Changes

*[[CubeCAD]]Generic Transmission Line*VisualizationImpedance Matching *[[EM.Tempo#Lumped Sources | Lumped Sources]]Generic Open Stub*[[EM.Tempo#Scattering Parameters and Port Characteristics | S-Parameters]] Generic Short Stub*[[EM.Tempo#Far Field Calculations in FDTD | Far Fields]] Smith Chart*[[Advanced Meshing in EM.Tempo]] Return Loss|All versions|{{download|http://www.emagtech.com/contentdownloads/project-file-download-repository|EMProjectRepo/RFLesson9.Tempo zip RF Lesson 1|[[EM.Cube]] 14.89}} }}

=== What You Will Learn ===

Tuning stubs are segments of open-ended or short-ended [[Transmission Lines|transmission lines]] that are used for distributed impedance matching. Both open and short stubs can be used for impedance matching. From the transmission line theory, we know that open and short stubs have a pure imaginary input impedance. In view of circuit topology, tuning stubs can be connected to the transmission line circuit in series or parallel configurations. In view of circuit complexity, there are single-stub and double-stubs matching network designs.

== A Summary of Series Stub Matching Theory == The design of the series tuning stub utilized in the previous part is now explained. Let the load admittance be Y_L = 1 / Z_L = G_L + j B_L. The admittance looking into a T-Line segment of length d terminated by the load Y_L is given by: <math>Y_{in} = Y_0 \frac{ \left(G_L + j B_L \right) + jY_0 t}{Y_0 + j \left( G_L + j B_L \right) t}</math> where t = tan (&beta; d). The impedance at this point can then be written as: <math>Z_{in} = \frac{1}{Y_{in}} = R_{in} + j X_{in} = \frac {G_L ( 1+ t^2)}{G_L^2+(B_L + Y_0 t)^2} + j \frac {G_L^2 t - (Y_0 - B_L t)(B_L + Y_0 t)}{Y_0 \left[ G_L^2+(B_L + Y_0 t)^2 \right]} </math> Now we choose the T-Line segment length d such that R_in = Z₀. This results in a quadratic equation for t:  <math> Y_0(G_L - Y_0)t^2 -2B_L Y_0 t + (G_L Y_0 t -G_L^2 -B_L^2) = 0 </math> which can be solved for t. In the special case G_L = Y₀, there is one solution t = -B_L / 2Y₀. Otherwise, two distinct roots for t are found. Once t is found, the segment length can be calculated by solving t = tan (2&pi; d / &lambda;_g). The stub reactance X is chosen such that X = -X_in. From this condition, you can find the length of the stub depending on whether you use a short or open stub. Recall that the impedance of an open-ended or shorted transmission line segment of length L is given by: <math> Z_{open} = -jZ_0 cot(\beta L) </math> and  <math> Z_{short} = jZ_0 tan(\beta L) </math> Therefore, the equations for the length L_s of the open stub or short stub are given by: <math> X_{open} = -Z_0 cot (2\pi L_s / \lambda_g) = -X_{in} </math> <math> X_{short} = Z_0 tan (2\pi L_s / \lambda_g) = -X_{in} </math> == Single-Stub Impedance Matching Using a Series Open Stub==

To verify this, run a network analysis of the circuit with the tuning stub matching networkas a one-port. Use Node 2 as (at the input portof T-Line segment XTL1) as Port 1. Plot Use the s11 [[parameters]] given in the table below:  {| border="0"|-| valign="top"||-{| class="wikitable"|-! scope="row"| Start Frequency| 1G|-! scope="row"| Stop Frequency| 3G|-! scope="row"| Steps/Interval| 10Meg|-! scope="row"| Interval Type| Linear|-! scope="row"| Parameter Set| S|-! scope="row"| Graph Type| Smith or Cartesian (Amplitude Only) with Decibels unchecked|} First, plot the S11 data on the Smith chart. Use the same start and stop frequencies as in the previous tutorial lesson, i.e. 1GHz and 3GHz, respectively, with a step size of 100MHz. You can see from the figure below that at f = 2GHz, the plot passes through the center of the Smith chart. It would be informative to plot the return lossThen, i.e. |s11| as a function of frequency on a Cartesian graph. In in the Output tab of the Network Analysis Test Panel, choose "Cartesian (Amplitude)" as the graph typewith the "Decibels" box unchecked. To obtain This will produce a smooth curve, set graph of the return loss, i.e. |s11|, as a function of frequency step size to 10MHzon a Cartesian graph. The results are depicted in the figure belowAgain, showing you can see a vanishing return loss quite good impedance match at 2GHz.

[[File:RF30.png|thumb|750px|The original RF Smith chart showing the input reflection coefficient of the transmission line circuit with an inductive loadseries open stub.]]

[[File:RF31.png|thumb|750px|The RF return loss of the transmission line circuit with a single-stub matching network using a series open stubplotted on a linear scale.]]

== DoubleSingle-Stub Impedance Matching Using Two Open Stubsa Shunt Short Stub ==

Additional The following is a list of parts you need needed for this part of the tutorial lesson: * A Generic T-Line (Keyboard Shortcut: T) * Two Generic Open Stubs In the last part of this tutorial lesson, you will explore a double-stub matching network. The following figure on the left shows the original transmission line circuit of RF Tutorial Lesson 2 with a capacitive loading. The double-stub matching network will be inserted between the source circuit and the capacitive load of 60 - j80 Ohms at f = 2GHz. The figure on the right shows a shunt open stub connected in parallel with the load and a second shunt open stub placed at a distance of &lambda;_g/8 = 18.75mm from the first stub towards the source through a segment of a 50&Omega; T-Line. When the lengths of the first and second open stubs are chosen to be 21.9mm and 30.6mm, respectively, the input impedance looking into the combination of the two stubs and the load to the right becomes 50&Omega;.

| valign="bottomtop"|[[File:RF25.png|thumb|400px|left|The original RF circuit with an inductive load.]]| valign="bottom"|[[File:RF35.png|thumb|500px|left|The RF circuit with a single-stub matching network using a series open stub.]]

Similar to the previous caseThis time, run you will design a matching network analysis of between the source circuit with and the tuning stub matching networkcapacitive load of 60 - j80 Ohms at f = 2GHz. Use Node 2 again Place and connect the parts as shown in the input portfigure below. Plot When the s11 data on the Smith chart with a frequency step size length of 100MHz and then plot the return loss connecting (|s11|spacer) on a Cartesian graph with a frequency step size of 10MHzT-Line is chosen to be 16. As you can see from 5mm and the results shown in length of the figures belowshort stub is chosen to be 14.25mm, this network has a high return loss over most the input impedance looking into the combination of the frequency range except around f = 2GHz stub and the load to the right becomes 50&Omega;.  <table><tr><td>[[File:RF32.png|thumb|600px|The RF circuit with a prefect match is achieved at 2GHzsingle-stub matching network using a series open stub. ]]</td></tr></table> To verify your matching network, run a network analysis of your circuit with the following [[parameters]]:

| valign="bottomtop"|[[File:RF36.png|thumb|500px|left|The original RF circuit with an inductive load.]]| valign="bottom"|[[File:RF37.png|thumb|500px|left|The RF circuit with a single-stub matching network using a series open stub.]]

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