# A Compact Rectifier Design Method Utilizing Harmonics
## 2 Design and Simulation  
### Principle  
The block diagram of the rectifier is shown in Figure 1. It consists of an input impedance matching network, a shunt diode, a DC-pass filter, and a load. The input impedance of the diode \(Z_{\text{in}}\) is the parallel connection of \(Z_{F}\) and \(Z_{D}\):  
\[Z_{\text{in}}\ =\ Z_{F}\parallel Z_{D} \tag{1}\]  
where \(Z_{F}\) is the input impedance of the DC-pass filter and \(Z_{D}\) is the diode impedance. The rectifier can utilize different harmonics by designing the \(Z_{F}\) at the specific harmonics. Table 2 shows the input impedances of the DC-pass filter in different harmonic utilization states. (1) Utilizing the 2 nd and 3 rd harmonics: When the input impedances of the DC-pass filter at fundamental (\(f_{0}\)), 2 nd harmonic (\(2f_{0}\)), and 3 rd harmonic (\(3f_{0}\)) are \(Z_{F,f_{0}}\), \(Z_{F,2f_{0}}\), and \(Z_{F,3f_{0}}\), respectively:  
\[Z_{F,f_{0}}\ =\ +\infty \tag{2}\]  
\[Z_{F,2f_{0}}\ =\ \text{jX or }+\infty \tag{3}\]  
\[Z_{F,3f_{0}}\ =\ \text{jX or }+\infty \tag{4}\]  
where \(\text{jX}\) is pure reactance and \(+\infty\) means open circuit state. The rectifier has two special features. Firstly, the DC-pass filter keeps total reflection at \(f_{0}\), \(2f_{0}\), and \(3f_{0}\), and only the DC component is transmitted to the load. Secondly, by adjusting the input impedances of the DC-pass filter (jX) at \(2f_{0}\) and \(3f_{0}\), the amplitudes of the harmonics can be controlled to meet the demand of the communication system. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Ref**} & \multirow{2}{*}{\begin{tabular}{c} **Frequency** \\ **(GHz)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Input Power** \\ **(dBm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Harmonic** \\ **Type** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Harmonic** \\ **Amplitude** \\ **(dBm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Efficiency (\%)** \\ **Type** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Implementation** \\ **(\(\mathbf{\lambda_{g}\times\lambda_{g}}\))** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Size** \\ **(\(\mathbf{\lambda_{g}\times\lambda_{g}}\))** \\ \end{tabular} } & \multirow{2}{*}{**Method**} \\ \hline
[10] & 2.45 & 6 & 3 rd & \(-\)22 & 76\% &
\begin{tabular}{c} Microstrip and \\ lumped \\ component \\ \end{tabular} & 1.16 \(\times\) 1.32 & coupler \\ \hline
[11] & 2.45 & 18 & 3 rd & \(-\)17.2 & 70.6\% &
\begin{tabular}{c} Microstrip and \\ lumped \\ component \\ \end{tabular} & 1.28 \(\times\) 1.52 & coupler \\ \hline
[12] & 0.915 & 15 & 2 nd & \(-\)2 & 71\% & \
\begin{tabular}{c} Lumped \\ component \\ \end{tabular} & 0.07 \(\times\) 0.17 &
\begin{tabular}{c} separate \\ harmonic \\ utilization path \\ \end{tabular} \\ \hline
[13] & 2.45 & 10.7 & 2 nd & \(-\)4.1 & 42.5\% & Microstrip & N.A. & N.A. \\ \hline
**This work** & **5.8** & **18.3** & **2 nd and 3 rd** & **\(-\)2.4 and 0.1** & **71.3\%** & Microstrip & **0.69 \(\times\) 1.38** & **DC-pass filter** \\ \hline \hline \end{tabular} \(\lambda_{g}\) is the guided wavelength in substrate.  
\end{table} 
Table 1: Comparison with the prior design methods. Figure 1: The block diagram of the proposed rectifier. The impedance matching design of the rectifier includes the input impedance matching network and the DC-pass filter. The former one is to match the input impedance of the diode to 50 \(\Omega\) at the fundamental frequency. The latter one is to utilize the 2 nd and 3 rd harmonics simultaneously. By designing the input impedance matching network and the DC-pass filter, the fundamental wave from the source will enter the diode to be rectified, while the 2 nd and 3 rd harmonics excited by the diode will be utilized towards the source direction.