# 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

$${g}_{2}$$ = 1.1132

Using the design equations Eq.(6.30) given in reference [1] on page no. 182 for n = 3 and $${Z}_{0}$$ = 50 Ω as , 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 given in Chapter 4 of reference [1]. 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,1,1:2)

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 $${f}_{1}$$ = 1.4 GHz and $${f}_{2}$$ = 3.4 GHz. The designed filter therefore has stopband response. The shift in band-edge frequencies $${f}_{1}$$ and $${f}_{2}$$ might be due to use of different full wave numerical solver used for EM simulation.

#### 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.