UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING The Edward S. Rogers Sr. Department of Electrical and Computer Engineering

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1 UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING The Edward S. Rogers Sr. Department of Electrical and Computer Engineering 1. Object: ECE357H1F: ELECTOMAGNETIC FIELDS EXPERIMENT 1: DESIGN OF A DOUBLE STUB MATCHING NETWORK The input impedance and the reflection coefficient of a transmission line are investigated. The transformation between the two is introduced with graphical aids. The measurement and interpretation of voltage standing wave ratio is discussed. 2. References: 1. Your lecture notes. 2. D. Cheng, Field and Wave Electromagnetics, 2 nd ed., Addison- Wesley. 3. Background 3.1 De-embedding of Measured Data A device is often measured in a test fixture, as illustrated in Fig. 1. Since the measurements are made at the VNA (Vector Network Analyzer) ports and not at the actual input and output ports of the device, the data includes the effects of the connecting feed lines. The process of de-embedding removes these effects and allows an accurate characterisation of the device. De-embedding is necessary here since the Device Under Test (the unknown load) is connected to the VNA cables by a connecting SMA cable. Even assuming this latter cable to be lossless, any length of transmission line causes a rotation of the impedance on the Smith chart, and so this rotation must be undone.

2 (a) Test fixture (b) Test fixture after de-embedding Fig. 1 Although circuit or mathematical models can be used to account for the effects of the test fixture, the de-embedding procedure you will use for this experiment is straightforward: an additional length of transmission line will be added virtually to the measured data as shown in the Fig. 1(b). Therefore, it is as though the VNA cable were directly attached to the device. Adding this cable length corresponds to a rotation of the input impedance on the Smith chart where the amount of rotation is the electrical length of the cable (i.e., its length in wavelengths). However, in this case the direction of rotation is counter-clockwise since the measurement port is moving closer to the load. 3.2 Introduction to a Double Stub Tuner A single stub matching network as shown in Fig. 2 suffers from the disadvantage of being frequency sensitive in that a change of frequency requires a change of separation between the stub and the load, a mechanically cumbersome operation. In a double stub tuner the separation between the stubs remains constant and a change of frequency is accommodated by an appropriate adjustment of the stubs resulting in an electrically flexible and mechanically simple system. A circuit diagram of a double stub matching network is shown in Fig. 3. Stubs d2 and d3 separated by distance d1 transform a specific admittance YA into Y0 at the input terminals of the network. Note also that there is an extra section of line d0 separating the first stub from the load which models the length of the connector between the tuning circuit and the load. The design procedure is illustrated on the Smith chart of Fig. 4 and formulated in the following steps. Design Procedure The operation of a double stub matching network is best understood by starting at the input and working back toward the load.

3 (1) For a perfectly matched load, yin is unity and therefore yc = 1 - jb2. This means that the yc point is located on the g = 1 circle of the Smith chart. (2) To find the yb point, the g = 1 circle is rotated counter clockwise (toward the load) on the Smith chart by a distance corresponding the stub separation d1 (in wavelengths). For yc to lie on the g=1 circle, yb point must lie somewhere on the rotated g = 1 circle as indicated on the Smith chart. (3) Since yb = ya + jb1 (ya and yb have the same conductance), matching is possible for any load ya which lies on a conductance circle intersecting the rotated g=1 circle. Note that for any load within the dark- shaded area in Fig. 4 double- stub matching with this arrangement is not possible. Since there are in general two intersection points of one conductance circle with the rotated g=1 circle, two different designs are possible for a given load ya. (4) The susceptance B1 is given by the required difference in susceptance between ya and the chosen yb on the Smith chart. (5) Since the points B and C are separated by a length d1 of transmission line, yb and yc lie on the same SWR circle. Therefore yc is located by moving clockwise (toward the generator) on the Smith chart a distance d1 (in wavelengths) from the yb point and by design intersecting with the g = 1 circle. (6) Since yc = 1 - jb2, the susceptance B2 is given by the required difference in susceptance between yc and the matched position at the centre of the Smith chart. (7) Determine the two stub lengths using the Smith chart by starting at the short circuit

4 position and rotating clockwise (toward the generator) along the Γ = 1circle until the required susceptance values are encountered. Then convert the wavelength readings from the Smith chart into physical lengths for each stub. Fig. 2 Fig. 3

5 Fig Experimental Procedure: Notation: In the following instructions, [Command] refers to a softkey on the VNA front panel while Command refers to an option appearing on the VNA touchscreen. 1. Calibrate the Vector Network Analyzer (VNA) for reflection measurement. (a) The first step is to set the frequency span over which the measurements and calibration will be performed. On the VNA front panel, press [Start]à 300 MHz and [Stop]à 1.3 GHz. (b) Set the number of points to be measured: [Sweep Setup]à Points à 201 à Return. (c) Enter calibration menu: [CAL] à CAL Kit 85032B/E à Correction ON à Calibrate à 1-Port Cal. Attach the Female-Female adapter to the VNA cable, connect the provided Short, Open, and Load terminations and select the corresponding button on the VNA screen. Press Return.

6 2. Measure the unknown load impedance. (a) Attach the SMA cable to the VNA F/F adapter and connect the load. Press [Meas] à S11 à [Format] à Smith à R+jX. Data markers may displayed using [Marker] à Marker 1 à 800 MHz. You may want to reduce the frequency range to 700 MHz to 900 MHz to provide a clearer graph. (b) As discussed in Section 3.1, the impedance seen on the screen must be de-embedded to account for the extra cable length. Press [CAL] à Port Extension à Extension ON à Auto Port Extension à Select Portsà Port 1 ON. Now attach the SMA Open and Short connection and press the corresponding screen buttons. Re-attach the load and record the impedance. Export the Smith Chart graph with [System]à Dump Screen Imageà Select save location. (c) Check the de-embedded length: Returnà Extension Port 1. Record this value (both time and length). (d) Demonstrate the de-embedding process graphically on a Smith chart: using the VNA s keypad increase the port extension by 0.2 ns, note the corresponding increase in length, and save the resulting image. How many wavelengths (at 800MHz) does the length increase correspond to? Using your own calculations, show how this increase corresponds to rotating the impedance measured in part (b) on the chart. Note: the Port Extension process corresponds to moving closer to the LOAD, and not the GENERATOR. (e) Restore the de-embedded length to its previous value (i.e., subtract 0.2 ns). 3. (a) Using the Smith Chart determine the normalized impedance of the load transferred to the connection point of the first stub (d 0 =3.4 cm). This is the impedance za. (b) Locate the corresponding admittance ya. 4. Follow the design procedure outlined in the previous section to design a double-stub matching network. Record both stub lengths in wavelengths as well as in cm. The distance d1 between the centerlines of the two stubs is 3.8 cm. Note that there are two solutions for each stub length. 5. Attach the double stub tuner and load to the SMA cable. Adjust the stub lengths to find a good impedance match for both sets of solutions and compare the final stub lengths with your calculated values. 6. Plot the resulting VSWR vs. frequency of the matched line using [Format] à SWR. Find the bandwidth of each solution for a VSWR of less than 2 (you may need to increase the frequency range for this). What does this correspond to in term of the reflection coefficient and its value in decibels ( 20 logγ )? Compare the two measured bandwidths and suggest reasons for this bandwidth limitation.