Create Upper Patches of Monopole Antennas

The MIMO array consists of two orthogonally placed planar monopole antennas lying in the horizontal plane. The size of the upper conductor of each monopole antenna is 10 mm by 16 mm. The dimension of the conductor backed dielectric substrate is 40 mm by 26 mm. The square radiator of the first monopole is at an offset of (7 mm, 14 mm, 0 mm) from one of the corners of the substrate. The second monopole's radiator is at an offset of (14 mm, 9 mm, 0 mm) from the diagonally opposite corner of the substrate.

% Specify the geometry dimensions in m
% The dimension of the square patch of each monopole radiator
Lp=10e-3;
% The length of the substrate along X-axis 
Xg=40e-3;
% The width of the substrate along Y-axis
Yg=26e-3;
% The offset of the first monopole radiator
px1=-Xg/2+7e-3; 
py1=-Yg/2+14e-3;
% Lower left patch
patch1 = antenna.Rectangle(Center=[0,0],Length=Lp,Width=Lp,Center=[px1, py1]);
% The offset of the second monopole radiator
px2=Xg/2-9e-3-Lp/2;
py2=Yg/2-8.1e-3-0.9e-3;
% Upper right patch
patch2 = antenna.Rectangle(Center=[0,0],Length=Lp,Width=Lp,Center=[px2, py2]);

Create Feed Lines of Monopole Antennas

Feed both monopole antennas using two orthogonally oriented identical planar feedlines with length and width of 9 mm and 1.8 mm, respectively.

% Upper left patch feedline
feed1 = antenna.Rectangle(Center=[0,0],Length=1.8e-3,Width=9e-3,Center=[px1, py1-Lp/2-9e-3/2]);
% Upper right patch feedline
feed2 = antenna.Rectangle(Center=[0,0],Length=9e-3,Width=1.8e-3,Center=[px2+Lp/2+9e-3/2, py2]);

Create and Visualize Upper Layer

Join the patches to create the upper layer of the MIMO array which consists of two square radiators and two feed lines of the monopole antennas. Use the show function to visualize the uppermost layer of the array.

% Join four components
patchUpper=patch1+patch2+feed1+feed2;
figure;
show(patchUpper)

Create and Visualize Ground Layer

The ground layer consists of two rectangular shapes, two rectangular slots and three stubs. The purpose of introducing such perturbation in the ground plane is to achieve good impedance matching across the entire UWB band and to minimize the mutual coupling between the two monopole antennas of the MIMO array.

% Create left ground plane
% Left rectangular ground block
ground1 = antenna.Rectangle(Center=[0,0],Length=29e-3,Width=8e-3,Center=[-Xg/2+29e-3/2, -Yg/2+4e-3]);
% Slot in the left rectangular ground block
groundcut1 = antenna.Rectangle(Center=[0,0],Length=4e-3,Width=1e-3,...
    Center=[-Xg/2+5e-3+4e-3/2, -Yg/2+8e-3-1e-3/2]);
% Subtract the slot from the ground in the left ground block
ground1=ground1-groundcut1;

% Create right ground plane
% Right rectangular ground block
ground2 = antenna.Rectangle(Center=[0,0],Length=8e-3,Width=26e-3,Center=[Xg/2-4e-3, 0]);
% Slot in the right rectangular ground block
groundcut2 = antenna.Rectangle(Center=[0,0],Length=1e-3,Width=4e-3,Center=[Xg/2-8e-3+1e-3/2, py2]);
% Subtract the slot from the ground in the right ground block
ground2=ground2-groundcut2;

% Ground interconnect
ground3 = antenna.Rectangle(Center=[0,0],Length=3e-3,Width=1e-3,Center=[Xg/2-8e-3-3e-3/2, -Yg/2+1e-3/2]);

% Connect the three ground blocks
ground=ground1+ground2+ground3;

% First ground stub
groundstub1= antenna.Rectangle(Center=[0,0],Length=1e-3,Width=18e-3,...
    Center=[-Xg/2+14e-3+1e-3/2, Yg/2-18e-3/2]);
% Second ground stub
groundstub2= antenna.Rectangle(Center=[0,0],Length=5e-3,Width=1e-3,Center=[-Xg/2+14e-3-5e-3/2, Yg/2-1e-3/2]);

% Third ground stub
groundstub3= antenna.Rectangle(Center=[0,0],Length=16e-3,Width=1e-3,...
    Center=[Xg/2-8e-3+1e-3-16e-3/2, Yg/2-16e-3-1e-3/2]);

% Connect all stubs with the ground block
ground=ground+groundstub1+groundstub2+groundstub3;
figure;
show(ground)

Assign Dielectric Properties

Design the entire MIMO array on a dielectric substrate with the relative permittivity and loss tangent values of 3.5 and 0.004, respectively. The thickness of the dielectric substrate is assumed to be 0.8 mm.

% Dielectric
d = dielectric;
d.EpsilonR = 3.5;
d.LossTangent=0.004;
h=0.8e-3;

Create pcbStack Object

Create a pcbStack object using the same dielectric substrate. Assign patchUpper and ground to the upper and bottom layers of the pcbStack object, respectively.

ps=pcbStack;
ps.BoardThickness=h;
d.Thickness = h;
r1bottom=antenna.Rectangle(Center=[0,0],Length=Xg,Width=Yg);
ps.BoardShape =r1bottom;
ps.Layers = {patchUpper,d,ground};

Excite Both Antennas

Define feed locations at the edge of the feedline of each antenna. Set the feed diameter manually to half of the feedline width. Excite each antenna with a unit amplitude and zero phase voltage source.

% Feed location of the first antenna
fx1=-Xg/2+6.1e-3+1.8e-3/2;
fy1=-Yg/2;
% Feed location of the second antenna
fx2=Xg/2;
fy2=Yg/2-8.1e-3-1.8e-3/2;
% Assign excitation to both feed locations
ps.FeedLocations=[fx1 fy1 1 3; fx2 fy2 1 3];
ps.FeedDiameter=1.8e-3/2;% in m
ps.FeedVoltage=[1 1];% in Volt
ps.FeedPhase=[0 0];% in degree

Mesh Geometry

Manually mesh the array geometry with the maximum edge length of 1.8 mm.

ax=figure;
mesh(ps,MaxEdgeLength=1.8e-3)

Visualize S-parameters of Array

Use the sparameters function to calculate the scattering parameters of the array. As it is a two-port array, it has four S-parameters, among which the S11 and S22 represent the reflection coefficient at the port 1 and 2, respectively. The mutual coupling between two ports is characterized by S12 and S21. Use the rfplot function to visualize the port parameters. Due to the large number of basis functions, simulation of the frequency variation can take several minutes. By default, simulation of the frequency variation is disabled and a precomputed model is used. To enable the simulation of the frequency variation, set runModel to true.

% Define the frequency range in Hz
f1=linspace(3,6,31)*1e9;
runModel = false;
if runModel
% Compute the S-parameters
s=sparameters(ps,f1);
else
% Load precomputed data if runModel is set to false
load('frequencyVariationData.mat')  
end
% Plot the s-parameters
figure;
rfplot(s)

Plot Directivity, Gain, and Realized Gain Patterns with Both Excitations

Use the pattern function to visualize different radiation patterns of the array with excitation in both antennas. The input argument 'Type' of pattern will determine whether it computes directivity, gain or realized gain pattern. By default, 'Type' is 'directivity' for a lossless antenna and 'gain' for a lossy antenna. The directivity is a ratio of the radiation intensity in a specific angular direction to the average radiated power. It does not depend on material loss or impedance mismatch. The gain is a product of the directivity and radiation efficiency. The radiation efficiency is the ratio of the total radiated power to the total input power going into the antenna's/array's input port(/s). The material losses like finite conduction loss and dielectric loss are accounted in the radiation efficiency and gain parameter. As a part of a complete RF system, antenna/array is commonly connected with an impedance matching network. The impedance mismatch of the antenna or the array with such impedance network leads to finite port mismatch loss which is characterized by the port efficiency. Port efficiency is a ratio of the input power provided by the external excitation port(/s) and the power received at the antenna's/array's input feeding edge(/s). The multiplication of gain with the port efficiency provides the realized gain. The directivity, gain, and realized gain patterns of the MIMO array at 3 GHz are shown below.

figure;
pattern(ps,3e9,Type='directivity');

figure;
pattern(ps,3e9,Type='gain');

figure;
pattern(ps,3e9,Type='realizedgain');

Comparison of the radiation patterns shows that the gain is lower than the directivity as the radiation efficiency is less than 1. Similarly, the realized gain is lower than the gain value due to finite impedance mismatch loss. Use the efficiency function to calculate the radiation efficiency of the array.

Efficiency=efficiency(ps,3e9);

Visualize Directivity, Gain, and Realized Gain Patterns with Single Excitation

Similar to [1], if only one antenna of the array is excited and the other is shorted, a corresponding excitation model is introduced through the FeedVoltage and FeedPhase. Only the first antenna is assumed to be excited here.

ps.FeedVoltage=[1 0];
ps.FeedPhase=[0 0];

Compute and plot the directivity, gain, and realized gain values over a broad frequency range.

if runModel
% Compute directivity, gain, and realized gain
for m=1:length(f1)
patD1=pattern(ps,f1(m),Type='directivity');
patG1=pattern(ps,f1(m),Type='gain');
patRG1=pattern(ps,f1(m),Type='realizedgain');
D1(1,m)=max(max(patD1));
G1(1,m)=max(max(patG1));
RG1(1,m)=max(max(patRG1));
end
end

% Visualize the directivity, gain, and realized gain patterns
figure;
plot(f1./1e9,D1,'k')
hold on
plot(f1./1e9,G1,'--b')
plot(f1./1e9,RG1,'--r')
xlabel('Frequency(GHz)')
ylabel('Values in (dB)')
legend('Directivity', 'Gain', 'Realized Gain')

The gain values are observed to increase with the frequency. This indicates that the array radiation pattern becomes more directional as frequency increases.

Conclusion

This example shows how to efficiently design any advanced complex PCB antenna array using Antenna Toolbox™ and evaluate its impedance and radiation characteristics using Method of Moment (MoM) solver based full-wave simulation.

References

[1] L. Liu, S. W. Cheung, T. I. Yuk and D. Wu. "A Compact Ultrawideband MIMO Antenna," 2013 7th European Conference on Antennas and Propagation (EuCAP), Sweden, 2013.