# Miniaturize Patch Antennas Using Metamaterial-Inspired Technique

This example shows how to design a miniaturized patch antenna at 2.4 GHz with a complementary split-ring resonator (CSRR) loading plane and evaluate its performance, with results as published in [1]. The antenna is miniaturized by shrinking its circular patch structure from the original radius of 23.1 mm to 6 mm.

### Define Patch Dimensions

The microstrip patch in this example has 3 layers: top layer, loading plane, and ground plane. The board is a square with the side length `B_d`

. `r_0`

is the original radius of the resonant patch in the top layer, which is shrunk to `r`

. The CSRR has `N`

complementary split rings in the loading plane, with the split width of `w`

and the inner and outer radius of `R2_in`

and `R2_out`

, respectively.

clc r_0 = 23.1e-3; r = 14e-3; B_d = 2.2*r_0; N = 7; w = 0.011*N; R2_in = 0.3521; R2_out = (R2_in*N/1.9079)-w; fw = 2e-3;

### Design Top Layer

Create a circular patch with the radius of `r`

.

circle_L1 = antenna.Circle(Center = [0 0],Radius = r);

Create the feed as a rectangle.

rect_L1 = antenna.Rectangle(Length = B_d/2,Width = fw);

Move the feed in the *x-y* plane to connect it to the circular patch.

translate(rect_L1,[-B_d/4 0 0]);

Create a polygon combining the patch and the feed, and then plot the resulting shape.

```
polygon_L1 = circle_L1+rect_L1;
show(polygon_L1);
title("Top Layer")
```

### Design Loading Plane

To create a CSRR with seven rings, first, create a variable `r_rad`

which generates multiplying factors for each of the seven rings. Then use a MATLAB `for`

loop to iterativley add and remove circles to create the ring slots that make up the CSRR.

r_rad = linspace(R2_out,R2_in,N); sign = -1; circ_outer_L2 = antenna.Circle(Center = [0 0],Radius = (R2_out+w)*r); for i = 1:length(r_rad) circle_Minus = antenna.Circle(Center = [0 0],Radius = r_rad(i)*r); circle_Plus = antenna.Circle(Center = [0 0],Radius = (r_rad(i)-w)*r); rect_Minus = antenna.Rectangle(Center = [0,sign*(r_rad(i)-w/2)*r],Length = w*r,Width = (w+w/1.3)*r); if i == 1 spliti = circ_outer_L2-circle_Minus+circle_Plus+rect_Minus; CSRR_L2 = spliti; end CSRR_L2 = CSRR_L2-circle_Minus+circle_Plus+rect_Minus; sign = sign*-1; end show(CSRR_L2) title("Loading Plane (CSRR)")

### Design Ground Plane

Design the ground plane as a rectangle with the same dimension as that of the board.

rect_L3 = antenna.Rectangle(Length = B_d,Width = B_d); show(rect_L3)

### Design Board

Define the shape of the board and create the stack with the layers mentioned above and specified dielectric layers in between.

boardShape = antenna.Rectangle(Length = B_d,Width = B_d);

Create PCB stack using previously defined layers and two dielectric layers.

p = pcbStack; p.BoardShape = boardShape; d1 = dielectric("FR4"); % d1 = dielectric("RT5870"); d1.Thickness = 2.34e-3; % d2 = dielectric("RT5870"); d2 = dielectric("FR4"); d2.Thickness = 2.34e-3; p.BoardThickness = d1.Thickness+d2.Thickness; p.Layers = {polygon_L1,d1,CSRR_L2,d2,rect_L3}; p.FeedLocations = [-B_d/2 0 1 5]; p.FeedDiameter = fw/2; figure show(p)

### Analyze Performance of Miniature Antenna

Before evaluating the board's performance, estimate the memory required to solve the mesh structure. You can do this by using the memory estimator.

memoryEstimate(p,2.6e9)

ans = '2.8 GB'

**Compute Return Loss**

This example uses the following commenteefine code to compute the return loss of the designed patch antenna.

[~] = mesh(p,'MaxEdgeLength',0.03,'MinEdgeLength',0.005); freq = linspace(2.35e9,2.75e9,21); figure; returnLoss(p, freq);

#### Plot Radiation Pattern

Plot the 3-D radiation pattern of the patch.

figure; pattern(p,2.6e9)

Visualize the current density of the patch.

```
figure;
current(p,2.396e9,scale = "log")
```

**Reference**

[1] Ouedraogo, Raoul O., Edward J. Rothwell, Alejandro R. Diaz, Kazuko Fuchi, and Andrew Temme. “Miniaturization of Patch Antennas Using a Metamaterial-Inspired Technique.” *IEEE Transactions on Antennas and Propagation* 60, no. 5 (May 2012): 2175–82. https://doi.org/10.1109/TAP.2012.2189699.