# A Low-Cost Printed Log-Periodic Dipole Array for DVB-T2 Digital TV Applications
## 2 LPDA Design  
The proposed printed LPDA for DVB-T2 Digital TV applications has been designed starting from standard Carrel design equations [7] with some modifications [4]. In fact, since the printed LPDA lies on a dielectric substrate, the geometric parameters of this antenna cannot be computed as in the case of a standard wire LPDA [7], which radiates in free space. Hence, the resonant length of the largest printed dipole at the lowest operating frequency is computed by using CST Studio Suite, a general-purpose software for the simulation and design of 3D electromagnetic components, whose results are in excellent agreement with experimental results [4; 11]. The final layout of the proposed printed LPDA is shown in Figure 1. The shaped dipoles are, as usual, alternately connected on the two sides of the paired strip feeding line. The paired strip is adequately connected to a coaxial cable, whose outer conductor is soldered to the dipoles' arms attached to the bottom face of the dielectric substrate, whereas the inner conductor is connected through a via to the dipole arms attached to the upper face of the substrate. This allows all the radiating elements to be fed with alternate signs, giving the LPDA the end-fire behavior. The structure of the printed LPDA is very close to a standard wire LPDA; thus, we can apply the standard strategy [7] for estimating the antenna directivity and the required number of radiating dipoles to cover a specified frequency band. The antenna's operating bandwidth and directivity are the design specifications of the proposed LPDA, and the design parameters are the log-period \(\tau\) and the spacing factor \(\sigma\), which can be chosen by using [PERSON]'s design curves [7]. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**REF** & \begin{tabular}{c} **F\({}_{\text{min}}\)** \\ **[MHz]** \\ \end{tabular} & \begin{tabular}{c} **F\({}_{\text{max}}\)** \\ **[MHz]** \\ \end{tabular} & \begin{tabular}{c} **F\({}_{\text{center}}\)** \\ **[MHz]** \\ \end{tabular} & \begin{tabular}{c} **\(\lambda\) [m]** \\ **[\%]** \\ \end{tabular} & \begin{tabular}{c} **BW\({}_{\text{load}}\)** \\ **[\%]** \\ \end{tabular} & \begin{tabular}{c} **L\({}_{\text{0}}\) [m]** \\ \end{tabular} & \begin{tabular}{c} **L\({}_{\text{V}}\) [m]** \\ **L\({}_{\text{norm}}\)** \\ \end{tabular} & \
\begin{tabular}{c} **A\({}_{\text{norm}}\)** \\ **[dB]** \\ \end{tabular} &
\begin{tabular}{c} **LPDA** \\ **Type** \\ \end{tabular} \\ \hline
[1] & 450 & 900 & 675 & 0.44 & 67 & 0.63 & 0.23 & 0.72 & 9.00 & Wire \\
[4] & 4000 & 18,000 & 11,000 & 0.03 & 127 & 0.06 & 0.03 & 2.45 & 8.00 & Printed \\
[9] & 470 & 790 & 630 & 0.48 & 51 & 0.62 & 0.32 & 0.87 & 8.74 & Wire \\
[10] & 465 & 800 & 632 & 0.47 & 53 & 356 & 302 & 0.5 & 8.00 & Wire \\
[11] & 3000 & 6000 & 4500 & 0.07 & 67 & 0.12 & 0.04 & 1.05 & 6.50 & Printed \\
[13] & 54 & 223 & 139 & 2.17 & 122 & 2.84 & 1.68 & 1.02 & 8.00 & Wire \\
[14] & 500 & 8500 & 4500 & 0.07 & 178 & 0.28 & 0.19 & 12.31 & 7.00 & Printed \\
[16] & 2300 & 8000 & 5150 & 0.06 & 111 & 0.11 & 0.08 & 2.75 & 5.00 & Printed \\
[17] & 3100 & 10,600 & 6850 & 0.04 & 109 & 0.11 & 0.07 & 4.01 & 5.00 & Printed \\
[19] & 500 & 10,000 & 5250 & 0.06 & 181 & 0.22 & 0.26 & 17.36 & 4.00 & Printed \\
[20] & 200 & 803 & 502 & 0.60 & 120 & 0.42 & 0.58 & 0.68 & 4.50 & Printed \\
[22] & 2400 & 5800 & 4100 & 0.07 & 83 & 0.11 & 0.06 & 1.15 & 6.00 & Printed \\
[This work] & 470 & 860 & 665 & 0.45 & 59 & 0.29 & 0.21 & 0.26 & 6.50 & Printed \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison with LPDAs proposed in recent literature. The printed LPDA design steps are summarized in the following:  
1. Select the LPDA's desired operating frequency band and maximum directivity;
2. Choose the desired values of the log-period \(\tau\) and the spacing \(\sigma\) from [PERSON]'s design curves [7];
3. Compute the required number N of LPDA elements to cover the frequency band selected in step 1 using Carrel expressions [7];  
Figure 1: Layout of the designed LPDA. (**a**) Top view; (**b**) Bottom view.