# CP Antenna with 2 × 4 Hybrid Coupler for Wireless Sensing and Hybrid RF Solar Energy Harvesting

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design Circuit Structure

#### 2.1. Dual Port CP Antenna

_{r}= 4.2, tanδ = 0.0018, h = 0.0035 mm) with a two-port patch antenna installed and a 50 Ohm SMA port utilized for network feeding. The FEM (Finite Element Method) analysis used to solve numerical differential equations for 3D electromagnetic modeling in the High-Frequency Structure Simulator Software is utilized to optimize the implementation and design of the structure.

_{11}mode [12,13]. The antenna configuration has a symmetrical geometry; therefore, the antenna’s electrical characteristics in the two feed states have the same behavior in orthogonal polarization. Briefly, the working frequency of the antenna can be represented by Formula (1) to determine the position of the feed circular polarization.

_{y}. It is an E-field linear polarized to the y axis. Additionally, E

_{x}linear polarization to the x-axis to produce a right-hand circular polarization can be achieved by feeding along the opposite radius, which starts from the lower right corner and continues to the upper left corner to produce a left-hand circular polarization. This method obtains circular polarization to place the via hole in a feed based on optimization. Thus, based on the optimization results, the via-hole position formulation for the antenna design is obtained by Formula (1).

_{y}− k

_{x}) − Qt. Tan δ is the loss tangent of the material. Based on the optimization, the angle ϕ separates the two via holes is determined. It is obtained to produce an orthogonal field to each other under the patch and outside the patch. The via hole is positioned at the point where the other via-hole generates the field; therefore, the reducing effect significantly changes the performance between ports to increase the antenna’s sensitivity to wave polarization [15]. The ground plane separating the primary patch connection and the double U slot is smaller than the resonance size so that radiation has propagated to the main patch element. Assuming the circular patch resonates in its dominant mode, the accumulation of the slot optimization model concerning the frequency formed on the patch surface is expressed in Equation (2).

^{8}m/s and ε

_{r}is the permittivity value of the antenna substrate, which is the phenolic white paper. The resonant frequency at each output port on the CP antenna is 2.4 GHz, which has the same resonant frequency with a lower axial ratio. Using the formula to estimate the operating frequency of the two ports to produce CP axial ratio, the double U slot is optimized, and the slot width calculation dst = R

_{so}− R

_{si}to determine the path distance to the ground. With a tolerance value of less than 4% when the slot width is 0.0001 m. The double U slot in the design has the advantage that most of them independently have a resonant frequency on the antenna with a specific band range on the performance of other antennas with changes in the frequency value in Figure 4a,b. Figure 4b has a lower slope point than Figure 4a. It is due to the wave reflection on port 1 in Figure 4a. However, it does not significantly affect the antenna’s resonant frequency.

_{st}) based on the radius of the circular patch dimension to the ground distance obtained from d

_{st}= R

_{so}− R

_{si}with a value of d

_{st}with a shifting accuracy up to 10–5 mm at the narrowband frequency so the correct frequency capture on the antenna settings according to the implementation.

#### 2.2. 2 × 4 Direction-Finding Hybrid Coupler and Hybrid Electromagnetic Solar Circuit

_{L1}, which has a complex impedance assuming that the loss coupler is negligible [7,18]. Suppose the circuit impedance between the feeds does not match from the coupler side. In that case, the reflected wave from port 4 is 1 so that the reflected wave at port 3 is jҐα1 where Ґ is the reflected wave coefficient on the wave propagation in the stripline hybrid coupler and α is the representation of the signal originating from port 4 which propagates with the reflected wave. β is the propagated reverse wave on the circuit with the numbers following, which is the port shown in Figure 6. Then, the signal is transmitted back to ports 4 and 3 through the coupler; therefore, the output waveform on the reflection coefficient at port 1 is from port 3 in the form of β

_{3}= −jҐα

_{1/}√2 (β

_{3}= −Ґα

_{1/}√2) and on port 4 β

_{4}= −Ґα

_{1/}√2 (β

_{4}= −jҐα

_{1/}√2) or the incoming feed-side coupler where 1 is the input waveform of port 1. Then, the reflection value can be expressed as α

_{3}= jҐҐe

^{−i2}

^{Φ}α

_{1/}√2 (α

_{3}= ҐҐe

^{−i}

^{2}

^{Φ}α

_{1/}√2), and α

_{4}= ҐҐe

^{−i}

^{2}

^{Φ}α

_{1/}√2 (α

_{4}= jҐҐe

^{−i}

^{2}α

_{1/}√2), which propagates to the coupler and then to Port 1 with Φ as the phase length of the propagated wave; on the feed, the coupler path propagates to the other side. The output wave propagation is β

_{1}= 0 (β

_{1}= −jҐҐe

^{−i}

^{2}

^{Φ}α

_{1}) and β

_{2}= −jҐҐe

^{−i}

^{2}

^{Φ}α

_{1}(β

_{2}= 0). β

_{1}and β

_{2}are the reflection coefficient values for ports 3 and 4. At a reflection value of 1, where one of the feeds goes towards the other side, the value of the matching circuit causes the deficiency of a reflected wave based on Port 1; it can be expressed as β

_{1}= 0 after reflection occurs. This happens when no reflected wave returns to Port 1.

_{1}= −jҐҐe

^{−i}

^{2}

^{Φ}α

_{1}. The feed structure differs from the antenna. The feed structure varies in input power and output load. However, this can work well as long as it can remain impedance-matched. So that there is no reflected wave, the wave structure can be reused even to increase the efficiency of the shifting conversion of the reflected wave.

^{2}[19]. Based on these regulations, the circuit design in this study uses a power rectifier with an intermediate input. The circuit design configuration is described in Figure 7. The circuit configuration design is printed on the FR4 substrate, which is identical to the antenna with a coplanar structure. The components in the rectifier circuit design include capacitors, series rectifier diodes, and circuits with a 3-stage voltage doubler configuration.

^{2}. Based on previous high-frequency research, rectifying is effective at a low threshold voltage (Vbi = 0.25 V); a single SMS 7621-079LF Schottky diode is utilized, with a bias capacitance value (Cj = 0.18 pF), which is connected in series [20,21]. It is based on the working principle of a multi-stage circuit doubler. In addition, the advantages of diodes in circuit design are that they have low power consumption and band switching at a frequency of 2.4 GHz according to antenna specifications. Optimization is additionally carried out. Line feed dimensions and capacitor values are based on the calculation of the electrical circuit. Then, by electromagnetic method analysis, the wave propagation is simulated using ADS software with an impedance following the feed on the antenna and thin-film solar cell with the circuit source scheme shown in Figure 7.

_{1}and D

_{2}, are placed in series and shunt circuits in the impedance circuit configuration. Then, to provide a long-lasting effect on the delivery of the waveform, a capacitor is embedded between the transmission lines with a C

_{ot}value, each with an impedance value of Z

_{li}and df with a DC output load at a load of R

_{l}.

_{if}can be described using Equation (3):

_{r}is the gain of the receiving antenna, and the power density in the receiving environment is expressed as W

_{r}. The value of G

_{r}is the antenna gain according to the design configured with the circuit. When measuring the rectenna, the W

_{r}value is tuned to 1 mW/cm

^{2}so that, at a distance of 30 cm, the P

_{if}value is 10.28 dBm. The analysis of the antenna circuit design can be represented in an equivalent circuit as a resonance circuit at the antenna’s instruction load value. The inductance is L

_{An}and capacitance C

_{An}in Equation (4). Adjustments the resonant frequency, which must meet Equation (2) by ω for generating f, the value of which is utilized later for process analysis [25,26] on the propagation of the transmitted RF wave.

_{An}and C

_{An}. However, to guarantee the minimum capacitance, the C

_{An}must be smaller than the charging pump capacitor. The L

_{An}and C

_{An}values are obtained as 6.5 nH and 0.65 pF by ensuring that no electrical charge is stored on the Can at a frequency of 2.4 GHz.

## 3. Performance and Analysis

#### 3.1. Double Feed CP Antenna—Double U Slot

#### 3.2. Rectifying Multistage Hybrid RF Solar Energy Harvesting and Wireless Sensing

_{Rx}(θ, φ, f ) = vP

_{r}(θ, φ, f)η

_{a}(P

_{if})

_{if}), which is correlated with the arrival angle (θ, φ, f) as an indicator of the transmission process in the communication system. In addition, to express the efficiency of the antenna based on the frequency function, it is represented by η

_{a}.

_{r}) is the RF-DC conversion efficiency which the following equation can express:

_{Rv}antenna, the load impedance is expressed by Z

_{L}, and the DC output voltage above the load is defined by V

_{Out}, thereby comprehensively identifying the DC output voltage in each circuit configuration. Before measuring the V

_{Out}of P

_{Rv}performance, this is done by testing and taking several power samples that the antenna can obtain in far-field conditions with the power spectrum level on the signal vector analyzer, which is represented on the spectrum in Figure 5.

**Rxx**is the estimated covariance matrix which can be expressed as ${\mathrm{\u0158}}_{xx}=\frac{1}{{M}_{s}}{\sum}_{\tau =1}^{{M}_{s}}\mathrm{y}\left(\tau \right){\mathrm{y}}^{H}\left(\tau \right)$, where the number of samples is defined by M

_{s}. Then, the decomposition of the eigenvalues on the covariance matrix can be described using Equation (9).

_{xx}= Ê

_{sg}Â

_{sg}Ê

_{sg}

^{H}+ Ê

_{ns}Â

_{ns}Ê

_{ns}

^{H}, and with values Ê

_{sg}= [ê

_{1}, ê

_{1}, …, ê

_{n}] including the eigenvector estimates for the signal subspace; Â

_{sg}= diag[â

_{1}, â

_{2}, …, â

_{n}] is diagonal matrix of the largest estimated eigenvalues. This is with the following subspace eigenmatrix values:

^{2}for each signal spectrum. From each spectrum level, the degree of signal arrival can be represented at each spectrum peak with angle values of 40°, 80°, 120°, and 160° according to the angle in the sample signal transmission process with high accuracy under ideal conditions. Therefore, the algorithm can effectively solve the communication process on wireless sensors supported by wireless energy harvesting with electromagnetic harvesting and solar energy.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**(

**a**) Arrangement via the hole on transmission feed (

**b**) Feed transmission on CP antenna configuration.

**Figure 4.**Arrangement S parameter calculation to the dimensions of the double U slot on (

**a**). S11 on port 1 (

**b**). S21 on port 2.

**Figure 9.**Implementation of the prototype CP Antenna with 2 × 4 Hybrid Coupler for Hybrid Electromagnetic Solar Energy Harvesting and wireless sensor.

**Figure 12.**Radiation Pattern of the Double U slot with the dual feed CP Antenna (

**a**) Rectangular plot (

**b**) Radian Plot.

**Figure 15.**Rectenna output voltage from the source: (

**a**). thin-film solar cells; (

**b**). dual feed CP Antenna.

**Figure 16.**The increased voltage on the integration of the CP Antenna with the 2 × 4 Hybrid Coupler for Hybrid Electromagnetic Solar Energy Harvesting.

**Figure 18.**(

**a**). Schematic analysis of antenna configuration on the wireless sensor (

**b**). CP antenna adaptive analysis of the radiation pattern.

**Table 1.**Comparison of the CP Antenna with the 2 × 4 Hybrid Couple with Energy Harvesting and wireless sensing with previous research.

Ref | Freq (GHz) | S11 | S21 | Polarization | Eff % | Working Mode | Structure | Communication Analysis |
---|---|---|---|---|---|---|---|---|

[36] | 1.8 and 2.45 GHz | −28dB | - | LP | 43 | Only energy harvesting | Multiple layers in the encapsulation | - |

[37] | 2.4 GHz | <−15 dB | <−15 dB | Dual CP | - | Communication and energy harvesting simultaneously | Two-layer Semiconductor | Multiple signal classification |

[33] | 1.7–2.6 GHz | <−10 dB | - | LP | - | Only energy harvesting | Single-layer Semiconductor | - |

[34] | 5.8 GHz | <−12.65 dB | <−12.04 dB | LP | 51.73 | Communication and energy harvesting separatedly | Single-layer Semiconductor | - |

[35] | 1.7–2.6 GHz | <−10 dB | - | LP | - | Only energy harvesting | Single-layer Semiconductor | - |

This work | 2.4 GHz | <−15 dB | <−15 dB | Dual CP | 53 | Communication and energy harvesting simultaneously or in independent operation | Two-layer Semiconductor | Multiple signal classification |

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## Share and Cite

**MDPI and ACS Style**

Mujahidin, I.; Kitagawa, A.
CP Antenna with 2 × 4 Hybrid Coupler for Wireless Sensing and Hybrid RF Solar Energy Harvesting. *Sensors* **2021**, *21*, 7721.
https://doi.org/10.3390/s21227721

**AMA Style**

Mujahidin I, Kitagawa A.
CP Antenna with 2 × 4 Hybrid Coupler for Wireless Sensing and Hybrid RF Solar Energy Harvesting. *Sensors*. 2021; 21(22):7721.
https://doi.org/10.3390/s21227721

**Chicago/Turabian Style**

Mujahidin, Irfan, and Akio Kitagawa.
2021. "CP Antenna with 2 × 4 Hybrid Coupler for Wireless Sensing and Hybrid RF Solar Energy Harvesting" *Sensors* 21, no. 22: 7721.
https://doi.org/10.3390/s21227721