Design and Analyze Compact UWB Low Pass Filter Using pcbComponent

This example shows how to design and analyze a compact low pass ultra-wide band (UWB) filter based on a U-shaped complementary split ring resonator using the pcbComponent object. The filter is designed to have very low insertion loss over a wide band of frequency from low 0.1 GHz to 10.8 GHz. The design of the filter is taken from the reference [1].

Design and Analyze UWB Low Pass Filter

This compact filter design employs U-shaped complementary split ring resonator (U-CSRR). U-CSRR is a uniplanar configuration of complementary split ring resonator (CSRR) as described in [1]. This structure has an advantage of simpler fabrication as it is formed on the top metal layer. The U-CSRR is formed using two concentric split square rings of outer length $$L_1$$, inner length $$L_2$$ as shown in Figure (a) below. This U-CSRR element is created on top metal layer of hosting transmission line. The equivalent circuit of the single U-CSRR cell shown in Figure (b) is represented by a parallel resonant circuit with inductance $$L_c$$ and capacitance $$C_c$$. The inductance $$L_R$$ and capacitance $$C_R$$ represent the inductance and capacitance of the host transmission. The U-CSRR particle is electrically coupled to the host transmission line.

The equivalent circuit of the U-CSRR particle suggests that at low frequency, the impedance of the parallel tank circuit is small and the circuit has passband characteristics. Figure (a) shows the schematic diagram of such a filter employing two U-CSRR cells in microstrip [1] representing various feature dimensions. As in [1], the choice of two U-CSRR particles in filter design is to have a compact size and ensure high attenuation in stop band.

Use the traceRectangular object to create feeding transmission line ZA and rectangular unit cell Cell_A. Perform the Boolean add operation for the microstrip shapes ZA, Cell_A and create LeftSection.

% Set variables for ground plane
gndL = 18e-3;
gndW = 7e-3;

% Set variables for feeding transmission line
ZA_Width = 4e-3;
ZA_Length = 4e-3;

% Define unit cell length
Cell_Length = 5e-3;

% Create feeding microstrip line
ZA = traceRectangular("Length",ZA_Length,"Width",ZA_Width,...
    "Center",[-ZA_Length/2-Cell_Length 0]);

% Create rectangular unit cell
Cell_A = traceRectangular("Length",Cell_Length,"Width",Cell_Length,...
    "Center",[-Cell_Length/2 0]);

% Join feeding line and rectangular unit cell
LeftSection = ZA + Cell_A;

Use traceLine object to create shapes s1, s2, s3, s4. Use traceRectangular object to create shape s5.

Subtract shapes s1,s2,s3,s4, and s5 from LeftSection. This operation creates various slots seen on U-CSRR particle. Visualize LeftSection using the show

% Create shapes for various slots 
s1 = traceLine('StartPoint',[-Cell_Length/2-0.2e-3  -1.9e-3],...
    'Angle',[-180 -270 0],'Length',[1.75e-3 3.8e-3 1.75e-3],'Width',0.2e-3);

s2 = traceLine('StartPoint',[-Cell_Length/2+0.2e-3  -1.9e-3],...
    'Angle',[0 90 180],'Length',[1.75e-3 3.8e-3 1.75e-3],'Width',0.2e-3);

s3 = traceLine('StartPoint',[-Cell_Length/2-1.2e-3  -0.2e-3],...
    'Angle',[-90 0 90],'Length',[0.8e-3 2.4e-3 0.8e-3],'Width',0.2e-3);

s4 = traceLine('StartPoint',[-Cell_Length/2-1.2e-3   0.2e-3],...
    'Angle',[90 0 -90],'Length',[0.8e-3 2.4e-3 0.8e-3],'Width',0.2e-3);

s5 = traceRectangular("Length",0.2e-3,"Width",1.8e-3,...
    "Center",[-Cell_Length/2 0]);

% Create slots of U-CSRR on hosted micrsotrip line
LeftSection = LeftSection -s1 -s2 -s3 -s4 -s5;
figure; 
show(LeftSection);

Use the copy and mirrorY methods on the LeftSection object to create a RightSection. This creates right portion of filter having another U-CSRR hosted transmission line. Visualize RightSection using show function.

RightSection = copy(LeftSection);
RightSection = mirrorY(RightSection);
figure; 
show(RightSection);

Perform theBoolean add operation for the shapes LeftSection, RightSection to create a filter. Visualize the filter.

filter = LeftSection + RightSection;
show(filter);

Define the substrate parameters and create a dielectric to use in the pcbComponent of the designed filter. Create a groundplane using the traceRectangular shape. Use the pcbComponent to create a filter PCB. Assign the dielectric and ground plane to the Layers property on pcbComponent. Assign the FeedLocations to the edge of the feed ports. Set the BoardThickness to 1.52 mm on the pcbComponent and visualize the filter. The below code performs these operations and creates the filter PCB.

% Define Substrate and its thickness
substrate = dielectric("RO4730JXR");
substrate.Thickness = 1.52e-3;

% Define bottom ground plane
ground = traceRectangular("Length",gndL,"Width",gndW,...
   "Center",[0,0]);

Use pcbComponent to create a filter pcb

pcb = pcbComponent;
pcb.BoardShape = ground;
pcb.BoardThickness = 1.52e-3;
pcb.Layers ={filter,substrate,ground};
pcb.FeedDiameter = ZA_Width/2;
pcb.FeedLocations = [-gndL/2 0 1 3;gndL/2 0 1 3];
figure; 
show(pcb);

Use the mesh function to have fine meshing and set MaxEdgeLength to 1mm.

figure;
mesh(pcb,'MaxEdgeLength',1e-3);

Use the sparameters function to calculate the S-parameters for the low pass filter and plot it using the rfplot function.

spar = sparameters(pcb,linspace(0.1e9,15e9,30));
figure;
rfplot(spar);

As there are four curves in the result, let us analyze the results.

Plot S-Parameters

Analyze the values of $$S_{21}$$, and $$S_{11}$$ to understand the behavior of low pass filter.

figure;
rfplot(spar,[1 2],1);

The result shows that the filter has $$S_{21}$$ values close to 0 dB and $$S_{11}$$ values less than -15 dB between wide band of frequencies $$f_1$$ = 0.1 GHz and $$f_2$$ = 10.0 GHz. The designed filter therefore has ultra-wide passband response. For frequencies greater than 10.8 GHz, $$S_{21}$$ values are less than -10 dB indicating stopband response.

Use the charge function to visualize the charge distribution on the metal surface and dielectric of low pass filter.

figure;
charge(pcb,5e9);

figure;
charge(pcb,5e9,'dielectric');

Use the current function to visualize the current distribution on the metal surface and volume polarization currents on dielectric of low pass filter.

figure;
current(pcb,5e9);

figure;
current(pcb,5e9,'dielectric');

References

[1] Abdalla, M. A., G. Arafa, and M. Saad, “Compact UWB LPF based on uni-planar metamaterial complementary split ring resonator,” Proceedings of 10th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS), 10–12, Chania, Greece, Sep. 2016