Design and analysis of the wideband rectifier

Compared to the single-diode rectifier topology, the voltage-doubler configuration not only improves the power handling capabilities but also is suitable for achieving broadband performance [Reference Kimionis, Collado, Tentzeris and Georgiadis8]. Therefore, the Schottky diode BAT15-04W with a series connected pair of diode chips in one package is selected for this design [21]. The design procedure of the proposed broadband rectifier includes two parts, as shown in Fig. 1. In Fig. 1(a), the rectifier is matched by four uncoupled transmission lines labeled TL1-TL4. Each transmission line has a characteristic impedance of Z _0i and an electrical length of θ_i (i = 1–4). The capacitors C ₁ and C_L are used to block the DC and filter the RF signal, respectively. In Fig. 1(b), TL1 and TL4 are coupled. The asymmetric coupled-line impedance transformer not only enhances the compactness of the rectifier but also widens its bandwidth. The rectifier is designed to operate from f_L to f_H with a load of 500 Ω, where f_L and f_H indicate the lowest and highest working frequencies, respectively.

Figure 1.

Schematic diagram of the proposed broadband rectifier: (a) without the coupled-line and (b) with the coupled-line.

The design strategy of the input impedance matching network is shown in Fig. 2. The start and end frequencies are f_L = 0.3 GHz and f_H = 3 GHz, respectively. First, the load impedance Z_L is evaluated by the following equation [Reference Zheng, Liu and Pan18]:

(1)\begin{equation}{Z_L} = \frac{{\pi {R_s}}}{{2{\theta _{on}} - \sin 2{\theta _{on}} + j\omega {R_s}{C_j}(2\pi - 2{\theta _{on}} + \sin 2{\theta _{on}})}}\end{equation}

(2)\begin{equation}\tan {\theta _{on}} - {\theta _{on}} = 2\pi \left( {{{{R_s}} \mathord{\left/ {\vphantom {{{R_s}} {{R_L}}}} \right. } {{R_L}}}} \right)/(1 + {{2{V_{bi}}} \mathord{\left/ {\vphantom {{2{V_{bi}}} {{V_o}}}} \right. } {{V_o}}})\end{equation}

Figure 2.

The input and load impedance on the Smith chart.

where R_s is the series resistance of the diode, C_j is the diode junction capacitance, and θ_on is the turn-on angle of the diode. In Fig. 2, from 0.1 to 3.2 GHz, Z_L is outside the circle where VSWR = 2. Our target is to compress the input impedance trajectory into the circle where VSWR = 2 over a wide frequency range.

To simplify the design process, the coupling between the transmission lines TL1 and TL4 is not considered in the initial stage. The total electrical length of the transmission lines TL1–TL4 is 180° @ 3 GHz, equivalent to 18° @ 0.3 GHz, and its effect at lower frequencies can be neglected. The electrical lengths of the transmission lines θ ₁ and θ ₂ are set to be 22.5° and 67.5° @ 3 GHz, respectively. To achieve a proper weak coupling, θ ₁ is chosen to be shorter than θ ₂. In our design, the coupling is approximately −30 dB at low frequencies and −20 dB at high frequencies, respectively. Consequently, it exerts a more pronounced impact on the high-frequency matching of the rectifier. By setting those electrical lengths to be constant, the number of unknown variables can be reduced, and we can solve the characteristic impedance of each transmission line by following procedures.

The transmission lines TL1 and TL2 convert the impedance at the center frequency to be 50 Ω:

(3)\begin{equation}{Z_{L1}}\left( {{{\left( {{f_H} + {f_L}} \right)} \mathord{\left/ {\vphantom {{\left( {{f_H} + {f_L}} \right)} 2}} \right. } 2}} \right) = 50\end{equation}

By solving Equation (3), we can get Z ₀₁ = 98.48 Ω, and Z ₀₂ = 87.39 Ω, respectively. After this step, the curve of Z_{L 1} from 0.59 to 2.3 GHz is within the VSWR = 2 circle. Then, the trajectory of Z_{in 1} is further compressed to the center of the Smith chart. By solving

(4)\begin{equation}\left| {{\Gamma _{in}}\left( {{f_L},\;{f_H}} \right)} \right| = 2\end{equation}

we can get Z ₀₃ = 98.48 Ω, and Z ₀₄ = 87.39 Ω, respectively. The bandwidth is broadened to 0.39–2.72 GHz.

Finally, the coupling between TL1 and TL4 is considered to broaden the bandwidth of the rectifier. The coupling has the effect of rotating the trajectory of Z_{in 1} anticlockwise on the Smith chart, as shown in Fig. 2. Thus, the impedance at around 3 GHz can be rotated and compressed into the circle where VSWR = 2. When TL1 is close to TL4, the coupling between them is stronger, and weaker when they are farther apart. By using simulation to vary their distance and observing the bandwidth of S11, we can obtain the final design parameters. Figure 3 compares the simulated |S ₁₁| and PCE of the rectifier with and without TL1 and TL4 coupled. As shown, with the coupling, the higher frequency edge for |S ₁₁| < −10 dB can be extended from 2.73 to 3.05 GHz, while the lower frequency edge remains nearly unchanged. Meanwhile, the higher frequency edge for efficiency over 70% is extended from 2.7 to 3 GHz with the same lower frequency edge. The electrical lengths of TL1 and TL4 are 22.5° @ 3 GHz, which is 2.25° @ 0.3 GHz. At low frequencies, the electrical lengths of TL1 and TL4 are very short, leading to weaker coupling between them. However, at high frequencies, their electrical lengths are longer, resulting in stronger coupling. Therefore, the coupling between TL1 and TL4 has a smaller impact on the rectifier at low frequencies.

Figure 3.

Comparison of |S ₁₁| and PCE with and without TL1 and TL4 coupled.

In order to further investigate the effect of electrical lengths θ ₁ and θ ₂ on the input matching, the return loss performance is simulated by changing θ ₁ and θ ₂ in Fig. 4. As shown, with the increment of θ ₁ and θ ₂, the higher operating frequency edge moves towards the lower frequency. Compared with θ ₂, although θ ₁ only changes slightly for low frequencies, the lower operating frequency changes more noticeably. Here, the coupling plays an important role.

Figure 4.

Comparison of |S ₁₁| changing with different electrical lengths, (a) θ ₁, (b) θ _2.

Implementation and measurement results

According to the above analysis, the initial dimensions of the rectifier can be obtained. Then, all the dimensions for the rectifier are optimized in ADS. The ultra-wideband rectifier, using Infineon BAT15-04 W Schottky diode, is fabricated on a 0.8 mm thick F4B substrate with a relative permittivity of 2.6 and a loss tangent of 0.002. Figure 5 depicts the layout and photograph of the fabricated rectifier with dimensions of 19 mm × 18 mm. The DC-blocking capacitor C ₁ is 47 pF, the by-pass capacitor C_L is 180 pF, and the load R_L is 500 Ω.

Figure 5.

Layout and photograph of the fabricated ultra-wideband rectifier.

The Agilent N5230A network analyzer with a maximum power of 14 dBm was used for |S ₁₁| measurement. The simulated and measured |S ₁₁| under power levels of 0, 5, 10, and 14 dBm are plotted in Fig. 6(a). The simulated |S ₁₁| is better than −10 dB at 14 dBm from 0.51 to 2.88 GHz, while the measured one is from 0.54 to 3 GHz. The measured results agree well with the simulated ones, except for a slight frequency shift, which may be attributed to fabrication and tolerance errors. Figure 6(b) depicts the simulated and measured PCEs changing with the frequency from 0.1 to 3.2 GHz when the input power is 0, 5, 10, and 18 dBm, respectively. These results confirm a good correlation between simulation and measurement. At an input power of 18 dBm, the simulated PCE is over 60% from 0.1 to 2.92 GHz, while the measured one is from 0.3 to 2.9 GHz. When the input power is reduced to 10 dBm, the measured PCE is still over 50% from 0.3 to 2.9 GHz.

Figure 6.

Simulated and measured |S ₁₁| and PCE versus frequency at different input power, (a) |S ₁₁|, (b) PCE.

Figure 7 shows simulated and measured PCEs and output DC voltage versus the input power at four typical frequencies, 0.3, 0.9, 1.6, and 3 GHz, respectively. The simulation and measurement agree well with each other, except for the best PCE point, which shows a notable discrepancy. This difference could be attributed to the breakdown voltage of the diode model being larger than the actual one. Also, the marginal difference observed between the measured and simulated results may be ascribed to the package parasitic effects, particularly notable at higher frequencies. In Fig. 7, at the four frequencies, the measured PCE reaches its maximum value of 65.8%, 79.8%, 75.2%, and 56.2%, respectively. At 0.9 GHz, the measured PCE is over 50% when the input power ranges from 5 to 22 dBm, with a dynamic range of 18 dB. Figure 8 shows the simulated and measured PCE changing with the load at 0.9 GHz when the input power is 0, 5, 10 and 18 dBm. As shown, the optimal load resistance of the rectifier is about 500 Ω. The measured PCE is slightly lower than the simulated PCE. When the load is larger than 1500 Ω, and the input power is 18 dBm, the measured PCE is much lower than the simulated one. In the simulation, the diode operates before breakdown, whereas in the measurement, the diode has undergone breakdown, leading to a significant drop in efficiency. It should be noted that the breakdown voltage specified in the model is higher than the diode’s actual breakdown voltage.

Figure 7.

Simulated and measured PCE and output DC voltage versus input power: (a) 0.1 GHz, (b) 0.9 GHz, (c) 1.6 GHz, (d) 3.1 GHz.

Figure 8.

Simulated and measured PCE changing with the load resistances under different input power levels.

The performance comparison of the proposed ultra-wideband rectifier and the recently published works in the literature is listed in Table 1. As shown, the proposed rectifier has a broader bandwidth than the majority of rectifiers, surpassing all except for those in papers [Reference Mansour and Kanaya10] and [Reference Gyawali, Thapa, Barakat, Yoshitomi and Pokharel19]. Notably, the efficiency over bandwidth in paper [Reference Mansour and Kanaya10] is 45%, while our design achieves 60%. Additionally, the rectifier in paper [Reference Gyawali, Thapa, Barakat, Yoshitomi and Pokharel19] operates at a much lower frequency of 0.06 GHz compared to our rectifier’s 0.3 GHz. Moreover, our design has a smaller size compared to the other works. In summary, our design showcases the merits of high efficiency, broad bandwidth, and compact size.

Table 1.

Comparison between the proposed rectifier and the references

BW: bandwidth.