  
\[Z_{0}=\frac{Z_{f}}{\sqrt{\varepsilon_{eff}}(1.393+\frac{w}{h}+\frac{2}{3}ln( \frac{w}{h}+1.444))} \tag{4}\]  
\[\varepsilon_{eff}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2}(1+12 \frac{h}{w})^{\frac{-1}{2}} \tag{5}\]  
In the formula, \(Z_{f}=376.8\)\(\Omega\) represents free space wave impedance, \(h\) represents the height of medium plate, \(w\) represents the width of microstrip line, and \(\varepsilon_{eff}\) represents the effective dielectric constant of the dielectric plate.  
We run the commercial software Ansoft HFSS to simulate the structure of the antenna. The effects of various parameters on the performance of the antenna are studied in the following.  
Changing the range of L2, which denotes the unit length of rectangular radiation, and keeping other parameters unchanged, the changes of return loss \(S_{11}\) with L2 are shown in Figure 4. It can be seen from the figure that L2 mainly affects the bandwidth and the resonant point at a high band. As L2 becomes larger, the resonant frequency of 2.4 GHz band moves to the left, the resonant frequency at high frequency significantly decreases, and the matching situation becomes worse.  
The width of the rectangular radiating element is L3. Figure 5 illustrates the results of \(S_{11}\) parameter varies with L3. L3 will not affect the resonant frequency of two frequency bands but will affect the matching of the antenna. As L3 becomes larger, the matching situation becomes worse, and the bandwidth is also reduced.  
The vertical part of the T-sharped element is L4, and the \(S_{11}\) varies with L4 as shown in Figure 6. The resonant frequency of 2.4 GHz band decreases with the increase of L4, and the resonant frequency of the high frequency band does not change with the L4. While the L4 becomes larger, the bandwidth of the high frequency band is obviously reduced.  
Figure 4: Parameter \(S_{11}\) varies with L2.  
The length of the horizontal part of the T-sharped element is L5. The value of L5 is changed, and the other parameters are constant, while the changes of \(S_{11}\) with L5 are shown in Figure 7. As shown in the chart, the resonance frequency of the low frequency band decreases with the increasing of L5, and the resonant frequency of the high frequency band does not vary with L5.  
Figure 5: Parameter \(S_{11}\) varies with L3.  
Figure 6: Parameter \(S_{11}\) varies with L4.  
Figure 7: Parameter \(S_{11}\) varies with L5.  
The folding part of the T-sharped unit is L6, and the changes of \(S_{11}\) with L6 are shown in Figure 8. As shown in the chart, the resonant frequency of the low frequency band decreases with the increasing of L6, and the resonance frequency of the high frequency band does not vary with L6.