#### Abstract

In this paper, a new viewpoint on the function of the Schottky barrier diode (SBD) in microwave rectifying circuit is proposed. In the analog circuit field, it has been formed a relatively mature theoretical system about the rectifying circuit, which constitutes the base of subsequent rectifier design schemes. The researchers take it for granted that the SBD selected as the core component in the microwave rectifying circuit should play the role of rectifying in the same way as the diode in the analog circuit. The fact that the one-directional conductivity of the SBD is not observed in microwave circuit by the means of simulation and experiment is proposed. The basis of the former rectification theory is in doubt here. Due to the interaction of the microstrip line and SBD, the DC component generated at the front end of SBD is the key reason for the DC output power of rectifying circuit. The way of DC generation is completely different from the previous idea. Accurate and in-depth understanding of the function of SBD in microwave rectifying circuit will help the researchers to make use of SBD rightly and design circuit in future applications.

#### 1. Introduction

A large number of attractions have been focused on wireless power transfer (WPT) in recent years for its unique characteristic. WPT system can meet the demand for self-sustained equipment and battery-free device, which have more advantages in the realizing contact-less energy harvesting. Therefore, the increasing research enthusiasm has been devoted to this field for its convenience [1–6].

Aiming to obtain high conversion efficiency from RF power, the design scheme of rectifying circuit focusing on the conversion from RF to DC is widely studied. The low conversion efficiency plagues the researchers. In WPT, the design of rectifying circuit has been instructed by the rectification theory from AC to DC always [7–13].

Rectification theory is a relatively complete theoretical structure, which has been used to design various rectifying circuits in the field of analog circuits. Different kinds of rectifying circuit topology have been proposed, such as half-wave rectifier, full-wave rectifier, and double voltage rectifier.

Until now, the previous rectification theory instructs the design of rectifying circuit containing SBD in the microwave field.

As everyone knows, the one-directional conductivity of the diode is the base of rectification theory and the key to realize rectification. Due to the mechanism of multicarrier transmission, SBD has the characteristic of high switching frequency, which is selected as the core component for rectifier in microwave circuit usually. The researchers naturally believe that SBD plays the role of the one-directional conductivity in microwave rectifier similar to the ordinary diode in the analog circuit.

In previous research, a variety of mathematical methods are used in the analysis of related circuits containing SBD. Ritz–Galerkin method and second-order differential equation are often used to analyze the related circuits [14, 15].

In this paper, based on analyzing the one-directional conductivity of SBD in microwave circuit, the opposite view will be put forward. In microwave rectifying circuit, the generated path of DC is completely different from the other by the one-directional conductivity of the diode and the effect of the capacitor in analog circuits. No matter how the diode is placed, the upper end of the diode will generate a DC component which constitutes the main source of DC output power of the whole circuit. The related microwave circuit will be analyzed gradually in this paper, which may be subdivided and verified experimentally step by step. The principles of the rectifier may be proposed on the basis of observing the change of signal in each segment.

#### 2. Previous Research Status

The realization of the rectifier relies on the one-directional conductivity of the p-n junction, which is the basic property of the diode. Different types of the diode, such as SiC and PIN, have the fundamental function of rectification for application.

The one-directional conductivity of the diode in the traditional rectifying circuit will be depicted by the waveform diagram as shown in Figure 1. The diagram of the bridge rectifying circuit is presented in Figure 2. The DC voltage on the load is obtained owing to the filtering function of the capacitor.

The one-directional conductivity of diode and the filtering function of capacitor are two necessary conditions for the design of rectifying circuits in analog circuits. SBD is selected as the rectifying diode by many researchers in the field of microwave rectifier for its characteristic of high switching frequency. The equivalent circuit of the physical mode of SBD is shown in Figure 3 [12].

In Figure 3, *V*_{j} is the voltage of the junction of SBD. *V*_{j} is composed of *V*_{j0} and *V*_{j1}. *V*_{j0} is the DC voltage, and *V*_{j1} is the voltage of the fundamental frequency. *R*_{s}, *R*_{j}, and *C*_{j} are the parameters of the physical mode of SBD.

Many associated formulas and derivation processes in the related papers have been analyzed on the base of Figure 3 [12, 14, 15]. Integral equations and differential equations are used to calculate the power and conversion efficiency. These formulas include many diode parameters, such as *θ*_{on}, *R*_{j}, and *C*_{j}. The *θ*_{on} is the opening angle of SBD. Until now, researchers believe that the power and conversion efficiency are relevant to these parameters.

Based on the understanding of electromagnetic theory [16, 17], the different views will be presented after analyzing the microwave circuit containing SBD in the next chapter.

#### 3. Analysis of SBD Characteristics in Microwave Field

Firstly, the one-directional conductivity of SBD will be verified by simulating the circuit in Figure 4 with advanced design system (ADS) software. Here, *R* = 300 ohm, and input power = 10 dbm. The model of SBD is HSMS286B. The output waveform at two input frequencies, respectively, will be given in Figure 5. It will not affect the output waveform obviously by changing the length of TL1. The amplitude will fluctuate in a small range.

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It can be clearly observed that the one-directional conductivity of SBD will disappear with the increase of the input frequency. The output waveform is closely related to the input signal frequency. When the input signal frequency is very low, the one-directional conductivity of SBD plays a role. If the input frequency is increased to 2 GHz, the sinusoidal output waveform will become more clear.

After analyzing the voltage on the resistor, the waveform and spectrum on the SBD are more illustrative. The microwave circuit integrating the transmission line and SBD can more clearly show the characteristics of SBD in the microwave field, which is depicted in Figure 6.

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This circuit has been analyzed in our previous paper [18]. Here, we give the conclusion directly. For Figure 6(a), the period-doubling phenomenon will be observed on the test point VR by adjusting the length of TL2 at GHz frequencies. By setting 1 GHz fundamental frequency, the diagram of the period doubling phenomenon obtained by simulating with advanced design system (ADS) software is given in Figure 7 [18].

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We have presented the theoretical and experimental analyses in the previous paper, and the experimental results are undeniable. In Figure 6(b), the same testing results can be achieved. The observed phenomenon is independent of the placement direction of the diode. When the waveform of VR is a single period, the waveform of VD is also a single period and has no DC component. When the waveform of VR is quadruple period, the waveform of VD is an irregular waveform and has a large DC component. The simulation results are shown in Figures 8 and 9.

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The causes of the period doubling phenomenon at the VR testing point have been explained in detail [18]. From this phenomenon, we are inspired to get the idea that the one-directional conductivity of the SBD does not appear at GHz frequencies. DC component will be generated at the upper end of the SBD which is close to the positive pole of the power source. DC component is not always available. When the length of the transmission line reaches a certain value, the amplitude of the DC component will reach the maximum.

The previous conclusions change the understanding of microwave rectifying circuit composed of microstrip lines and SBD directly. DC component can be generated under the condition that only microstrip line and SBD are needed. In the next section, the essence of DC power generation will be put forward by experimental verification using decomposed circuit structure.

#### 4. Experimental Analysis of Rectifying Circuit Gradually

Then, it will be studied by decomposing the related microwave circuits combining with microstrip line and SBD gradually and observing the signal at each stage.

The current design scheme for rectifying circuit is to calculate the input impedance of SBD firstly and then design filter and matching circuit to obtain a good *S*11 value. The measuring circuit of SBD input impedance and rectifying circuit based on this impedance are presented in Figure 10. Compared with Figure 9, similar measuring results may be obtained at the VD testing point in Figures 10(a) and 10(b). An excellent *S*11 value is to ensure that more energy enters the SBD. From Figures 6 and 9(b), it can be learned that the DC component can also be generated at the front end of the diode. The cause of the DC component is from the nonlinear characteristic of SBD and the function of the microstrip line. Transmission line TL3 and capacitor C form a DC-pass filter (DPF) to obtain DC power on the load. From these results, we can infer that the rectification effect is not related to the diode’s own parameters, such as *θ*_{on}, *R*_{j}, and *C*_{j}. Under certain input power, if more DC components can be accumulated at the front end of the diode, more DC power can be obtained at the load end. The process of obtaining DC power of microwave rectifying circuit is completely different from that of the analog circuit.

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To further verify the previous simulation results and assumptions, the following is a physical test. In Figure 11, the overall measuring environment may be appreciated. The fabricated prototype of the test board is shown in Figure 12. After adjusting the length of microstrip line and the position of SBD in circuit, the change of signal in the frequency domain is obvious.

The circuit diagrams of the first seven channels are shown in Figures 13 and 14. In the following figure, TL1 = 38 mm, and TL3 = 60 mm. The choice of the TL1 and TL2 length is based on the data in reference [18]. When the length of TL1 is 38 mm, the single period will appear at the VR test point. When the length of TL1 is 91.1 mm, the quadruple period will appear. Meanwhile, the length of TL3 is close to *λ*/4 [11].

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The circuit diagrams of the last seven channels are the same as those of the first seven channels, but the length of the microstrip line is different. Here, TL1 = 91.1 mm, TL3 = 60 mm, *f* 0 = 1 GHz, and pw = 10 dbm. The selected SBD is HSMS286B.

Firstly, the one-directional conductivity of SBD should be analyzed because it is the base of the whole rectification theory. In Figure 13(a), the output waveform is equivalent to the input waveform if the input signal frequency is low. For example, the sinusoidal waveform of 90 MHz is input, and the sinusoidal waveform of 90 MHz is also obtained at the output end.

With the increasing of the input frequency, high-order harmonics will be generated due to the nonlinearity of SBD. 2 GHz and 3 GHz harmonics will appear as the result of the input of 1 GHz. The same result will appear whether the diodes are connected in series or in parallel. The spectrum measured with a spectrum analyzer in Figure 13(b) is shown in Figure 15.

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In Figure 15(a), we will get −3.14 dbm in 1 GHz and −22 dbm in 2 GHz. In Figure 15(b), we will get −1.12 dbm in 1 GHz and −18 dbm in 2 GHz. The waveform in the time domain can be depicted in Figure 16. The same result will be derived by measuring the spectrum of Figure 14(b).

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The one-directional conductivity of SBD is not observed in these experiments. Previous rectification theory from AC to DC is not sufficient to explain the current phenomenon. So, a new viewpoint needs to be presented about the conversion of RF-DC in microwave field. SBD in the microwave frequency band is completely different from the other diode in the analog circuit. Because SBD have no characteristic of the one-directional conductivity in the microwave rectifying circuit, researchers should transform their understanding of rectifier in WPT. Therefore, due to the deviation in understanding the basis of rectifier, other problems arise in the discussion of SBD.

In Figures 13(c) and 14(d), the capacitance and load are added, and the capacitance and TL3 form a DPF. The DC voltage can be obtained at the load end for the reason of DPF. The similar results will be achieved when the circuits of the last seven channels are measured in the same way. When the length of the transmission line changes, it not only play a phase delay role but also change the amplitude of the main frequency.

#### 5. Further Analysis of Test Results

As everyone knows, power is transmitted in the form of electromagnetic waves in the microwave circuit. The times of harmonic frequency will be observed as the result of the nonlinear equipment. The working mechanism here cannot be analyzed by the working mode of the p-n junction behavior or the metal-semiconductor junction behavior. It is fully explained that the previous rectification theory is inappropriate here.

The generally accepted topology of the rectifier is shown in Figure 17. Figures 13(c) and 14(d) are simplified rectifying circuits.

It is inappropriate to analyze the voltage and current value across the two ends of SBD from the perspective of electronics. It is only suitable for analyzing voltage and current value on load. The obtained DC power at the load is as the result of the DPF not the one-directional conductivity of SBD.

The amplitude of the high-order harmonics caused by SBD is very low. So, the DC power obtained from higher harmonics is also very low. The treatment measures for harvesting high-order harmonics energy are meaningless.

SBD used to be adopted in detection circuit more. Therefore, researchers still analyze these problems about SBD from the previous point of view. In the microwave field, detection is concerned with the frequency of the signal, while rectification is concerned with power. These are not always the case.

From the previous analysis, we think about the following questions. It should be presented that many previous design idea and formula derivation are not suitable for circuit containing SBD in the microwave domain. The associated mathematical methods and equations are obviously inappropriate to deduce relevant results. Half-wave rectifier, full-wave rectifier, and double voltage rectifier need to be reconsidered here. Is it meaningful to improve SBD from the perspective of materials and parameters? Does it make sense to blindly reduce the *θ*_{j}, R_{j}, and C_{j} [19]? Is SBD suitable for rectifying circuit really?

#### 6. Conclusion

In this paper, the essence of rectifying circuit is found more thoroughly. Starting with the one-directional conductivity of diode, it compares the differences in rectification idea in analog circuit and microwave circuit in this paper. It is a major discovery of this paper that the one-directional conductivity of SBD does not appear in microwave rectifying circuits. Furthermore, a new understanding about the role of SBD in microwave rectifying circuit is presented. The judgment that the previous rectification theory is not suitable in the current design at GHz frequencies is proposed. The combined action of microstrip line and SBD produces DC component, which is the source of DC power. Whether changing materials and parameters of SBD can improve conversion efficiency need further consideration. Various rectifying circuit topologies based on SBD need to be reconsidered and analyzed. The different understanding of SBD proposed in this paper will help researchers to further study this problem in the future.

#### Data Availability

The data and the values of components used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.