View source for EM.Picasso Tutorial Lesson 9: Designing a Microstrip Wilkinson Power Divider

{{projectinfo|Tutorial| Designing a Microstrip Wilkinson Power Divider|Picasso_L9_Fig14_title.png|In this project, you will build a microstrip Wilkinson power divider using three scattering wave ports and a lumped element.|
*PEC Trace
*Rectangle Strip
*Circle Strip
*Scattering Wave Port Source
*Port Definition
*Lumped Element
*Resistor
*Planar Mesh
* S-Parameters
|All versions|{{download|http://www.emagtech.com/downloads/ProjectRepo/EMPicasso_Lesson9.zip EMPicasso_Lesson9}} }}

== What You Will Learn ==

In this tutorial you will build and simulate a three-port planar circuit. You will also learn how to define a lumped element on a strip object to represent a lumped resistor.  

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== Getting Started ==

Open the [[EM.Cube]] application and switch to [[EM.Picasso]]. Start a new project with the following parameters:

<div class="noprint" style="float:left;margin-right:10px">
{| border="1" class="wikitable"
|+ Starting Parameters
|-
! Name
| EMPicasso_Lesson9
|-
! Length Units
| Millimeters
|-
! Frequency Units
| GHz
|-
! Center Frequency
| 2.4GHz
|-
! Bandwidth
| 1GHz
|}
</div>

<div class="noprint" style="float:left;margin-right:10px">
{| border="1" class="wikitable"
|+ Substrate Configuration
|-
! Number of Finite Layers
| 1
|-
! Top Half-Space 
| Vacuum
|-
! Middle Layer
| ROGER RT/Duroid 5880: &epsilon;<sub>r</sub> = 2.2, &mu;<sub>r</sub> = 1, &sigma; = &sigma;<sub>m</sub> = 0, thickness = 0.787mm
|-
! Bottom Half-Space 
| PEC
|}
</div>

<div class="noprint" style="clear:both"></div>

== Drawing the Power Divider Structure & Assigning Its Ports ==

Create a PEC group called "PEC_1" on the navigation tree. The Wilkinson power divider will will consist of two different microstrip line types with characteristics impedance values of Z<sub>0</sub> = 50&Omega; and &radic;2Z<sub>0</sub> = 70.7&Omega;. On the particular substrate of this project as specified in the above table, the widths of the two microstrip lines will be 2.4mm and 1.4mm, respectively. The ring strip will serve as the two 70.7&Omega; quarter-wave arms of the Wilkinson power divider. You can use '''Circle Strip Tool''' to draw rings and arcs using its "Outer Radius", "Inner Radius", "Start Angle" and "End Angle" parameters. 

Draw a circle strip object with the following parameters. 

{| class="wikitable"
|-
! scope="col"| Label
! scope="col"| Object Type
! scope="col"| LCS Origin
! scope="col"| Inner Radius
! scope="col"| Outer Radius
! scope="col"| Start Angle
! scope="col"| End Angle
|-
! scope="row"| Circ_Strip_1
| Circle Strip
| (0, 0, 0.787mm)
| 8.25mm
| 9.65mm
| 20&deg;
| 340&deg;
|-
|}

To draw a rectangle, click the '''Circle Strip''' [[Image:CircleStripToolIconx.png]] button of the Object Toolbar or select the menu item <b>Object &rarr; Surface &rarr; Circle Strip</b>.

<table>
<tr>
<td>
[[Image:Picasso L9 Fig1A.png|thumb|left|720px|Selecting the Circle Strip tool in the object toolbar.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:Picasso L9 Fig1.png|thumb|left|480px|The property dialog of the Circle Strip object.]]
</td>
</tr>
</table>

Next, draw six rectangle strip objects with dimensions and locations given in the table below:    

{| class="wikitable"
|-
! scope="col"| Label
! scope="col"| Object Type
! scope="col"| LCS Origin
! scope="col"| X Dimension
! scope="col"| Y Dimension
|-
! scope="row"| Rect_Strip_1
| Rectangle Strip (50&Omega; Input Line)
| (-10.75mm, 0, 0.787mm)
| 5mm
| 2.4mm
|-
! scope="row"| Rect_Strip_2
| Rectangle Strip (50&Omega; Input Line)
| (8.95mm, -5.3mm, 0.787mm)
| 2.4mm
| 5mm
|-
! scope="row"| Rect_Strip_3
| Rectangle Strip (50&Omega; Input Line)
| (8.95mm, 5.3mm, 0.787mm)
| 2.4mm
| 5mm
|-
! scope="row"| Rect_Strip_4
| Rectangle Strip (50&Omega; Input Line)
| (-17.25mm, 0, 0.787mm)
| 8mm
| 2.4mm
|-
! scope="row"| Rect_Strip_5
| Rectangle Strip (50&Omega; Input Line)
| (8.95mm, -11.8mm, 0.787mm)
| 2.4mm
| 8mm
|-
! scope="row"| Rect_Strip_6
| Rectangle Strip (50&Omega; Input Line)
| (8.95mm, 11.8mm, 0.787mm)
| 2.4mm
| 8mm
|-
|}

Define three scattering wave port sources and assign them to the last three strip objects according to the table below:

{| class="wikitable"
|-
! scope="col"| Source Label
! scope="col"| Host Strip Object
! scope="col"| Direction
|-
! scope="row"| WP_1
| Rect_Strip_4
| +X
|-
! scope="row"| WP_2
| Rect_Strip_5
| +Y
|-
! scope="row"| WP_3
| Rect_Strip_6
| -Y
|}

Your physical structure will look like this:

<table>
<tr>
<td>
[[Image:Picasso L9 Fig2.png|thumb|left|720px|The geometry of the Wilkinson power divider with three scattering wave ports.]]
</td>
</tr>
</table>

Open the planar mesh settings dialog and change the mesh density to 30 cells per effective wavelength. Generate the mesh of your physical structure as shown in the figures below.  

<table>
<tr>
<td>
[[Image:Picasso L9 Fig7.png|thumb|640px|The planar mesh of the Wilkinson power divider.]]
</td>
</tr>
</table>

== Running a Frequency Sweep of the Power Divider ==

Run a frequency sweep of your Wilkinson power divider to examine its frequency response including return losses and insertion losses. Open the frequency sweep settings dialog from the run dialog and set the following uniform frequency sweep parameters:

{| class="wikitable" 
|-
! scope="row"| Start Frequency
| 2GHz 
|-
! scope="row"| End Frequency
| 3GHz
|-
! scope="row"| Number of Frequency Samples
| 11
|}

So far in all the previous tutorial lessons, when you ran a frequency sweep (either uniform or adaptive), you kept the default option of meshing the structure at the highest frequency. For this project, select another option and mesh the structure at the center frequency of the project, <i>i.e.</i> at 2.4GHz. For non-resonant structure, these options don't make too much of a difference. 

<table>
<tr>
<td>
[[Image:Picasso L9 Fig11.png|thumb|left|480px|EM.Picasso's frequency sweep settings dialog.]]
</td>
</tr>
</table>

At the end of the sweep simulation, graph three data files: “S11_Sweep.CPX”, “S22_Sweep.CPX”, “S21_Sweep.CPX” and “S32_Sweep.CPX”. <u>Make sure to scale the plots properly</u>. From the figures below, you can see that the insertion loss values |S21| and |S31| are about -3dB over the entire frequency range. However, the output return losses |S22| and |S33| are about -6dB, which aren't good at all. You would also like to decrease the coupling |S32| between the two output ports to much lower than -7dB.  

<table>
<tr>
<td>
[[Image:Picasso L9 Fig3.png|thumb|left|480px|The graph of the S11 parameter of the Wilkinson power divider.]]
</td>
</tr>
<tr>
<td>
[[Image:Picasso L9 Fig4.png|thumb|left|480px|The graph of the S22 parameter of the Wilkinson power divider.]]
</td>
</tr>
<tr>
<td>
[[Image:Picasso L9 Fig5.png|thumb|left|480px|The graph of the S21 parameter of the Wilkinson power divider.]]
</td>
</tr>
<tr>
<td>
[[Image:Picasso L9 Fig5A.png|thumb|left|480px|The graph of the S32 parameter of the Wilkinson power divider.]]
</td>
</tr>
</table>

== Adding a Lumped Resistor Between the Output Arms ==

In this part of the tutorial lesson, you will add a lumped resistor between the two output ports of your power divider to complete the Wilkinson design. But first you need to draw a narrow microstrip line segment between the two objects Rect2 and Rect3 to hold the lumped element. 

{{Note| In [[EM.Picasso]], a lumped element can only be defined in association with an existing rectangle strip object to serve as its host.}}

Draw a new rectangle strip object with the following parameters:

{| class="wikitable" 
|-
! scope="col"| Label
! scope="col"| Object Type
! scope="col"| LCS Origin
! scope="col"| X Dimension
! scope="col"| Y Dimension
|-
! scope="row"| Rect_Strip_7
| Rectangle Strip
| (8.95mm, 0, 0.787mm)
| 0.5mm 
| 5.6mm
|-
|}

Now you can define a lumped element to model your resistor. Go to the "Sources" section of the navigation tree, right-click on the <b>Strip Gap Circuits</b> item and select <b>Insert New Source...</b> from the contextual menu. in the source dialog, choose the name of the host line "Rect_Strip_7" from the drop-down list. Select '''Passive RLC''' for the lumped circuit type. 

<table>
<tr>
<td>
[[Image:Picasso L9 Fig12.png|thumb|left|650px|EM.Picasso's lumped gap circuit dialog showing "Passive RLC" as the lumped circuit type.]]
</td>
</tr>
</table>

Click on the {{key|Impedance...}} button of this dialog to open the lumped element impedance dialog. By default the box labeled "Rs (Ohm)" is checked with a default resistance value of 50&Omega;. Change the value of resistance to 100&Omega;, <i>i.e.</i> 2Z<sub>0</sub>. Close the two nested dialogs and return to the project workspace. You will see a yellow lumped element appear at the center of the last strip object.    

<table>
<tr>
<td>
[[Image:Picasso L9 Fig13.png|thumb|left|480px|The Lumped Element dialog.]]
</td>
</tr>
</table>

<table>
<tr>
<td>
[[Image:Picasso L9 Fig14.png|thumb|left|640px|The geometry of the Wilkinson power divider with the lumped resistor.]]
</td>
</tr>
</table>

== Examining the Planar Mesh of the Power Divider with the Lumped Resistor ==

The presence of the narrow microstrip line segment hosting the resistive lumped element acts like a discontinuity. As a result, it requires a high resolution mesh even though the segment's size is quite small. Open the planar mesh settings dialog and check the box labeled '''Refine Mesh at Gap Locations'''. 

<table>
<tr>
<td>
[[Image:Picasso L9 Fig6.png|thumb|left|480px|EM.Picasso's mesh settings dialog.]]
</td>
</tr>
</table>

Now generate the mesh of the planar structure with the same mesh density of 30 cells per effective wavelength. 

<table>
<tr>
<td>
[[Image:Picasso L9 Fig15.png|thumb|640px|The planar mesh of the Wilkinson power divider with the lumped resistor.]]
</td>
</tr>
</table>

== Simulating the Complete Wilkinson Power Divider ==

Run a frequency sweep of your Wilkinson power divider with the added resistor. Set the following uniform frequency sweep parameters and keep the option to mesh the structure at the center frequency of the project during the entire sweep. 

{| class="wikitable" 
|-
! scope="row"| Start Frequency
| 2GHz 
|-
! scope="row"| End Frequency
| 3GHz
|-
! scope="row"| Number of Frequency Samples
| 11
|}

At the end of the sweep simulation, graph three data files: “S11_Sweep.CPX”, “S22_Sweep.CPX”, “S21_Sweep.CPX” and “S32_Sweep.CPX”. <u>Make sure to scale the plots properly</u>.

<table>
<tr>
<td>
[[Image:Picasso L9 Fig8.png|thumb|left|480px|The graph of the S11 parameter of the Wilkinson power divider with the lumped resistor.]]
</td>
</tr>
<tr>
<td>
[[Image:Picasso L9 Fig9.png|thumb|left|480px|The graph of the S22 parameter of the Wilkinson power divider with the lumped resistor.]]
</td>
</tr>
<tr>
<td>
[[Image:Picasso_L9_Fig10_new.png|thumb|left|480px|The graph of the S21 parameter of the Wilkinson power divider with the lumped resistor.]]
</td>
</tr>
<tr>
<td>
[[Image:Picasso_L9_Fig10A_new.png|thumb|left|480px|The graph of the S32 parameter of the Wilkinson power divider with the lumped resistor.]]
</td>
</tr>
</table>

From the above figures, you can see that all three port are well matched. The insertion loss at the two output ports is -3.14dB, and the coupling between the output ports has dropped to lower than -18dB. The table below shows the values of all the S-parameters at the center frequency of the project fc = 2.4GHz. 

{| class="wikitable" 
|-
! scope="col"| S-Parameter
! scope="col"| Complex Value
! scope="col"| Magnitude
|-
! scope="row"| S<sub>11</sub>
| 0.127755 +0.137375j
| -14.535409dB
|-
! scope="row"| S<sub>12</sub>
| -0.399210 -0.570641j
| -3.142585dB
|-
! scope="row"| S<sub>13</sub>
| -0.396975 -0.572491j
| -3.139583dB
|-
! scope="row"| S<sub>21</sub>
| -0.400058 -0.570110j
| -3.141940dB
|-
! scope="row"| S<sub>22</sub>
| 0.054326 +0.044426j
| -23.075952dB
|-
! scope="row"| S<sub>23</sub>
| -0.065975 -0.102684j
| -18.269098dB
|-
! scope="row"| S<sub>31</sub>
| -0.396755 -0.572401j
| -3.142068dB
|-
! scope="row"| S<sub>32</sub>
| -0.065172 -0.103138j
| -18.272559dB
|-
! scope="row"| S<sub>33</sub>
| 0.052328 +0.038422j
| -23.752571
|-
|}

<p>&nbsp;</p>
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