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The mutual coupling effect between antenna elements on an array's bandwidth is investigated using scattering parameters instead of the mutual impedance. First, an approximate expression is derived for matched voltage standing wave ratio (VSWR) bandwidth of a tuned antenna, which reveals that the bandwidth is inversely proportional to the magnitude

Antenna arrays are widely used in many practical systems to enhance gain or provide beam scanning capability. Mutual coupling between antenna elements is an important issue in designing antenna arrays. It modifies radiation pattern, beamwidth, and directivity of an array, and even degrades the performance of adaptive arrays [

First, we derive an approximate expression for the matched VSWR bandwidth of a tuned antenna from the definition given in [

Finally, numerical simulation and experimental verification are carried out to verify the bandwidth enhancement. Printed slot antennas have extensive applications in phased arrays, satellite communication systems, and airborne systems due to their compact size and high efficiency [

Yaghjian and Best investigated the bandwidth and

The reflection coefficient of the antenna is then

The matched VSWR bandwidth for an antenna tuned at a frequency

In this paper, we would like to analyze mutual coupling effect on the bandwidth enhancement of antenna arrays. It is known that mutual coupling effect in an antenna array is commonly modeled as a change in the driving impedance of the elements and it is usually referred to as mutual impedance variation [

For an array with all elements excited simultaneously, it is not the element’s self-impedance but the driving-point impedance that should be matched. If the array is tuned at a frequency

Through above analysis, we show that mutual coupling effect on array bandwidth could be analyzed in the view of the mutual impedance. However, the analysis associated with mutual impedance is usually quite complicated, especially for a larger array. The expressions of element’s open-circuit voltage are usually needed to calculate the mutual impedance while array element’s port voltage is difficult to be measured for most practical configurations or even to be defined in some situations. On the other hand,

Figure

A two-element array fed through a T-branch power divider.

For a lossless 3-dB T-branch power divider [

Finally, we obtain the reflection coefficient of the overall network at the input port of the divider as

We further discuss a linear array with 4 identical elements fed through a 4-way power divider which is shown in Figure

A four-element array fed through a 4-way power divider.

Because

Let

Finally, the reflection coefficient of the overall array is derived as

Assuming that

Generally, we assume all the elements to be fed with equal powers,

The active reflection coefficient of the overall array is derived as

Taking an

We substitute (

Equations (

The closed-form expressions derived in the previous section imply that the bandwidth enhancement of the overall array can be achieved by invoking appropriate mutual coupling between elements. In this section, numerical simulation and experimental verification are conducted to investigate mutual coupling effect on array bandwidth. Two types of antenna are underanalysed. Firstly, we consider slot antenna arrays, which are normally narrowband and only have one antiresonant frequency. Then, a broadband two-element Vivaldi array is investigated, which has a combination of two or more resonances and antiresonances that are so close together to build a broad bandwidth. To optimize the array bandwidth, we will vary element spacing

We consider a single-slot antenna and an array of two identical slots shown in Figure

The layout of slot antennas.

Single slot antenna

Array no. 1

Array no. 2

Array no. 3

Array no. 4

Obviously, it is the element spacing

Calculated phase differences between

Simulated magnitudes of

Calculated phase differences between

Simulated and measured return loss results of single-slot and two-slot array no. 2 (

Simulated and measured gain results of single-slot and two-slot array no. 2 (

Next, we consider arrays consisting of four identical slots shown in Figure

Simulated and measured return loss results of single-slot and four-slot array no. 4 (

Simulated and measured gain results of single-slot and four-slot array no. 4 (

The tapered slot antenna (TSA) was initially introduced as an array element by Lewis et al. in 1974 [

We consider a two-element Vivaldi array shown in Figure

Schematic graph of Vivaldi antenna array.

A two-element Vivaldi array

Definition of element configuration

The Vivaldi antenna element has theoretically unlimited bandwidth, and the upper operating frequency is mainly limited by the transition. However, for a Vivaldi array, the upper operating frequency is limited by the onset of grating lobes, which is determined by the element spacing. Therefore, we usually prescribe the element spacing and optimize antenna parameters to achieve desired bandwidth of the array. When the element spacing is prescribed, the mutual coupling between elements

Here, we prescribe the element spacing ^{-1}. To clarify the relationship between ^{-1}, the minimum operating frequency is about 5.5 GHz while the frequency of one element is about 10.7 GHz. For a specified upper operating frequency 18 GHz, an optimum 3 : 1 bandwidth of the array has been achieved. Figure ^{-1}, and Figure

The active reflection coefficient Γ with various opening rates

The phase difference between ^{-1}.

The phase difference between ^{-1}.

In this paper, mutual coupling between array elements has been utilized to achieve bandwidth enhancement based on the formulations for the matched VSWR bandwidth and the reflection coefficient of arrays with corporate feed. Instead of sticking to analysis of the mutual impedance, the active reflection coefficient of the array has been investigated to directly guide the optimization of bandwidth. Our theoretical analyses show that bandwidth enhancement of the overall array can be achieved when the element passive reflection coefficient