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RF Electronics Chapter 9: Impedance Matching of Power Amplifiers Page 319 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. For a transmission-line of characteristic impedance Z 0 and length L, shown in figure 9.23, the impedance looking into a transmission-line that is terminated in a load Z L is: ) tan( ) tan( 0 0 0 l jZ Z l jZ Z Z Z L L s Eqn. 9.20 By substituting Z S =R S +jX S and Z L =R L +jX L and then solving for Z 0 and the transmission- line length =l as an electrical length, one obtains the following equations: s L s L L s R R Z R Z R Z 2 2 0 Eqn. 9.21 s L L s L s X R X R R R Z Arc ) ( tan 0 Eqn. 9.22 This assumes that Z 0 is real and tan(l) is real. These equations do not always give a match, but if no match is possible, shifting the impedance by using a short length of transmission-line will always result in a match. Equations 9.20 to 9.22 are included in the AWR DE project file for the transmission-line matching network. For matching a 10.7 - j1.2 impedance, being the same impedance match as is used in figures 9.8 to 9.20, these equations give Z 0 = 23.09 Ω and = 93.78 degrees and this can be included in the AWR DE circuit diagram as the variables shown in figure 9.23. Figure 9.24, shows the frequency range of the resulting impedance match. It can be seen that transmission-line matching gives a broadband impedance match. The only limitations are that firstly, it is difficult to tune the matching impedances to allow for device variations and secondly the line lengths can physically become too large. This is why this technique is predominantly used above 100 MHz. Transmission-lines can replace the inductors used in the LC matching. This will then allow for some tuning of the matching network by changing the values and locations of capacitors. The replacement of the inductors used in Lowpass T matching networks of figure 9.11, with transmission-lines is often done in commercial applications above 100 MHz. Figure 9.23. Values for the transmission-line matching network. RF Electronics: Design and Simulation 319 www.cadence.com/go/awr