# Compact-Transmission-Line Decoupling and Matching Network of Three-Element Array for Wireless Applications

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Decoupling Technique

#### 2.1. Network Analysis

_{1}is circularly symmetric as well. The main diagonal elements denoting self-admittance are equal, and the values of other elements denoting mutual-admittance are also equal as shown in the following equation

_{3}, which means that the diagonal elements of the admittance matrix must be ${Y}_{0}$, and any other elements must be 0, [34] i.e.,

_{2}, that is, after the series impedance transformation section: the real part of the main diagonal element is ${Y}_{0}$, and the other elements are pure imaginary numbers.

#### 2.2. Impedance-Transforming Section

_{1}are given by [34].

_{2}should be equal to ${Y}_{0}$ [40].

_{2}, the odd and even mode admittances are transformed into

#### 2.3. Neutralization Section

_{2}reference plane equal ${Y}_{0}$. According to Equation (2), the admittances of the odd and even mode admittances at t

_{3}should equal ${Y}_{0}$, if the decoupling and matching conditions are satisfied. In other words, the neutralization circuit has the function of eliminating the imaginary parts of the odd mode and even mode admittances.

## 3. Design Example

#### 3.1. Coupled Array

_{a}= 1.12 mm are installed vertically at a distance of d = 18 mm on a circular ground with a diameter of 120 mm, forming a symmetrical three-element array. The dielectric substrate is made of F4 B material with a dielectric constant of 2.6 and a thickness of 0.8 mm.

_{a}= 28.6 mm. The designed operating frequency is f

_{0}= 2.5 GHz, and its corresponding quarter wavelength is 30 mm. The length of h

_{a}is smaller than it, because the strong couplings between the antennas are equivalent to the loads of the antennas resulting in the antenna-operating frequency shifting to lower frequencies. Figure 6 illustrates the simulated scattering parameters. Due to the symmetry of the three ports, only the self and mutual parameters between ports 1 and 2 are presented here. As can be seen, the antenna operates at 2.5 GHz, and the port isolation is only 7.5 dB.

#### 3.2. Realization of the Decoupling and Matching Network

_{1}are calculated as follows:

_{1}can be calculated by substituting the entries of the admittance matrix into Equation (4):

_{2}= 0.01 S, and substituting the odd and even mode admittances into Equation (7), one can derive TL2’s electrical length as follows:

_{1}= 53.25 mS. As the susceptance value is greater than zero, an open-circuit transmission line stub is selected to realize it. A characteristic admittance of Y

_{1}= 0.01 S is determined for TL1, so an electrical length of 79.4° is obtained.

_{0}= 0.02 S at the t

_{2}reference plane, with:

_{3}= 0.01 S, and substituting the odd and even mode susceptances into Equation (11), one can derive TL3’s electrical length as follows:

_{4}= −4.38 mS. As the susceptance value is less than zero, a short-circuit transmission line stub is selected to realize it. A characteristic admittance of Y

_{4}= 0.01 S is determined for TL1, so an electrical length of 66.3° is obtained.

_{3}, the odd and even mode admittances are Y

_{0}, thereby meeting the decoupling and matching condition and achieving the circuit function determined in the specification. As illustrated in Figure 10a, the surface current distribution of the DMN at 2.5 GHz can be verified. When one port feeds power, there is no energy coupling to the other two ports. Table 1 presents the parameters and dimensions of each segment of the transmission line of the DMN shown in Figure 10b.

## 4. Measurements and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

## References

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**Figure 2.**Equivalent circuit diagram of the symmetrical three-port network at reference plane t

_{1}.

**Figure 4.**Equivalent circuit diagram of the neutralization section: (

**a**) the star-shaped circuit; (

**b**) the even mode circuit; and (

**c**) the odd mode circuit.

**Figure 8.**Y parameters at the reference plane t

_{2}: (

**a**) real part of the even and odd admittances; and (

**b**) imaginary part of the even and odd admittances.

**Figure 10.**(

**a**) The simulated current distribution on the DMN at the center frequency; and (

**b**) the layout of the DMN.

**Figure 13.**Radiation patterns of the decoupled array when port 1 is activated: (

**a**) xoz plane; (

**b**) yoz plane; and (

**c**) xoy plane.

TL | Z (Ohm) | Θ (deg) | Width (mm) | Length (mm) |
---|---|---|---|---|

1 | 100 | 79.1 | 0.61 | 9.5 + 2 + 8.5 = 20 |

2 | 100 | 15.9 | 0.61 | 5.34 |

3 | 100 | 83.9 | 0.61 | 2.5 + 3.5 + 2 + 3 + 2 + 3.69 + 2.5 + 4 = 22.9 |

4 | 100 | 66.3 | 0.61 | 2 + 4 + 2 + 6 + 2 + 7.5 = 23.5 |

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**MDPI and ACS Style**

Zhang, C.; Jiao, Y.-C. Compact-Transmission-Line Decoupling and Matching Network of Three-Element Array for Wireless Applications. *Electronics* **2023**, *12*, 1567.
https://doi.org/10.3390/electronics12071567

**AMA Style**

Zhang C, Jiao Y-C. Compact-Transmission-Line Decoupling and Matching Network of Three-Element Array for Wireless Applications. *Electronics*. 2023; 12(7):1567.
https://doi.org/10.3390/electronics12071567

**Chicago/Turabian Style**

Zhang, Chi, and Yong-Chang Jiao. 2023. "Compact-Transmission-Line Decoupling and Matching Network of Three-Element Array for Wireless Applications" *Electronics* 12, no. 7: 1567.
https://doi.org/10.3390/electronics12071567