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This paper presents a comprehensive numerical and experimental study of Planar Inverted-F Antennas (PIFA) involving all the parameters which may affect the characteristics of PIFA. It is found that PIFA characteristics are affected by a number of parameters including the dimensions of the ground plane, length, width, height and position of the top plate, positions and widths of shorting pin/plate and feed pin/plate. It is also found that the width of feed plate plays an important role in broadening the antenna bandwidth. It is shown that a fractional impedance bandwidth up to 65% can be obtained using an optimized design. Furthermore, a new empirical formula is introduced for the estimation of the central operational frequency of PIFA. These results are very useful for aiding PIFA design in practical applications.

The Planar Inverted-F Antenna (PIFA) can be viewed as evolved from a quarter-wavelength monopole antenna and is now widely used in mobile and portable radio applications due to its many attractive attributes such as simple design, lightweight, low-cost, low-profile, conformal nature and reliable performance [1-4]. Many antenna types for portable applications are extensions of PIFA antenna [5-7], which is considered as one of the strongest candidates for multiple-input multiple-output (MIMO) systems [8,9].

It is well-known that, for a monopole antenna, the desired length is a quarter-wavelength as it is resonant in this case. Using the same analogy, the following empirical equation was proposed for finding the resonant frequency of PIFA [3,10,11].

where c is the speed of light/radio wave, L and W are the length and width of the radiating top plate of the PIFA and f_{0} is the resonant/operating frequency. This equation means that the sum of the length and width of the top plate should be a quarter-wavelength. However, it is actually a very rough approximation and does not cover all the parameters which significantly affect the resonant frequency of PIFA as it will be shown later. It can hardly be used to guide the design in practice, thus a more accurate, robust and comprehensive design equation is required. In [_{s}) was incorporated with two degrees of freedom. The formula is given as follows for W_{s} ≥ 20 mm:

where DL = 2.741, k_{1} = 0.0188 and k_{2} = 0.0767. Note that this equation has a restricted application due to the condition on W_{s}. This equation also does not cover all the significant parameters of PIFA which affect the resonant frequency.

In the case of a wire Inverted-F Antenna (IFA), design curves are available for a given resonant frequency and impedance bandwidth through which IFA can be easily designed [

This paper presents a comprehensive experimental and numerical investigation on PIFA that includes all the parameters that may affect its characteristics. The effects on the characteristics of PIFA due to changes in the dimensions of ground plane, the position of PIFA on ground plane, the length, width, and height of the top radiating plate, and the distance of the shorting plate from the edge of top plate are presented. Similarly, the effects of changing the widths of the feed plate and the shorting plate, and the feeding positions are also discussed in this paper. At the end, a new empirical equation is proposed that describes the behavior of the PIFA antenna resonance; a very useful tool to predict the resonant frequency of PIFA. This new equation is compared with the two equations presented previously, with respect to its accuracy. The information given in this paper should be very helpful for antenna engineers to design the PIFA antenna for a given resonant frequency and impedance bandwidth.

The configuration of the PIFA used for this study is shown in _{g} × W_{g} as shown in _{r} = 4.4. The space between the ground and the top plate with height h is empty for this investigation although supporting materials may be used in practice. The shorting plate has dimension W_{s} × (h + t) and the feed plate has dimensions W_{f} × h. The horizontal and vertical distances of the feed plate from the side and upper edges of top plate are L_{b} and L_{u} respectively. The distance between the shorting plate and the side edge of the top plate is L_{s}. The vertical and horizontal distances of the PIFA structure from the ground plane edges are L_{z} and X respectively, as shown in

The procedure adopted for this study is that only one parameter is changed at a time to observe its effects on the PIFA characteristics while all other parameters are held constant. Different sets of parameters are taken for study to cover a wide range of values and also at different resonant frequencies. The operational frequency ranges from 0.5 GHz to 3 GHz to cover most popular mobile frequency bands. Most of the simulated and measured results are very similar, but some results are different. The major courses for their differences are 1)

the cables: which are not included in the simulation but presented in the measurements; 2) the connector: which is also not considered in the simulation; 3) The inaccuracy of exact parameters in manufacturing the PIFAs as they are made manually in the lab.

The numerical simulation software is Ansoft’s High Frequency Structure Simulator (HFSS) which is based on the finite element method, very flexible and suitable for this study. The simulation results were compared against measurements, therefore several PIFA antennas were fabricated and tested, some of them are shown in

For convenience, a reference PIFA antenna is chosen with the following parameters (13 in total): 1) Width of top plate W = 37.5 mm, 2) Length of top plate L = 18

mm, 3) Height of PIFA h = 12 mm, 4) Width of feed plate W_{f} = 10 mm, 5) Width of shorting plate W_{s} = 5 mm, 6) Distance between feed and shorting plates L_{b} = 15 mm, 7) Vertical distance of PIFA from the upper edge of the ground plane L_{z} = 0 mm, 8) Horizontal distance of PIFA from the side edge of the ground plane X = 0 mm, 9) Distance of shorting plate from the side edge of top plate L_{s} = 0 mm, 10) Length of ground plane L_{g} = 75 mm, 11) Width of ground plane W_{g} = 65 mm, 12) Vertical distance of feed plate from the upper edge of top plate L_{u} = 0 mm and 13) Thickness of substrate t = 1.5 mm.

The width of ground plane W_{g} is varied from 45 mm to 85 mm and all other parameters are same as reference antenna. Similarly, the length of the ground plane L_{g} is varied from 45 mm to 105 mm and W_{g} = 75 mm, W = 75 mm, L = 30 mm, h = 30 mm, W_{f} = 24 mm, W_{s} = 1 mm, L_{b} = 21 mm while all other parameters are same as the reference antenna. The simulated and experimental results are shown in _{g} or W_{g} decreases the resonant frequency but increases the fractional bandwidth. The resonant frequency is not very sensitive to the dimensions of the ground plane—this could be due to the fact that the antenna dimension is the dominant factor for radiation.

After extensive simulations, it is also observed that minimum ground plane length plus width required for maximum impedance bandwidth is λ/2.

The changes are made in the horizontal distance X and vertical distance L_{z} of the PIFA from the edges of the round plane to see their effects on the characteristics of the PIFA. The value of X is changed from 0 mm to 20 mm and the value of L_{z} is changed from 0 mm to 50 mm while all other parameters are same as the reference antenna. The simulated and experimental results are shown in _{z} change the resonant frequency and impedance bandwidth,

and also have significant effects on the radiation pattern. The increase in either X or L_{z} increases the resonant frequency and decreases the fractional bandwidth.

It can be concluded that the placement of PIFA on the ground plane significantly affects the characteristics of the PIFA: the antenna should be placed near the edges (L_{z} = 0, X = 0) of the ground plane to obtain the maximum impedance bandwidth.

Now the changes are made in the length and the width of the rectangular top plate and their effects are observed on the characteristics of the PIFA. The width of the top plate is varied from 38 mm to 50 mm and length of the top plate is changed from 5 mm to 25 mm and L_{g} = 60 mmW_{g} = 50 mm, h = 14 mm W_{f} = 15 mm, W_{s} = 2 mm, L_{b} = 10 mm, while other parameters are same as the reference antenna. The simulated and experimental results are shown in

PIFA is a quarter-wavelength antenna, increasing either the length or width of the top plate will result in the decrease of the resonant frequency. Small changes in length and width do not have a significant effect on the radiation pattern but as we know from the theory of characteristic modes, the radiation pattern is basically dependent on size and shape of top plate [

It can also be concluded that the greater the size of the top plate of the PIFA, the more directive the radiation pattern, i.e. the directivity will be higher as shown in

The height of the top plate h is now varied from 12 mm to 20 mm to observe its effects while all other parameters are same as the reference antenna. The simulated and experimental results are shown in

diation pattern. The decrease in the resonant frequency is obvious as h increases, the wavelength increases. The height of PIFA can be increased to enhance the impedance bandwidth but a small height of the top plate is preferred in practice as the antenna has to be small enough to fit it in the chassis of small terminal devices. So the height of antenna cannot normally be used to enhance the impedance bandwidth in applications.

The distance of shorting plate from the side edge of the top plate L_{s} is varied from 0 mm to 15 mm to observe its effects on the characteristics of PIFA and W_{g} = 75 mm, L = 20 mm, W = 50 mm, L_{b }= 10 mm, while all other parameters are unchanged and simulated and experimental results are shown in _{s} increases the resonant frequency and changes the fractional impedance bandwidth but has little effect on the radiation pattern.

The position of the feeding configuration is investigated by altering the values of horizontal distance L_{b} from 5 mm to 15 mm and vertical distance L_{u} from 0 mm to 18 mm to observe their effects on the PIFA characteristics while other parameters are the same as the reference antenna. The simulated and experimental results are shown in

suitable positions of the feeding configuration, so when the feeding position is changed under the top plate, a different mode or a number of modes may be excited which change the resonant frequency, impedance bandwidth and radiation pattern [

The width of shorting plate is varied from 1 mm to 20 mm while other parameters remain unchanged; the simulated and experimental results are shown in _{s} = 20 mm as shown in

The feed plate width is changed from 6 mm to 14 mm and L_{g} = 60 mm, W_{g} = 50 mm, W = 50 mm, L = 24 mm, h = 14 mm, W_{s} = 2 mm L_{b} = 24 mm, while all other parameters are the same as the reference antenna and simulated and experimental results are shown in

Based on our comprehensive parametric study, a large

database of different set of parameters using different ground plane dimensions is created and a new empirical equation is derived to find the centre frequency by using the function “nlinfit” (Nonlinear least-squares data fitting by the Gauss-Newton method) of MATLAB, taking into account all those parameters which significantly affect the value of the resonant frequency as seen in Figures 3- 10. These parameters are length, width and height of the top plate, widths of shorting and feed plates, and loca-

tions of shorting plate and feeding configuration under the top plate. Only horizontal distances of locations of shorting and feed plates are chosen. The vertical distances of feed and shorting plates from the edge of top plate are neglected to make the equation simple and also because their role is found not as significant as compared to the horizontal distances. The new proposed equation is therefore obtained as follows.

where W, L and h are the width, length and height of the top plate respectively. W_{f} and W_{s} are the widths of feed and shorting plates whereas L_{b }is_{ }the horizontal distance between these plates and L_{s} is the distance of shorting plate from side edge of the top plate.

_{b} should be taken between the feed plate and one side edge of the top plate and the equation still holds.

frequency of the PIFA. This new equation can provide much more accurate prediction of the resonant frequency when the whole PIFA structure is placed on the edge of ground plane and the feed is provided at the upper edge of the top plate i.e. X = L_{z} = L_{u} = 0 mm. We can have even better prediction of the resonant frequency by adding the dimensions of ground plane in above equation but these dimensions are ignored due to the fact that the resonant frequency is less affected by the variations of these dimensions and also it will make the equation complex. This new equation gives the prediction of the first resonant frequency of the antenna. It has been tested that the new equation can be applied for applications where the antenna size is smaller than one wavelength, i.e., h + W + L < λ.

We have shown that the PIFA characteristics are affected by a number of parameters. The conclusions are summarised as follows:

1) The radiation pattern of PIFA is basically dependent on the size and shape of the top plate and is affected by the dimensions of the ground plane and the position of PIFA on the ground plane.

2) By increasing the length, width or height of the top plate, the resonant frequency decreases.

3) By increasing the height of the top plate, the fractional impedance bandwidth increases but as PIFA needs to be of low profile so it limits the height to be used for increasing the impedance bandwidth.

4) The greater the size of the top plate, the more directive will be the radiation pattern which means that it will have higher gain and directivity as well. If we decrease the size (length or width) of the top plate, the directivity of antenna decreases and the intensity of radiation pattern behind the ground plane increases.

5) By increasing the widths of shorting plate or feed plate, the distance of shorting plate from the edge of the top plate and the horizontal distance of feeding position from shorting plate, the resonant frequency increases.

6) The width of feed plate is very effective parameter in broadening the bandwidth of the PIFA. The maximum fractional bandwidth achieved is up to 65%. As the increase in feed and shorting plates increases the resonant frequency, the shorting plate should be narrow and the feed plate should be larger to get the maximum impedance bandwidth.

7) The resonant frequency is also affected by the ground plane dimensions and position of PIFA on the ground plane.

8) The minimum total ground dimensions for maximum impedance bandwidth should be equal or greater than λ/2 i.e. length + width of the ground plane ≥ λ/2.

9) A new empirical equation is presented for predicting the resonant frequency of PIFA. The average percentage error found between the predicted and the actual operational frequencies is less than 3%.