Welcome, this article is about modeling the Meander inverted-F antenna (MIFA) in Ansys HFSS. Step-by-step instructions for designing an antenna. Make your MIFA!

The version of the program HFSS 15.0 is used, but there are not so many differences between the versions, therefore it can be modeled in other versions.

A bit about the antenna

The Meander Inverted-F Antenna is a modification of the IFA antenna, which has the main printed conductor in the form of a meander. This modification allows you to make the antenna even more compact, which is often necessary in modern mobile devices. MIFA can be integrated directly into the board of the device under development. The appearance is shown in the figure below.

Used in the ranges of decimeter, centimeter and millimeter wavelengths. It allows constructive solutions for working in multi-frequency modes. The radiation pattern (LH) of such an antenna is a closed toroid with an axis of rotation along the input channel and is presented in the figure below. MIFA has a vertical polarization parallel to the axis of rotation of the toroid.

Changing the geometry of the antenna allows you to change its impedance, which eliminates additional matching devices and circuits. Designing MIFA for a specific device under development is individual, since the antenna uses the entire earth test ground on the board to emit electromagnetic waves.

Advantages:

simplicity of construction;
relatively small weight and size characteristics;
production cost;
high repeatability of sizes.

Getting down to modeling

First you need to decide on the source model. The picture below shows the MIFA antenna model.

The structural parts of the antenna:

ground landfill;
the antenna input channel (on the right, it is given the size W), the RF path is connected to it;
earth channel of the antenna (left);
meander part.

The figure shows the letter designations of various geometric sizes that will be used in the program and will be recorded as parameters:

HP - the vertical size of the polygon;
LP - horizontal size of the polygon;
H - antenna height, also the length of the input and ground channels;
H2 is the distance between the meander and the landfill;
YG is the distance between the channels;
W is the thickness of the printed conductors;
L1, L2, ..., L7 are the lengths of the horizontal lines of the meander;
LEnd - the length of the end line of the meander.

The dimensions of the polygon usually do not change (the antenna is often made for the developed board), i.e. it remains to optimize only the lengths of the printed conductors of the antenna itself.
By the way, you can experiment with the number of meander bends, there is no clear limit.

The essence of the simulation is as follows: you need to find the antenna geometry so that it is matched to a certain frequency and has a gain that matches your task (for example, you need the antenna to radiate more in the horizontal plane parallel to the plane of the board and less in the vertical one.

1. Creation of the project and model of the board in HFSS

Open HFSS, click File -> New . A new project is created. If it is empty, then click RMB on the project in the Project manager window, then Insert -> Insert HFSS Design . A file with the 3D design of the project has been created, you see the axes and the grid.

First you need to create the necessary variables, for this, click RMB on HFSSDesign , then Design Properties . Click Add , enter a name, for example, HP, indicate the type Length , units mm, value Valuethe value you need in mm, for example, 75. Click OK. Variable created. Now you need to do the same operation with all other variables. For variables L1 - L7 and LEnd, set values, for example, at 3 mm. YG equal to at least 5 mm. W Equal to the required width of the printed conductors. Since your board already has some dimensions, and a certain place is allocated for the antenna on the board, in parameter H specify the following value (in my case, the antenna is located along the short side of the board, you can have it along the long one): from the length value on the long side of the board, subtract the polygon length and another minus 0.5 mm (0.5 mm is the indent from the edge of the board to the antenna). Also create a PortW variable and set it to 0.2 mm (this will be the width of the input port).

Go to the tabModeler -> New Object Type -> Model . Now all new objects will be models.

Next, we need to create a substrate for our printed circuit board, for this, click on the top of the Draw -> Box toolbar , click LMB on the workspace and draw a rectangle, then click LMB again and drag up to create a three-dimensional shape, click LMB again. The result in the picture below.

Now let's set the dimensions for our substrate, for this click LMB on the CreateBox element (in the picture above, the red arrow indicates where to click). On the left in the Properties window (or RMB by CreateBox -> Properties ), specify the required dimensions: enter “HP + H + 0.5mm” in the Xsize field, similar to the board width: in the Ysize field, enter “LP”, and in the Zsize field specify the board thickness in mm, for example, 1.5. Also fill in the Position field: separated by comma "-H-0.5mm, -LP / 2, -1.5mm". The center of coordinates will now be in the middle of the narrow side of the polygon.

Rename “Box1” to “PCB” by clicking on it with PCM and going to Properties . In the same place, specify the material, for example, FR4_epoxy, typing in the search. Also select the appropriate color by changing Color. Change the Transparent transparency to 0.3. It should turn out like in the picture:

Now you need to create 2 landfills. To do this, click Draw -> Rectangle . And make a small rectangle from the origin on the board. Change its size and position. To do this, in its properties, set the values in the Xsize field “HP”, in Ysize - “LP”, and in the Position field - “0, -LP / 2, 0”. Rename the object "Rectangle1" to "Top" and change its color. Right click on Top -> Assign Boundary -> Perfect E -> OK . So we set the object properties of an ideal conductor. You should get the same as in the picture below.

Conducting objects will be flat, it does not affect the result strongly, however, it speeds up the calculations significantly. If you need super precision, you can create a three-dimensional object from this rectangle by clicking Modeler -> Thicken Sheet and specifying the required thickness. You can also specify the material “cooper”. But in our project this is not necessary, therefore, we work with flat ideal objects.

Now you need to create an earth test site on the other side of the board. To do this, click RMB on Top in the design tree, then Edit -> Copy . RMB on Top again, then Edit -> Paste. We have created exactly the same layer with the name "Top1". Rename it to “Bottom” and change its position by writing “0mm, -LP / 2, -1.5mm” in the Position field. Also give this object the properties of Perfect E. Now we have 2 ground polygons on both sides of the board.

2. Creating an antenna model in HFSS

The next step is to design the antenna itself. We will create the antenna from the rectangles.

Create a variable to set the distance from the center of coordinates to the middle of the input channel on the board as in the previous paragraph: name PortY, set the length, for example, -10 mm. Minus because the input channel will shift to the left relative to the origin.

Create an input channel: draw a small rectangle by clicking Draw -> Rectangle and spreading it on the plane of the board. Change its size and position. Xsize equate to "H-PortW", Ysize - "W", Position - "-H, PortY, 0mm". Rename the object to “Feed” and set the color as for polygons. Also give it the properties of an ideal conductor. The result should be as in the picture below.

Now create an earthen canal. To do this, draw a rectangle in the same way as with the input channel, do the same operations, just set the size in the Xsize field “H”, the width is the same, and in the Position field enter “-H, PortY-YG, 0mm”. Also name it “Back” and give the object the same color and properties of an ideal conductor. Now, using the YG variable, you can adjust the distance between the input and ground channels. Try to click on HFSSDesign and change the YG variable on the left in the Properties window , your earth channel will shift relative to the input one. Below in the picture it should turn out like this. At the same time, note that in the design tree in the Perfect E tab there are all our elements.

Create a jumper between the channels. To do this, draw a rectangle again and set its size to Xsize “W”, Ysize to “YG-W”, Position to “-H, PortY-YG + W, 0mm”. Also give the object the name “FeedBack”, the properties of the ideal conductor and color. The result in the picture below.

Great, it remains to draw a meander:

We draw the first rectangle, call it “LineL1” and set its size Xsize - “W”, Ysize - “L1”, Position - “-H, PortY + W, 0mm”.
We draw the second rectangle and call it “Ver1” and give it the size Xsize - “H-H2”, Ysize - “W”, Position - “-H, PortY + W + L1, 0mm”.
We draw the third rectangle and call it “LineL2” and give it the size Xsize - “W”, Ysize - “L2”, Position - “-H + H2-W, PortY + L1 + 2 * W, 0mm”.
«Ver2» Xsize — «H-H2», Ysize — «W», Position — "-H, PortY+L1+L2+2*W, 0mm".
«LineL3» Xsize — «W», Ysize — «L3», Position — "-H ,PortY+L1+L2+3*W, 0mm".
«Ver3» Xsize — «H-H2», Ysize — «W», Position — "-H, PortY+L1+L2+L3+3*W, 0mm".
«LineL4» Xsize — «W», Ysize — «L4», Position — "-H+H2-W, PortY+L1+L2+L3+4*W, 0mm".
«Ver4» Xsize — «H-H2», Ysize — «W», Position — "-H, PortY+L1+L2+L3+L4+4*W, 0".
«LineL5» Xsize — «W», Ysize — «L5», Position — "-H, PortY+L1+L2+L3+L4+5*W, 0".
«Ver5» Xsize — «H-H2», Ysize — «W», Position — "-H, PortY+L1+L2+L3+L4+L5+5*W, 0".
«LineL6» Xsize — «W», Ysize — «L6», Position — "-H+H2-W, PortY+L1+L2+L3+L4+L5+6*W, 0mm".
«Ver6» Xsize — «H-H2», Ysize — «W», Position — "-H, PortY+L1+L2+L3+L4+L5+L6+6*W, 0".
«LineL7» Xsize — «W», Ysize — «L7», Position — "-H, PortY+L1+L2+L3+L4+L5+L6+7*W, 0".
We draw the fourteenth rectangle and call it “VerLEnd” and give it the size Xsize - “LEnd”, Ysize - “W”, Position - “-H, PortY + L1 + L2 + L3 + L4 + L5 + L6 + L7 + 7 * W, 0 ".

Do not forget to put down the colors and properties of an ideal conductor. It should turn out like in the picture below.

Now hold Ctrl and click LMB on “Top”, and then on other conductors on the upper plane of the board. All objects will be highlighted. Next, click on “Top” RMB -> Edit -> Boolean -> Unite , now these objects are combined, and if you click on one of them in the workspace, they will all be selected as one object. Also look at the design tree, there the Unite tab will appear in the Top object , where all the combined components are displayed.

Now you need to add the port. To do this, draw a rectangle between the input channel and the ground polygon according to the size of the input channel. Set the port rectangle to Xsize - “PortW”, Ysize - “W”, Position - “-PortW, PortY, 0”. Next, click on this RMB rectangle and select Assign Ecitation -> Lumped Port. Click Next, select Integration Line -> New Line and draw a line as shown in the figure below, then click Next and Finish.

Now expand HFSSDesign by clicking on the plus sign , and in the Excitations tab your port will appear, and it will also appear in the Sheets tab in the design tree.

And the last step: you need to add the volume in which the calculations will be made. To do this, create a Box with dimensions Xsize = 400 mm, Ysize = 200 mm, Zsize = 200 mm and Position "-200, -100, -100". Set transparency 1. You can also completely disable its visibility. To do this, click on the top panel View -> Visibility -> Active View Visibility and uncheck this box. After that, right-click on your Box in the design tree and select Assign Boundary -> Radiation and click OK.

Congratulations, done! The picture below shows the final version of the MIFA model.

3. Set up a project for analysis

First you need to click RMB on Analysis -> Add Solution Setup . Since the antenna in this project is tuned to a frequency of 868 MHz, we enter the frequency of 0.868 GHz. You will have your own frequency. We immediately indicate Maximum Number of Passes = 36. So the calculation will be as accurate as possible. Click OK. Right click

on Setup1 in the Analysis tab , then select Add Frequency Sweep , interpolating type , LinearStep and set the range from 750 MHz to 1100 MHz in 1 MHz steps.

Next, on the left in the project tree, click RMB on Radiation -> Insert Far Field Setup -> Infinite Sphere. You can not change anything, i.e. leave the Phi angles from 0 to 360 in increments of 10 degrees and Theta from 0 to 180 in increments of 10 degrees and click OK.

On the top panel, click HFSS -> Solution Type and select Modal .

Done!

4. Initial optimization

It is necessary to carry out optimization, with the help of which the program itself will select the necessary geometric parameters.

You must specify ranges for each variable to be changed. Right-click on HFSSDesign -> Design Properties , select the Optimization tab , in which you need to check the Include column next to the variables that will be optimized, and also set a certain range using the Min and Max columns.

Since the exit point of the RF path is often already fixed, the PortY variable and the parameters of the landfill remain constant and are not included in the optimization. All geometric meander parameters, as well as the distance between the input and earthen channels, will change.
Sometimes the maximum antenna height is determined by the dimensions of the developed board, then the parameter H should also be left constant.

Some antenna data

: H, () . , , H. , H , , H, , H , , , 50 .

.

, YG.

Therefore, we put the necessary checkmarks and determine the variable range. Click OK.

Now click RMB on Optimetrics on the left in the project tree, then Add -> Optimization . You need to choose an optimization algorithm (you should not choose a “quasi-Newtonian” algorithm, since this algorithm uses the gradient of the S parameter change, and it can fall into a local minimum), you can choose, for example, a “genetic” algorithm.

Next, click Setup Calculations in the same window , select the parameters from the S column, select S (1,1) on the right, and dB to the right. Go to the Calculation Range tab and check the frequency.

Check in the Variables tab the minimum steps for changing the parameterMin ste p, make them at least 0.1 or less, so the optimization accuracy will be higher, but the optimization may take longer.

Click Add Calculation . Correct Condition to "<=", in Goal, enter, for example, -40, in Weight, enter 1. Thus, optimization will continue until there is a solution where the reflection coefficient S (1,1) is less than or equal to - 40 dB Click OK.

Right-click on the OptimizationSetup1 that appears on the left in the Optimetrics -> Analyze tab . Optimization will begin. The number of iterations can reach several thousand. On one computer core (if you do not have an HPC license), the optimization time can be hours or days, so you can put it overnight.

Also, during the optimization process, you can click RMB on OptimizationSetup1 -> View Analysis Result . There are two tabs: Plot and Table . The Plot tab displays a graph of the results. The lower the value of Cost , the better. After the optimization is completed or after the optimization process is stopped, you can click on the Table tab , sort by Cost value by clicking on the corresponding column, select the option with one of the lowest values and click Apply . You will apply the selected configuration.

Now you can do the analysis. Right- click on Setup1 in the Analysis -> Analyze tab .

After calculation it is necessary to display the results. To do this, create the following “reports”:
RMB by Results in the project tree -> Create Modal Solution Data Report -> Rectangular Plot , select the parameter S (1,1) in dB of frequency. Click New Report . And we have a tab in Results , and also a graph of the frequency dependence of the reflection coefficient S (1,1) is displayed. The image below shows an example of this graph for solving after the initial optimization, which lasted 1060 iterations (parameter H here is 14 mm).

As you can see from the graph, the reflection coefficient at a frequency of 868 MHz is -7.46 dB, which is quite small, a good result starts from -20 dB. Moreover, there is a second minimum to the right, which must be reduced.

Let's create the following report: for this, right-click again on Results -> Create Far Fields Report -> 3D Polar Plot , select gain -> GainTotal in dB at all angles. Click New Report. Below is a graph of KU for the same solution.

The maximum KU in the horizontal plane is 1.5 dB.

Add the graphs of the input active and reactance of the antenna: click RMB on Results -> Create Modal Solution Data Report -> Rectangular Plot , select Z parameter -> Z (1,1) -> re and click New Report . Now in the same window, click on im and Add Trace , and another curve is added to the same graph. The picture below shows the graphs of the active and reactance of the antenna.

The antenna resistance is 21.59 Ohms, and the reactance is 11.74 Ohms. The coordination task is to have an active resistance of 50 ohms and a reactance of 0 ohms.

5. An example of a geometry change

Remember what “a bit of antenna data” was in the spoiler? So, for example, increasing the parameter H by 2 mm, we obtain the following data:

And the change in S (1,1) is caused by the fact that the active and reactive resistances have changed, the graphs of which are shown in the figure below, the KU has changed, because the dimensions of the antenna have increased.

6. We carry out a parametric analysis

In order to get closer to the full antenna matching, you should do a parametric analysis (you can start by parameterizing the distance between the channels): click RMB on Optimetrics -> Add -> Parametric , in the Sweep Definitions tab on the right click Add , select the parameter YG -> Linear step and enter a range, for example, from 0.2 mm to 12 mm (the maximum value is chosen so that there is a distance to the edge of the board, for example, 0.5 mm), in the Table tab there are all calculated values (it turned out 60), in the Options tab, check the Save Fields checkbox and mesh, this is necessary in order to then draw a lot of curves on one graph and choose the right one. Click OK. RMB Analysis -> Analyze .

After finishing the calculations on the first graph, output the family of curves S (1,1) for each calculated variation. To do this, open the XY Plot 1 graph tab (if you did not change the name), double-click on dB (S (1,1)) or RMB on XY Plot 1 -> Modify Report , open the Families tab , select the desired family, for example, by clicking the button in the Edit column opposite the variable YG -> check Use all values . Next click Apply Trace. A graph will appear in front of you, select the most suitable curve by pointing or clicking on it, remember: with what parameter this graph is built, and change it in all project parameters. Below is a graph of parametric analysis for one of the geometric parameters.

It can be seen from the graph that there is a purple curve at which S (1,1) reaches -40 dB. Just select the value of this parameter, change our parameter to it and optimize further if necessary.

You can carry out such short parametric analyzes on any geometric parameters.

By the way, if you want to simultaneously change several geometric parameters, then you can simply create a variable, for example, k and add it to all these geometric parameters, and conduct parametric analysis on the variable k. You can also try to add and subtract this variable from different geometric parameters, then one of them will increase with increasing k, and the other will decrease. Do not forget to add “mm” after the digital value in the Value fieldgeometric parameter, otherwise there will be an error with units. For example, click RMB on HFSSDesign -> Design Properties -> create the parameter k and equate it to 0 (Length), then click on any geometric parameter -> Edit and in the Value field enter “15mm + k”. Now there will be no mistakes.

7. Final optimization

When you have chosen the best geometric design after parameterization, you can achieve maximum results. To do this, we will carry out another optimization in the vicinity of the values of geometric parameters already obtained, i.e. it is necessary to reduce the range of parameter changes in HFSSDesign -> Design Properties for all mutable variables.

Right click on Optimetrics on the left in the project tree, then Add -> Optimization . You must select a Pattern Search optimization algorithm . Add the S (1,1) variable again as in the initial optimization, now add the second variable by pressing Setup Calculation . And selecting Far Fields on the left in the Report type field , click ongain -> GainTotal in dB. Next, add Add Calculation and enter in the Condition field "> =", in the Goal field "10", in the Weight field "0", so that the first variable is more important in weight, since coordination is more important to us than KU.

Check in the Variables tab the minimum steps for changing the parameter Min ste p, the smaller the better, since the optimization accuracy will be higher, but the optimization may take longer.

We start the analysis. Most likely, the optimization will pass quickly, and you will automatically get the result, i.e. your geometric parameters themselves will change to new ones, since in the General tab of the optimization analysis there is a checkmark to update the parameters after optimization.

Congratulations, your MIFA is ready!

An example of a fully optimized antenna:

As well as the Smith chart.

But how does the antenna emit?

You can create an animation of the radiation of the E field: open Planes -> press XY or XZ, then click RMB on the work area -> Plot Fields -> E -> Mag E -> Done . After expand the Field Overlays tab , RMB by Mag_E1 -> Animate .

You can create an animation of the radiation of the H field: open Planes -> press XY or XZ, then right-click on the workspace -> Plot Fields -> H -> Mag H -> Done . After expand the Field Overlays tab , RMB by Mag_H1 -> Animate .

The GIFs show strong electromagnetic radiation. The current at the end of the meander side of the antenna is minimal.

Conclusion

I would like to add that the most accurate simulation of the MIFA antenna will be, if you create the most realistic model with all the vias, electronic components and other nearby objects installed on the board, the conductors should be voluminous and have, for example, copper properties.

As practice shows, often simplified and idealized models are often enough. It is better to put contact pads under the filter or matching circuits, measure the SWR and other input characteristics of the antenna with the device, calculate the values of the filter components for maximum real matching and install the components on these pads.

Thank you for your attention, I hope you enjoyed this article.

Modeling a meander inverted-F antenna is easy

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