# EM.Tempo Tutorial Lesson 5: Analyzing A Planar Microstrip Band-Stop Filter

 Tutorial Project: Analyzing A Planar Microstrip Band-Stop Filter Objective: In this project, a planar microwave circuit made of microstrip line segments is modeled and its frequency response is analyzed in EM.Tempo. Concepts/Features: Computational Domain Boundary Conditions Microstrip Port Source Port Definition S-Parameters Minimum Version Required: All versions ' Download Link: EMTempo_Lesson5

## What You Will Learn

In this tutorial you will model a two-port planar filter that is excited by two independent sources. You will first use a wizard to create a basic two-port microstrip through line. Then, you will add additional microstrip segments to complete your filter construction.

## Getting Started

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

 Name EMTempo_Lesson5 Mils GHz 13GHz 26GHz

The figure below shows the geometry of the planar filter and its microstrip line segments:

 The geometry of the planar filter and position of the microstrip components.

## Constructing the Base Geometry of a Two-Port Microstrip Line

Make sure you have changed the project units to "Mils". Click on the Two-Port Microstrip Wizard button of the Wizard Toolbar or select the menu item Tools → Transmission Line Wizards → Two-Port Microstrip Line.

 EM.Tempo's wizard toolbar.

A default two-port microstrip line structure appears in the project workspace. The microstrip line extends across the whole length of the dielectric substrate. Two microstrip port sources are used to excite the microstrip through line from its two ends. These are indeed special distributed sources that are placed between PEC lines and a ground plane and are used to compute the scattering parameters.

 The initially created two-port microstrip geometry.

At this point, you are going to change the parameters of microstrip geometry the wizard created for you including the dielectric substrate properties. Open the variables dialog and change the definition of the following variables:

Variable Name Original Definition New Definition
er 2.2 9.9
h 0.0015*to_meters 5
sub_len 0.1*to_meters 200
sub_wid 0.05*to_meters 60
cetner_len 0.05*to_meters 100.6
feed_wid microstrip_design(z0,er)*h 4.8

Some of the above length variables have original definitions that convert default meter-scaled values to the project units of your current project. This is done using the system variable "to_meters". You can simply replace this kind of variables with numeric values expressed in the current project units. Also, note that on a 5-mil substrate with εr = 9.9, a 50Ω microstrip line has a width of 4.815 mils. Here you change the width of the micostrip to a rounded value of 4.8 mils.

 The variables dialog showing all the modified variables.

The figure below shows the geometry of the microstrip through line after affecting all the above changes:

 The modified two-port microstrip geometry.

## Drawing the Additional Microstrip Components

The next step is adding four additional microstrip segments to turn the microstrip through line into a planar filter. But first you have to make sure that the objects you are going to draw will belong to the right material group. To do so, select the item "CONDUCTOR" under PEC Objects in the navigation tree, right-click on it and select Activate from the contextual menu. This makes the PEC group called "CONDUCTOR" the active material group of the project for drawing and adding new objects.

 Making a material group active in the navigation tree.

Below is a list of the rectangle strip objects you need to draw in the project workspace:

Part Object Type Coordinates Dimensions
Rect1 Rectangle Strip (0.5mils, 8.8mils, 5mils) 90mils × 4.8mils
Rect2 Rectangle Strip (-0.5mils, -8.8mils, 5mils) 90mils × 4.8mils
Rect3 Rectangle Strip (47.9mils, 6.8mils, 5mils) 4.8mils × 8.8mils
Rect4 Rectangle Strip (-47.9mils, -6.8mils, 5mils) 4.8mils × 8.8mils

There are many different ways of drawing, moving and manipulating objects in EM.Cube. As you learn more about EM.Cube's CAD tools and become more skilled in using them, you will find a number of facilitating shortcuts that take advantage of object snap points. But for now, you can simply draw the objects below on a blank space in the project workspace and then place them in the right locations by changing their coordinated according to the above table.

To draw a rectangle, click the Rectangle Strip button of the Object Toolbar or select the menu item Object → Surface → Rectangle Strip.

 Selecting the Rectangle Strip tool in the object toolbar.

With the rectangle strip tool selected, click on a blank space in the project workspace and drag the mouse to draw the planar rectangle object. A property dialog pops up at the lower right corner of your screen. As you drag the mouse, you will see that the X-dimension and Y-dimension of your new object continuously change. When the base reaches the desired size or something close to that, click the mouse. You can always fine-tune the size of your object by entering exact numeric values for its dimensions. You will notice four small red balls on the four sides (edges) of the rectangle strip object. These are called edit handles and can be used to change the dimensions of the object. Or you can simply type in any value for the X- and Y-dimensions of your rectangle. Next, you have to position your rectangle strip in the right location by entering the given values for the coordinates of the center of the local coordinate system (LCS).

 The property dialog of the rectangle strip object.

After drawing and positioning all the four rectangle strip, you filter geometry will look like the figure below:

 The completed two-port microstrip filter geometry.

## Examining the Sources & Ports

The wizard automatically initiated two microstrip port sources and associated them with the two feed strips objects at the two edges of the substrate. Two port observables were also defined and associated with the sources. In other words, the wizard already took care of the excitation and observables for your project. A microstrip port/source is associated with a narrow long rectangle strip object. It is a special distributed source that is placed underneath the strip object having the same width as the strip plus an additional height parameter, which represent that height of thickness of the substrate. You can open the property dialog of the two microstrip source and examine their parameters.

 The microstrip port dialog.

Also, open the port definition dialog and see how the two ports have defined and associated with the two sources.

 The port definition dialog showing the two ports associated with the two sources.

Both ports have reference impedance of 50Ω. These are the port characteristics impedances that are used to define and compute the scattering parameters in the FDTD method:

$S_{ij} = \sqrt{\frac{Re(Z_i)}{Re(Z_j)}} \cdot \frac{V_j - Z_j^*I_j}{V_i+Z_i I_i}$

In the above equation, Vi and Vj are the voltages across ports i and j, respectively, and Ii and Ij are the currents that flow through those ports. During the FDTD simulation of a two-port structure like your planar filter, a "port sweep" takes place behind the scenes. First, the source MS_1 is turned on with a voltage of 1V and source MS_2 is turned off (shorted). The voltage and currents at the locations of these distributed sources are measured after a complete FDTD time marching loop. Next, the source MS_2 is turned on with a voltage of 1V and source MS_1 is turned off (shorted).

 Calculation of the port characteristics of an N‐port structure in EM.Tempo requires a port sweep that generates N binary excitations of all the ports and requires N separate FDTD time marching loops.

## Setting the Computational Domain

EM.Tempo automatically places a domain box around your physical structure. The default box is positioned a quarter free-space wavelength away from the largest bounding box of your structure. You can change the values of the Domain Offset parameters individually at all the six faces of the domain box. To do so, open the domain settings dialog by clicking the Domain button of the Simulate Toolbar or selecting the menu item Simulate → Computational Domain → Domain Settings... or using the keyboard shortcut Ctrl+A.

Note that the six walls of the domain box represent perfectly matched layer (PM) boundary conditions by default. They are used to model an open-boundary problem. A filter structure does not radiate. Therefore, you can afford placing the domain walls much closer to your physical structure. In the domain settings dialog, change the default domain offset values in wavelengths from 0.25 to 0.1 along all the six ±x, ±y and ±z directions.

 EM.Tempo's Domain Settings dialog.

## Analyzing the Planar Filter

At this point, your filter is ready for simulation. Before starting the simulation, try to mesh your physical structure. The wizard set the mesh density to 40 cells/λeff. It would be interesting to examine the mesh grid planes and see how EM.Tempo's adaptive mesh generator discretizes the substrate layer and the microstrip discontinuity regions. The figures below show the XY and ZX grid planes of your microstrip filter structure.

 The top view of EM.Tempo's XY grid plane. The perspective view of EM.Tempo's ZX grid plane.

In the Engine Settings dialog, set the value of Power Threshold to -40dB and increase Max No. Time Steps to 20,000. Run a Wideband Analysis. In this case, the port sweep process involves two binary excitations.

## Plotting the Frequency Response of the Filter

Once the two-port FDTD simulation is finished, a number of output data files appear in the Data Manager. These include N2 = 4 scattering parameter files with names like “DP_Sij.CPX”, N2 impedance parameter files with names like “DP_Zij.CPX”, N2 admittance parameter files with names like “DP_Yij.CPX”. The figure below shows the return loss (S11) and insertion loss (S21) of the band-stop filter. The filter features a 4.5GHz stop band over the frequency range [10GHz - 14.5GHz].

 The plot of S11 parameter of the microstrip filter structure. The plot of S21 parameter of the microstrip filter structure.