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RF Electronics Chapter 9: Impedance Matching of Power Amplifiers Page 322 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. Figure 9.28. Starting broadband match S 11 and S 22 on a Smith Chart. Figures 9.27 and 9.28 show the frequency response and return loss of the initial design, obtained from the equations in figure 9.25. It can be seen that simply using 3 Pi matching sections is a good starting point for the design. Figure 28 shows S 11 plotted on a Smith Chart. It can be seen that a good match is obtained over a wide frequency range. The impedance match for the initial matching network of figure 9.25 does not meet the required S 11 < -20 dB over the 250 MHz to 500 MHz bandwidth as shown in figure 9.27. The -20 dB limit can be obtained by optimising the network. There are different ways of optimising this circuit. Firstly, the individual elements can be optimised, by simply replacing the variables for the component values figure 9.26 with the calculated values that can be optimised. The calculated component values in figure 9.25 are used as the starting values for the element values in figure 9.26. Alternately one can keep using the equations in figure 9.25, in the Global Definitions of the AWRDE project, but allow the Q values, centre frequencies and impedance transformation ratios (KR) for each of the three matching sections to be optimised. Q1 has a minimum value of 0.5972, a lower value will result in a negative Cp11. For a broadband match, low Q values are required As a result Qmin is used for Q1, resulting in Cp11 = 0, and requiring some minor changes to the equations used in the Global Definitions, as can be seen by comparing figure 9.25 and 9.29. The initial values for Q2 and Q3 are the design value Q = 0.6 used in figure 9.27 and the initial values for Wm1, Wm2 and Wm3 are the design value Wm = 2353e6 = 2.218 x 10 9 . As part of the optimisation, the normalised impedance transformation ratios for the first two sections are optimised (KR1 and KR2) and the transformation ratio for the third section is calculated to obtain the total transformation ratio required for the input match. The Q, Wm and KR optimisation results in the final values shown in figure 9.30. The optimisation limits for Q and KR need to be set carefully otherwise simulation errors with inductors or capacitors with imaginary values result. There is no unique optimum match for the network of figure 9.30 and neither of the element or the Q, Wm and Impedance RF Electronics: Design and Simulation 322 www.cadence.com/go/awr

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