Super detailed explanation of system antenna design method based on eigenmode theory

Constantly increasing the communication capacity and quality of communication systems is the eternal theme of wireless communication. With the rapid development of wireless communication technology, people have put forward more and more requirements on the design of the antenna. Using ultra-wideband (UWB) technology and multiple-input multiple-output (MIMO) technology has great potential in improving data transmission rate. MIMO technology can improve the signal-to-noise ratio of the communication system, improve channel capacity and suppress channel fading, for mobile devices. In this case, multiple units need to be integrated together to reduce the size of the entire antenna, which requires a low mutual coupling between MIMO multiple antenna units, so as to achieve low correlation between the signals of the respective channels. The use of the characteristic mode technique based on the moment method is a best choice.

The eigenmode analysis method is an analytical method that has emerged in recent years. It is a new method that uses a relatively wide moment method combined with analytical eigenmode theory to solve electromagnetic problems. It provides an antenna designer with an optimal antenna design method that helps the antenna designer understand the working mechanism of the antenna. Using the information obtained from the analysis of different modes to grasp its resonant characteristics and radiation characteristics of different modes, etc., to select the best feed location to stimulate the desired mode with the distribution of the characteristic currents of different modes, it also helps to guide the designer The antenna is slotted to fine tune its resonant position [1]. In this paper, the eigenmode analysis tools of FEKO V14 version [2] are used to simulate the eigenmode parameters of several common antenna types. The mode method defines a series of eigenmodes that are similar to analytical methods for arbitrarily complex electromagnetic problems. These modes can describe the intrinsic properties of electromagnetic problems and have orthogonal characteristics between modes. The size of the eigenvalue directly determines The mode contributes to the electromagnetic parameters. It makes the moment method have a clearer physical view. The antenna designer can use the information provided by the pattern analysis to understand the working principle of the antenna in more depth, design the antenna with the best performance, and even design a new antenna form [3 ].

The eigenmode theory was first proposed by Garbacz in his doctoral dissertation [4] in 1968. In 1971, Harrington and Mautz adopted the generalized impedance matrix of diagonalized conductors to obtain the same pattern as that defined by Garbacz [5]-[6] The formula called the eigenmode theory described in [5] is easier to deduce than the one proposed by Garbacz in [4], and it is very effective to validate the arbitrarily shaped structures. Later, Harrington et al. extended the eigenmode theory to handle electrolytes, magnetic media, and electrical/magnetic hybrids [7]. Since its introduction, the eigenmode theory has received extensive attention in the fields of computational electromagnetics and antenna design.

The eigenmode theory defines a series of mutually orthogonal eigenmodes for conductors of arbitrary shape, and these mutually orthogonal eigenmodes are the inherent properties of the conductors. They have astringency and completeness in themselves, and can accurately represent the solutions of electromagnetic problems. The physics concept of the eigenmode theory is clear, and the working mechanism of the electromagnetic structure can be clearly given. At the same time, the characteristic mode is only related to the shape, size and operating frequency of the electromagnetic structure, and has nothing to do with the source point, so it is easy to guide the engineering design.

The eigenmode theory is based on the MoM method. Its eigen equation is:

(2.1)

The current on the conductor is developed using the characteristic current as a basis function:

(2.2)

In addition, it is derived:

(2.3)

(2.4)

The expansion coefficient αn in equation 2.3 represents the characteristic current Total current The importance of medium is called the mode weighting factor Modal Weigh TIng Coefficient (MWC). For characteristic currents, λn is the eigenvalue and Ei is the incident field. In Equation 2.4, Vn is the Modal ExcitaTIon coefficient (MEC). When the excitation signal is added, it is determined which mode is easily excited.

Since R and X are HermiTani operators, they are also real symmetry operators, and operator R is a positive definite operator. Therefore, according to the generalized eigenvalues ​​and the properties of R and X, the eigenvalues ​​λn and the characteristic currents Jn are both real numbers. (ie the same phase). It can be proved that the characteristic current satisfies the following orthogonality [30]:

<Jm, RJn>=δmn (2.5-1)

<Jm, XJn>=λnδmn (2.5-2)

<Jm, ZJn>=(1+jλn)δmn (2.5-3)

Here, the characteristic current is normalized, ie <Jn, RJn>=1. Indicates that the radiated power is 1. Since Pmn=<Jm, ZJn>, in the case of a radiation power of 1, the energy storage is only related to λn, and the sign of λn determines the type of energy storage: when λn is closer to 0, it means that the mode is more at this frequency. Near resonance; λn>0 indicates that the mode stores magnetic energy at this frequency; λn<0 indicates that the mode stores energy at this frequency.

Since the range of values ​​of λn varies greatly, it is inconvenient to observe. Modal Significance (MS) and characteristic angles CharacteresTIc Angle (CA) are also used in engineering to represent the resonance of each mode of the antenna:

(2.6-1)

CA=180° -tan-1 λn (2.6-2)

From equation (2.6-1), we can see that the range of MS is (0,1 ). When the MS is closer to 1, it means that the mode is closer to the resonance state; conversely, it means that the mode is far from resonance and it is difficult to be excited and effectively radiate. From (2.6-2), when CA=180 degrees, this mode is in resonance.

The MS parameter can be used to define the radiation bandwidth BWn of the pattern, ie, the frequency range where the radiant energy is greater than or equal to half of the radiant energy of the resonance point within the frequency band.

(2.7-1)

(2.7-2)

The above equations fU and fL are two frequency points when the MS value is 0.707, fres is the resonance frequency of the current mode, and the bandwidth can be calculated from the formula (2.7-2). Similarly, the operating bandwidth of each mode can also be When the characteristic angle (CA) is read from the frequency variation curve, it is not difficult to find that when the MS value of each mode is 0.607, the corresponding λn=1 and λn=-1, CA=135 degrees and CA=225 degrees.

Through eigenmode analysis, the eigenvalues ​​(λn), eigencurrents (Jn), characteristic angles (CA), and mode current coefficients of the antenna can be obtained directly. After adding the port excitation, the mode excitation coefficient (MEC) can be obtained. , Mode weighting coefficients (MWC), different modes of excitation power, reflection coefficients of different modes, and antenna efficiency.

In this section, several commonly used line antennas and MIMO antenna PCBs will be listed, and FEKO v14 software will be used to analyze the characteristic modes of the antenna.

For wideband eigenmode analysis, mode tracking [8][9] is challenging because the resonant mode changes with frequency, and the initial mode number is based on the starting frequency mode. , According to the number of energy from high to low, some models will gradually disappear as the frequency changes (the energy occupancy rate is getting smaller and smaller), and some new modes will gradually appear. The following example applies to the pattern tracking technique. There is also a pattern tracking processing technique that determines several modes of the starting frequency and tracks only a few determined patterns throughout the wide frequency range, which may lose some new modes.

The typical eigenmode analysis flow [10] mainly includes three steps: selecting the desired working mode based on the analysis of the geometric shape, selecting the feed position to add the excitation verification to obtain the desired mode, and verifying whether the antenna parameters meet the design requirements.

A. Analysis of characteristic modes of dipole antenna

The dipole antenna element used in Example 1 has a total length of 1.5 meters, a frequency sweep range of 50 MHz to 400 MHz, and 201 frequency points.

Figure 1. Dipole antenna geometry model

Figure 2-1. Curves of the eigenvalues ​​(λn) of the first three modes with frequency

Figure 2-2. Characteristic angle (CA) of the first three modes as a function of frequency

Figure 2-3, the first three modes MS with frequency curve and bandwidth

Figure 3: Reflection coefficient vs. frequency curve (blue curve antenna port total reflection vs. green curve mode 1 reflection coefficient vs. red curve mode 3 reflection coefficient)

Figure 4-1. Variation of the mode weighting coefficient with frequency (blue curve is mode 1 vs. green curve is mode 2)

Figure 4-2. Active power added to the port after excitation (purple curve antenna total active power vs. blue curve for mode 1 active power vs. green curve for mode 3 active power)

Figure 4-3. The active power of the port after the excitation is added (the blue curve is the active power vs. the green curve is the active power of the mode 3). Both are calculated using formulas, and the results are shown in Figure 4-2. Anastomosis

Figure 5-1. Oscillator current distribution in the first six modes

Figure 5-2, 3D pattern of the first six modes

B, rectangular ring antenna eigenmode analysis

The rectangular loop antenna used in Example 2 has a side length of 0.229 meters, a sweep frequency range of 100MHz ~ 1400MHz, and sampling 131 frequency points.

Fig. 6. Curve of the characteristic angle (CA) of the first eight patterns with frequency

Figure 7. Current distribution of the first six modes at 100 MHz

Figure 8. Curves of the first eight modes of MS with frequency

Figure 9. Comparison of the VSWR vs. VSWR vs. frequency for the port VSWR at the beginning of the square ring antenna feed

Figure 10. Comparison of the VSWR of the port and the VSWR of the different modes as a function of frequency when fed at the midpoint of the edge of a square loop antenna

C, MiMO antenna eigenmode analysis

Multiple-input multiple-output (MIMO) technology means that multiple transmit and receive antennas are used at the transmit end and the receive end, respectively, so that signals are transmitted and received by multiple antennas at the transmit end and the receive end, thereby improving the communication quality. It can make full use of space resources and achieve multiple transmissions and multiple receipts through multiple antennas. Without increasing the frequency spectrum resources and antenna transmission power, it can double the system channel capacity, showing clear advantages and being considered as the next generation mobile. The core technology of communications, the current research hotspot, CMA technology is very suitable for the design and application of MiMO antenna.

The PCB size [11] used in Example 3 is 130mm X 70mm, as shown in the left figure of FIG. This example [12] focuses on the determination of the change of the feed position and the degree of isolation between the antennas. The right picture in Figure 11 shows that the PCB can work in two frequency bands. Considering that there are few modes to choose from at low frequencies, it is difficult to optimize the isolation. The operating frequency is 700 to 960 MHz.

Figure 11. PCB geometry model (left) and S11 curve (right)

Figure 12, the first three modes MS curve and characteristic current cloud

It can be seen from Figure 12 that Mode #1 and #2 currents are distributed along the PCB's wide and narrow sides; mode #3 current is along the PCB's circumference; Modes 1 and 2 are very suitable for MIMO diversity strategy. Mode #3 MS values Very low, so it is difficult to stimulate in this band.

Figure 13. Current distribution in the middle (left) and side (right) feed modes

It can be seen from Figure 13 that when the feed point is in the center position, the current on the antenna flows from the two edges to the middle and flows through the PCB in the opposite direction. When the feed point is in the edge position, the current on the antenna has only one direction and is coupled to The current of the PCB flows in the same direction. Understanding the current flow of the antenna's mode current and the PCB's feed location will help us to inspire the desired mode.

Figure 14. Current distribution and mode weighting coefficient MWC at different positions of the short-edge feed

It can be seen from Figure 14 that when the antenna branch is on the short side, it is very easy to stimulate mode #1, and the feed point is preferably in the middle. In this band, there are only mode #1 and mode #5, and mode #1 is more than mode. #5 7 dB, expectation!

Figure 15. Current distribution and mode weighting coefficient MWC at different positions of wide-side feed

It can be seen from Fig. 15 that when the antenna branch is located on the wide side, it is very easy to stimulate mode #2, and the position of the feed point is preferably in the middle. In this band, only mode #2 and mode #5 are available, and mode #2 is more than mode. #5 7 dB, expectation! Other feeding methods will inspire more modes and cause the isolation to deteriorate.

Figure 16. Different excitation combinations inspire different patterns

It can be seen from FIG. 16 that when the antenna 1 works, there is mode 1 and mode 5, and when the antenna 2 works, there are modes 2 and 5, but since the MS value of the mode 5 is very small, there is a good isolation.

Figure 17: Comparison of MIMO performance under different feed modes

(CMA design results vs. three scan parameters optimization results)

It can be seen from Figure 17 that Antenna 1 does not cover the entire frequency band, but Antenna 2 is well-matched across the entire frequency band, and the best separation between the two antennas is available; it has the best ECC performance (0.1) and 0.5 dB. MEG; Antenna 1 and Antenna 2 respectively stimulate different modes.

Fig. 18, CMA analysis results in 3D patterns under two excitation combinations

This paper briefly introduces the theoretical basis of eigenmode, and uses commercial software FEKO v14.0 version of CMA analysis module to analyze several simple antenna forms for eigenmode analysis, and obtains a wealth of model feature parameters, and analyzes it to make it easy for everyone to understand Understand the application of CMA technology. The CMA method is widely used in antenna design, and is also applied to antenna layout [13][14], electromagnetic compatibility, and target stealth.