AWR eBooks

RF Electronics Chapter4: Transmission Line Transformers and Hybrids Page 66 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. 4Z L . The total length of the transformer is thus half a wavelength. Solving for l gives l = 59.6 i.e. l = 0.166. The bandwidth is thus 2(90-59.6)/90 = 67.5% For very high frequencies, many sections can be cascaded and the line will have an exponential change of impedance for each of the quarter wavelength sections. This can readily be produced using RF PCB technology. Figure 4.2 shows a plot of the input impedance variation of a transmission line transformer, transforming a 12.5 load into a 50 load. For the one line transformation, the impedance transformation is done in one transmission line section with a characteristic impedance of 25 . The Magenta curve is for a 2-line transformation, with the impedance transformation ratio R = 2 for each line. If the impedance transformation ratio of the two lines in a two line impedance transformer is changed from the R = 2 for each of the lines, such that the total impedance transformation is still a 4:1 impedance transformation, but that each line has a slightly different transformation ratio, then a very good match can be obtained over a specified bandwidth. For this design, the transformation ratio is made a variable constant, which is optimised to provide the minimum deviation from 50 , over the required frequency range. For a two-line matching network, a good match can be obtained over the 800 MHz to 1200 MHz frequency range. The result of this optimisation is shown by the red curve in figure 4.2. The first line has R = Z in /Z d1 = 1.638, where Z d1 is the impedance of line 1, corresponding to a characteristic impedance of 30.53 and the second line has R = Zd2/Zout = 1.222 corresponding to a characteristic impedance of 15.28 , instead of the R = 2 for the un-optimised transmission line transformer. (Note: The numerical results obtained from CADENCE AWR DE project files are normally presented in this book with the default 4 digit display accuracy of AWR DE. Results that are more accurate can be obtained by running the corresponding CADENCE AWR DE project files.) Applying similar principles to a 3-line section gives an even wider bandwidth. The brown curve in figure 4.2 shows the optimisation result of matching 50 to 12.5 , using 3 quarter-wavelength long lines over a 600 MHz to 1400 MHz bandwidth. Instead of all the three transformer ratios being 3 2 = 1.260, the ratios are 1.450, 1.357, 1.087 and this corresponds to transmission line impedances are 34.48 , 18.71 and 13.58 as shown in figure 4.3. Figure 4.3. Optimised transformation ratios for 3 line flat transformer of figure 4.2 Instead of being as close to 50 as possible over the specified frequency range, it is possible to specify optimisation limits to be say >45 and < 55 , and then making the RF Electronics: Design and Simulation 66 www.cadence.com/go/awr

• Cover