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In this tutorial you will learn how to construct coplanar waveguide (CPW) transmission line structures with different termination types. You will also learn about lumped devices like linear resistors and nonlinear diodes. You will examine temporal waveforms of different types for exciting your CPW structure and will investigate the transient response of your circuit. You will also learn how to parameterize geometric objects using independent and dependent variables.  [[Image:Back_icon.png|30px]] '''[[EM.Tempo | Back to EM.Tempo Manual]]''' [[Image:Back_icon.png|30px]] '''[[EM.Cube#EM.Tempo_Documentation | Back to EM.Tempo Tutorial Gateway]]''' [[Image:Download2x.png|30px]] '''[http://www.emagtech.com/downloads/ProjectRepo/EMTempo_Lesson9.zip Download projects related to this tutorial lesson]'''

A coplanar waveguide with a slot width of w = 1mm and center metal strip width of s = 2mm on a dielectric substrate of thickness h = 1.5mm and ε_r = 2.2 has a characteristic impedance of Z₀ = 99.18Ω and effective permittivity of ε_eff = 1.48. At an operating frequency of f_o = 6GHz, the free-space and guide wavelengths are λ₀ = 50mm and λ_g = λ₀/√ε_eff = 41.13mm, respectively. You can verify these results using the CPW Transmission Line Calculator tool in the Device Manager of [[RF.Spice A/D]], if you have installed it on your computer. You can access the Device Manager directly from the Tools Menu of [[EM.Tempo]].

<td> [[Image:Tempo L9 Fig1.png|thumb|left|480px|The coplanar waveguide transmission line calculator tool of RF.Spice A/D.]] </td>

Click on the <b>CPW Wizard</b> [[Image:CPWWizardIconx.png]] button of the Wizard Toolbar or select the menu item '''Tools &rarr; Transmission Line Wizards &rarr; Coplanar Waveguide'''.

<td> [[Image:Tempo L9 Fig2.png|thumb|left|720px|EM.Tempo's Object Toolbar.]] </td>

A one-port CPW structure is created in the project workspace. The transmission line segment is fed from the right edge of the substrate using a "Coplanar Waveguide Port Source" called "CPW_1". The two lateral ground planes "Ground_1" and "Ground_2" extend to the entire length of the substrate. The center metal strip is terminated in an open end at x = -25mm. The open-ended center strip itself consists of two rectangle strip objects called "ANCHOR" and "Feed".

<td> [[Image:Tempo L9 Fig3.png|thumb|left|720px|The geometry of the original one-port CPW structure created by the wizard.]] </td>

| center_widfeed_wid

| feed_widcenter_wid

<td> [[Image:Tempo L9 Fig3D.png|thumb|left|640px|The geometry of the one-port CPW structure with an open-ended center strip and shrunken domain box.]] </td>

<td> [[Image:Tempo L9 Fig4.png|thumb|left|480px|The CPW port/source dialog.]] </td>

<td> [[Image:Tempo L9 Fig5.png|thumb|left|480px|Setting the port reference impedance in the port definition dialog.]] </td>

! scope="col"| Cone Length Ratio! scope="col"| Cone Radius Ratio

[[Image:Tempo L9 Fig6.png|thumb|600pxleft|640px|The CPW structure with all objects in freeze mode and two field probes and three orthogonal field sensor planes.]]

Run an FDTD simulation of your transmission line circuit and visualize its field distributions. The figure below shows the electric field distribution on a horizontal plane at z = 1.2mm5mm, <i>i.e. </i> the surface of the CPW line. The E-field is almost zero everywhere except on the two slots. The fields are uniform longitudinally along the two slot lines, meaning that a decent impedance match has been accomplished and there is little wave reflection that would cause a standing wave pattern.

[[Image:Tempo L9 Fig7.png|thumb|left|540px640px|The vector plot of the electric field distribution on the horizontal plane at Z = 1.5mm.]]

[[Image:Tempo L9 Fig8.png|thumb|left|540px640px|The vector plot of the magnetic field distribution on the horizontal plane at Z = 1.5mm.]]

[[Image:Tempo L9 Fig10.png|thumb|left|450px|The vector plot of the magnetic field distribution on the vertical plane at the center strip's open termination at Z X = -25mm.]]

[[Image:Tempo L9 Fig11.png|thumb|left|540px640px|The intensity plot of the electric field distribution on the vertical plane at Y = 1.5mm.]]

[[Image:Tempo L9 Fig12.png|thumb|left|540px640px|The intensity plot of the magnetic field distribution on the vertical plane at Y = 1.5mm.]]

Note that the electric field at the open end is at its maximum while the magnetic field is at its minimum at that location. You can also clearly see the standing wave pattern of the fields along the transmission line. The distance between two consecutive field minima or maxima is equal to the half guide wavelength. This can easily be verified from the 2D graphs of field distributions. Open the data manager and plot the data file "Sensor_1_X_ETotal.DAT" in EM.Grid. Similar to the previous tutorial lesson6, use EM.Grid's Delta line mode or measure the distance between two field peaks in the graph. The figure below shows a spacing of 20.2mm. According [[RF.Spice A/D]], half the guide wavelength for this CPW line is &lambda;_g/2 = 20.56mm, .

[[Image:Tempo L9 Fig13.png|thumb|left|480px|Measuring the spacing between to field maxima in EM.Grid's 2D field graph.]]

The excitation source in an a FDTD simulation pumps up energy into the computational domain and sets the initial conditions of the boundary value problem. By default, [[EM.Tempo]] uses modulated Gaussian waveform to excite all the sources. The default waveform starts after a short delay from t = 0, oscillates over a certain amount of time determined by the project bandwidth, reaches a maximum value in this interval and gradually decays to zero as t &rarr; &infin;. In the CPW source dialog and all other source dialogs, you can click the {{key|Waveform...}} button to open the Excitation Waveform dialog. You can see a graph of the excitation waveform along with its mathematical expression and parameters in this dialog.

[[Image:Tempo L9 Fig16.png|thumb|left|720px|EM.Tempo's excitation waveform dialog.]]

Open the data manager and plot the data file "Probe_1_Y_E_Time.DAT" in EM.Grid. This graph represents the temporal waveform at the locations of "Probe_1 " at x = 25mm. EM.Grid graphs You can be customized see two pulses in many respects. For example, you can change the scale of the time axisgraph below. Click The first one represents the '''Edit Axes''' tab of EM.Grid on incident wave and the left edge of its window. In second one represents the "Settings Panel", select "Bottom Axis" from reflected wave after hitting the top drop-down list labeled '''Select Axis'''open end discontinuity. Uncheck You can measure the "Auto" box, enter 0 and 1.4 for time interval between the min and max values peaks of the axis, respectivelytwo pulses. Press the bottom labeled {{key|Apply Above Changes}}It is about 0. At the bottom of settings, select the radio button labeled '''Number of Intervals''' and enter a value of 14 for it42ns. The graph should look like this:

[[Image:Tempo L9 Fig14Fig15.png|thumb|left|550px|Temporal waveform at the location of the field probe.]]

You can see two pulses in the graph below. The first one represents the incident wave and the second one represents the reflected wave after hitting the open end discontinuity. Using EM.Grid's Delta line mode, you can measure the time interval between the peaks of the two pulses. It is about 0.42ns.  <table><tr><td>[[Image:Tempo L9 Fig15.png|thumb|550px|Measuring the time interval between the two pulses at the location of the field probe.]]</td></tr></table> Next, you will verify this result using the fact that &lambda;_g = &lambda;₀/&radic;&epsilon;_eff. Therefore, &epsilon;_eff = (50/40.4)² = 1.532, which is very close to the value calculated by RF.Spice A/D. The round-trip distance between the location of "Probe_1 " and the open end discontinuity is d_rt = 100mm. The phase velocity of the propagation mode is v_p = c₀/&radic;&epsilon;_eff. We can now calculate the round-trip time as:

In this section of the tutorial lesson, you will terminate the CPW line with a resistive load and will perform a parametric sweep of your circuit as a function of the load resistance. First, you will create two draw a horizontal lines at line to connect the open end discontinuity to connect of the center strip to the two lateral object "Rect1", which is part of the ground planesplane. This will effectively short out the center strip. You have to make sure that the PEC material group called "CONDUCTOR" is the active group in the navigation tree. Under the PEC group, draw the following line objectsobject:

! scope="row"| Line_1L1

| 1mm gap | (-25mm, 1mm0, 1.5mm) | (0&deg;, 0&deg;, 90-180&deg;) |} To draw a horizontal line, select the <b>Line</b> [[Image:LineToolIconx.png]] button of the Object Toolbar or select the menu item <b>Object &rarr; Curve &rarr; Line</b>.  <table><tr><td> [[Image:LineInToolBar.png|thumb|720px|EM.Tempo's Object Toolbar.]] </td></tr></table> With the line tool selected, click on a block space and drag the mouse to start drawing a line. Observe the changing '''Length''' value in the dialog box and lock it in when the length reaches a desired value. Change the coordinates of the short vertical object to (-25mm, 0, 1.5mm) and the rotation angles to (0&deg;, 0&deg;, -180&deg;).  <table><tr><td> [[Image:Tempo_L9_Fig_Line.png|thumb|left|480px|The property dialog of the line object.]] </td></tr></table> Next, open the variables dialog and define a new variable called RR with a definition (numeric value) of 0. This will represent the resistance of the termination load. Also reduce the gap size to 1mm according to the table below: {| class="wikitable"

! scope="rowcol"| Line_2Variable Name! scope="col"| LineOriginal Definition! scope="col"| PEC New Definition| 1mm -| gap| 8| (-25mm, -1mm, 1.5mm) | (0&deg;, 0&deg;, -90&deg;) | RR| N/A| 0

Next, open the variables dialog and define a new variable called RR with a definition (numeric value) of 100. This will represent the resistance of the termination load. Now, right-click on the '''Lumped Devices''' item in the "Sources" section of the navigation tree and select '''Insert New Source...''' from the contextual menu. The lumped device dialog opens up. Keep Change the default name to "LC_1LC1". From the '''Line Object''' drop-down list, choose "Line_1L1". For the '''Offset''' parameter, enter the expression "gap/2". The '''Type''' drop-down list offers four options: Resistor, Capacitor, Inductor and Diode. Select '''Resistor''' and replace its default '''Resistance''' value of 100&Omega; with the expression variable "2*RR". Repeat this process one more time, call the second lumped device "LC_2", associate it with the line object "Line_2" and select the resistor type with a resistance equal to "2*RR". Note that two resistors are effectively shunted to the ground. Therefore, the total load resistance will be (2*RR) || (2*RR) = RR.

[[Image:Tempo L9 Fig17.png|thumb|left|480px|EM.Tempo's lumped device dialog.]]

The two lumped resistors resistor at the end of the center strip will look like this: <table><tr><td>[[Image:Tempo L9 Fig18A.png|thumb|left|640px|The CPW structure with a horizontal line and a resistive lumped device at the end of the center strip.]]</td></tr></table>

[[Image:Tempo L9 Fig18.png|thumb|550pxleft|360px|A close-up of the discontinuity region with two a horizontal lines line and two a resistive lumped devicesdevice.]]

Open [[EM.Tempo]]'s simulation engine settings run dialog and restore the default convergence criteria, i.e. set the "Max No. Time Steps" equal to 10,000, power threshold to -30dB, and select the third radio button labeled "Both". In the Simulation Run dialog, select '''Parametric Sweep''' as the simulation mode. Open the parametric sweep settings dialog by clicking the {{key|Settings}} button. Select "RR" as your uniform sweep variable and set its start, stop and step values equal to 500&Omega;, 150200&Omega; and 1025&Omega;, respectively, as shown in the figure below:

[[Image:Tempo L9 Fig21.png|thumb|left|720px|Defining the sweep variable in EM.Tempo's parametric sweep dialog.]]

Run a parametric sweep simulation of your resistively terminated CPW line and plot the S₁₁ parameter and voltage standing wave ratio (VSWR) in EMDP_S11.GridCPX). As you can see from the figure below, the return loss attains a minimum value of -22dB 13.0dB for RR = 100&Omega;.

[[Image:Tempo L9 Fig22.png|thumb|480pxleft|600px|The graph of S11 parameter of the resistively terminated CPW line segment.]]

The VSWR In the last part of your circuit attains a minimum value of 1.173 for this section, open the variables dialog and set the value of the sweep variable"RR" equal to 100 Ohms. In an EM.Grid graphThen, you can find and mark run a "Wideband Analysis" of your CPW structure. Visualize the minima field distributions on the sensor planes and compare them to the mxima case of your plotsno lumped resistor. Open From the '''Edit Plots''' tab from figures below you can see that both the left edge electric and check magnetic field distributions on the box '''Show Minima''' in this caseCPW line are more uniform, an indicator of a reasonable impedance match.

[[Image:Tempo L9 Fig23Fig18B.png|thumb|480pxleft|640px|The graph vector plot of VSWR the electric field distribution on the horizontal plane with the resistive load RR = 100&Omega;.]]</td></tr><tr><td>[[Image:Tempo L9 Fig18C.png|thumb|left|640px|The vector plot of the resistively terminated CPW line segmentmagnetic field distribution on the horizontal plane with the resistive load RR = 100&Omega;.]]

Plot the data file "Sensor_1_X_ETotal.DAT". From this figure, too, you can see that the standing wave pattern along the CPW has subsided significantly compared to the previous case. The maximum and minimum field values are read to be |E_max| =453V/m and |E_min| = Using a Nonlinear Diode 363V/m. The voltage standing wave ratio (VSWR) is defined as VSWR =|V_max|/|V_min| =|E_max|/|E_min| = 453/363 = 1.248.

In the last part of this tutorial lesson, you will use a nonlinear diode as the termination load of your CPW structure<table><tr><td>[[Image:Tempo L9 Fig18D. First, you need to delete the line objects "Line_1" and "Line_2". Select each object and use the {{keypng|thumb|Delete}} of your keyboard to delete them or select '''Delete''' from their contextual menu. Note that when you delete a line object, any source or device associated with it will be deleted, too. Thus, deleting left|480px|The 2D field distribution graph along the two line objects will also result in the deletion center of the lumped devices "LC_1" and "LC_2"slot. Next, make sure the PEC group "CONDUCTOR" is the active material group in the navigation tree. Then, add a PEC rectangle strip and a new PEC line object according to the ]]</td></tr></table below: >

{| class="wikitable"|-! scope="col"| Part! scopeUsing a Nonlinear Diode ="col"| Object Type! scope="col"| Material Type! scope="col"| Dimensions! scope="col"| Coordinates! scope="col"| Rotation Angles|-! scope="row"| Rect1| Rectangle Strip| PEC | 24mm &times; 4mm | (-38mm, 0, 1.5mm) | (0&deg;, 0&deg;, 0&deg;) |-! scope="row"| Line_3| Line| PEC | 1mm | (-25mm, 0, 1.5mm) | (0&deg;, 0&deg;, 180&deg;) |}

To define the diode, right-click on the [[EM.Tempo]]'''Lumped Devices''' item of the navigation tree and select '''Insert New Source''' from the contextual menu. In the s lumped device dialog, select "Line_3" as gives you the host line object and select '''Diode''' as the device typeoption to define a nonlinear diode. A diode is a rectifying device. The time-domain relationship between the voltage and current of a diode is given by the nonlinear equation:

where I_s is the saturation current, k = 1.3806488 &times; 10^-23m²kg.s^-2K^-1 is the Boltzmann constant, q = 1.60217657 &times; 10^-19 is the electron charge, T is the temperature in degrees Kelvin, and n is the ideality factor. The diode allows the flow of positive current in the direction from anode to cathode, but it blocks the flow of current in the opposite direction. Open the property dialog of the lumped device "LC1", and from the '''Type''' drop-down list, select '''Diode'''. Enter the following parameters for the diode device:

| Line_1 L1

| +Y -X

[[Image:Tempo L9 Fig24.png|thumb|left|480px|Changing the lumped device "LC_1LC1" to a nonlinear diode.]]

<table>Define an additional temporal field probe at the location of the lumped diode device according to the specifications below:<tr><td>{| class="wikitable"[[Image:Tempo L9 Fig27.png|thumb-! scope="col"|720pxField Probe! scope="col"|The geometry of the modified CPW line segment with a diode termination.]]Coordinates</td>|-</tr>! scope="row"| Probe_2</table>| (-25.5mm, 0, 1.5mm)|-|}

Also, open Uncheck the property dialog of the first field probe called "Probe_1Compute Fields at the Center of Yee Cell" and change its coordinated to (-25.5mm, 0, 1.5mm)checkbox for both Field Probes.

[[Image:Tempo_L9_uncheck.png|thumb|left|350px|EM.Tempo L9 Fig28's temporal field probe dialog corresponding to Probe_1.]]</td><td>[[Image:Tempo_L9_uncheck_2.png|thumb|400pxleft|A close-up view of the CPW termination area350px|EM.Tempo's temporal field probe dialog corresponding to Probe_2.]]

 For this part of the tutorial lesson, you are also going to change the excitation waveform for the first time. Open the property dialog of the CPW port source "CPW_1 " and click its {{key|Waveform...}} button. In the Excitation waveform dialog, select the second radio button labeled '''Use Custom Frequency Domain Specifications'''. From the drop-down list labeled '''Waveform Type''', select the '''Sinusoid''' option and enter a value of 5V for the '''Amplitude'''. Note that the default frequency is "fc". This means that your excitation waveform will be a single-tone harmonic waveform with f = fc = 6GHzwith a period equal to T = 1/f = 0.167ns.

[[Image:Tempo L9 Fig25.png|thumb|left|720px|Defining a large-signal sinusoidal waveform in the Excitation Waveform dialog.]]

Run an FDTD simulation of your structure with a fixed number of 2,500 time steps. Plot the data files "Probe_1_X_E_TimeProbe_1_Y_E_Time.DAT" and "Probe_2_Y_E_TimeProbe_2_X_E_Time.DAT", corresponding to the waveforms of Probe_1 and Probe_2, respectively, in EM.Grid. Note that the sinusoidal waveform starts after a delay of about 0.3ns, the time it takes to travel from the source location to the diode's location. Also, the period of the sinusoidal waveform is measured to be 0.1662ns 167ns as expected.

[[Image:Tempo L9 Fig26.png|thumb|left|480px|The graph of the waveform of Probe_1 Probe_2 (at the terminating load) as a function of time with a diode load.]]

[[Image:Tempo L9 Fig26AFig27.png|thumb|left|480px|The graph of the waveform of Probe_2 Probe_1 (on the CPW line) as a function of time with a diode load.]]

You can clearly see the rectifying action of the nonlinear diode device from the above waveform. During the positive negative half-cycles, the input sinusoid is delivered to the load. During the negative positive half-cycles, the waveform is clipped from the bottomtop. This happens when the diode is reverse-biased. The negative positive constant field value during the reverse bias cycle is due to the voltage drop across the diode. Also, note that the waveform of the Probe_2 "Probe_1" close to the source is pure sinusoidal for the first 0.525ns and then starts to get distorted. This is when the reflected wave from the discontinuity reaches the location of this probe.

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