# Dual-Band Rectifier Circuit Design for IoT Communication in 5G Systems
## 4 Numerical Results  
We designed a dual-band rectifier on RT/Duroid 5880. The proposed IMN is a network with two branches, one for 3.5 GHz and one for 5 GHz. As we analyzed in Section 3, each branch is a T-type network with radial and rectangular stubs. In each branch, we designed and then connected a full-wave Greinacher voltage doubler. Each voltage doubler was built with HSMS-286C Schottky diodes and two 100 pF capacitors. Furthermore, the circuit contains various conductor lines of suitable length (L) and width (W) to connect all the other components (capacitors, diodes). All of these conductor lines are the proper size to aid the impedance-matching network. The output load is connected in a differential way. As a result, we designed a differential rectifier circuit topology to produce higher output power and voltage at low input power [60]. The commercial software Advanced Design System (ADS) from Keysight Technologies, uses the gradient optimizer algorithm, which is used to design and optimize this circuit. Figure 5 depicts the complete design of the proposed dual-band rectifier. Figure 4: Proposed impedance-matching network. We used an antenna port of \(Z_{A}=50\,\Omega\) as an input to design the proposed rectifier. We selected an output load with a resistance of 2 k\(\Omega\). The initial impedance of the proposed circuit is 8.068 + j9.927 at 3.5 GHz and 6.764 + j27.956 at 5 GHz. With the design of the impedance-matching network, we want to match the impedance of the rectifier with the 50 \(\Omega\) impedance of the antenna. We achieved the impedance of the circuit to be 50.057 - j0.161 at 3.5 GHz and 49.921 - j0.267 at 5 GHz by implementing the IMN, which we analyzed in the previous section. Figure 6 illustrates the reflection coefficient frequency response. The \(S_{11}\) value at 3.5 GHz and 5.0 GHz design frequencies is \(-55.335\) dB and \(-51.114\) dB, respectively. Furthermore, as shown in Figure 6, the \(S_{11}<-10\) dB impedance matching this dual-band rectifier is equal to 80 MHz at 3.5 GHz and 90 MHz at 5 GHz. We note that the proposed circuit performs well in all the above cases. Figure 5: Proposed dual-band rectifier. One of the most noteworthy parts of the design is the output load. The choice of the output load determines the total RF-to-DC efficiency n% of the circuit. Equation (1), shows that when the output load increases, the efficiency of the circuit decreases. The total RF-to-DC efficiency n% is computed as follows:  
\[n=\frac{P_{in}}{P_{out}},P_{out}=\frac{V_{out}}{R_{L}}, \tag{1}\]  
we classify the RF input power \(P_{in}\), the output power \(P_{out}\), the output voltage \(V_{out}\), and the output load \(R_{L}\). Since we want to maximize the efficiency n%, we set a harmonic balance (HB) simulation to see the values of \(R_{L}\) and \(P_{in}\), thus having better power conversion efficiency n%. Figure 7 displays the power conversion efficiency versus the output load \(R_{L}\) of the proposed rectifier circuit. In this graph, we observe that the initial design has an output load of 2 k\(\Omega\) and an input power of 12 dBm and achieves PCE 52.4%. Moreover, we can easily derive that the maximum power conversion efficiency of the proposed circuit is 53% for an input power of 12 dBm and output load value of 1.74 k\(\Omega\). In addition, the proposed dual-band rectifier works well enough for low input power. The circuit achieves PCE, 22.5% for input power \(-6\) dBm and output load of 3.4 k\(\Omega\), 32.1% for input power \(-3\) dBm and output load of 3.4 k\(\Omega\), 40% for input power 0 dBm and output load of 3.16 k\(\Omega\) and 49.5% for input power 3 dBm and output load of 2.32 k\(\Omega\). Figure 8 displays the power conversion efficiency versus the input power \(P_{in}\) for the 3.5 GHz and 5 GHz bands separately. In this graph, we observe that the proposed rectifier has an output load of 1.74 k\(\Omega\) achieves in 12 dBm PCE 22.7% at 3.5 GHz and 30.7% at 5 GHz. Figure 6: \(S_{11}\) Reflection coefficient.