Design and Analyze Band Stop Filter using `pcbComponent`

This example shows you how to design and analyze band stop filter using the `pcbComponent` object. Design the band stop filter with a fractional bandwidth (FBW) of 1.0 at a midband frequency ${f}_{0}$ of 2.5 GHz for the band-edge frequencies of ${f}_{1}$ = 1.25 GHz and ${f}_{2}$ = 3.75 GHz as defined in Figure 6.11b of reference [1].

Design Band Stop Filter

Design the microstrip band stop filter based on a three-pole (n = 3) Chebyshev lowpass prototype with 0.05 dB passband ripple. The element values of the lowpass prototype are ${g}_{0}$ = ${g}_{4}$ = 1.0, ${g}_{1}$ = ${g}_{3}$ = 0.8794, and ${g}_{2}$ = 1.1132. Using the design equations for n = 3 and ${Z}_{0}$ = 50 Ω, you can obtain ${Z}_{A}$ = ${Z}_{B}$ = 50 ohm, ${Z}_{1}$ = ${Z}_{3}$ = 106.8544 ohm, ${Z}_{12}$ = ${Z}_{23}$ = 93.9712 ohm, ${Z}_{2}$ = 44.9169 ohm. Choose a commercial substrate `(RT/D 6006)` with a relative dielectric constant of 6.15 and thickness of 1.27 mm. Calculate the microstrip widths using the microstrip design equations. The figure shows the schematic diagram of the microstrip band stop filter [1] representing various feature dimensions.

Use the `traceRectangular` object to create `ZA`,` Z1`, `Z12.` Perform a Boolean add operation for the microstrip shapes `ZA`, `Z1`, `Z12 `and create a `LeftSection `object. Visualize the `LeftSection` using `show `function.

```ZA_Width = 1.85e-3; ZA_Length = 7e-3; Z1_Length = 0.3e-3; Z1_Width = 15.15e-3; Z12_Length = 14.05e-3; Z12_Width = 0.45e-3; Z2_Length = 2.3e-3; Z2_Width = 14.85e-3; gndL = 45e-3; gndW = 30e-3; ZA = traceRectangular("Length",ZA_Length+Z1_Length/2,"Width",ZA_Width,... "Center",[-gndL/2+ZA_Length/2+Z1_Length/4 0]); Z1 = traceRectangular("Length",Z1_Length,"Width",Z1_Width+ZA_Width/2,... "Center",[-gndL/2+ZA_Length+Z1_Length/2 (Z1_Width/2+ZA_Width/4)]); Z12 = traceRectangular("Length",Z12_Length+Z1_Length,"Width",Z12_Width,... "Center",[-gndL/2+ZA_Length+Z1_Length/2+Z12_Length/2 0]); LeftSection = ZA+Z1+Z12; figure; show(LeftSection);```

Use the `copy`, `rotateZ` and `rotateX` functions on `LeftSection` object to create a `RightSection`. Visualize the `RightSection` object.

```RightSection = copy(LeftSection); RightSection = rotateZ(RightSection,180); RightSection = rotateX(RightSection,180); figure; show(RightSection);```

Perform a Boolean add operation for the shapes `LeftSection `and `RightSection` to create a `combineSection `object. Use the `traceRectangular` object to create centerArm `Z2`. Perform a Boolean add operation for the shapes `combineSection`, `Z2`, and create a `filter `object. Visualize the `filter` object.

```combineSection = LeftSection + RightSection; Z2 = traceRectangular("Length",Z2_Length,"Width",Z2_Width,... "Center",[0 -Z12_Width/2+Z2_Width/2]); filter = combineSection + Z2; 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.

```substrate = dielectric("EpsilonR",6.15,"LossTangent",0.0027,... "Name","custom","Thickness",1.27e-3); ground = traceRectangular("Length",gndL,"Width",gndW,... "Center",[0,6e-3]);```

Create PCB Filter Using `pcbComponent`

Use the `pcbComponent` to create a filter PCB. Assign the dielectric and ground plane to the `Layers` property of the `pcbComponent`. Assign the `FeedLocations` to the edge of the feed ports. Set the `BoardThickness` to 1.27 mm on the `pcbComponent` and visualize the filter.

```pcb = pcbComponent; pcb.BoardShape = ground; pcb.BoardThickness = 1.27e-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);```

Plot and Analyze the S-Parameters

Use the `sparameters` function to calculate the s-parameters for the band stop filter and plot it using the `rfplot` function.

```spar = sparameters(pcb,linspace(0.1e9,6e9,50)); figure; rfplot(spar);```

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

Analyze the values of ${S}_{12}$, and ${S}_{11}$ to understand the behavior of band stop filter.

```figure; rfplot(spar,1,1); hold on; rfplot(spar,1,2); hold on;```

The result shows that the filter has center frequency ${f}_{0}$ = 2.5 GHz for the band-edge frequencies ${f}_{1}$ = 1.75 GHz and ${f}_{2}$ = 3.4 GHz. The ${S}_{11}$ values are close to 0 dB and ${S}_{12}$ values are less than -10 dB between frequencies ${f}_{1}$ = 1.75 GHz and ${f}_{2}$ = 3.4 GHz. The designed filter therefore has stopband response.

Visualize Charge and Current Distribution

Use the `charge` function to visualize the charge distribution on the metal surface and dielectric of band stop filter.

```figure; charge(pcb,2.4e9);```

```figure; charge(pcb,2.4e9,'dielectric');```

Use the `current` function to visualize the current distribution on the metal surface and the volume polarization currents on dielectric of band stop filter

```figure; current(pcb,2.4e9);```

```figure; current(pcb,2.4e9,'dielectric');```

References

[1] Jia-Sheng Hong "Microstrip Filters for RF/Microwave Applications", p. 184, John Wiley & Sons, 2nd Edition, 2011.