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Figure 336 Various legitimate pi networks before and after combining components
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Figure 337 A pi network used in a resistive and reactive source and load
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Figure 338 Pi network before combining calculated components
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Thus, if XCSTRAY XC1, then XCTOTAL will not be able to reach the proper XC value Also, increase XC1 until: XC1 XCSTRAY1 XC1 XCSTRAY1 XCTOTAL XC1 or XC1 XCSTRAY1 XC1 XCSTRAY1 XCNEW
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This is so XC1 and XCSTRAY1, in parallel, will still equal the computed value of XC1 (XCTOTAL) 7 Convert the reactances calculated to L and C values by: L X 2 f and C 1 2 fX
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The completed network is as shown as Fig 339 T networks are required when two low impedances need to be matched with a high Q, and must be of a higher Q than that available with the L network type
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Amplifier Design
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Figure 339 Pi matching network after combining components
Follow this procedure to match two unequal and pure resistances, as shown in the example of Fig 340 1 Decide on the loaded Q (in this case 15), and the frequency (in this case 15 GHz) 2 Find the R value by R RSMALL (Q2 1); R 12 (152 1); R 2712 ohms RSMALL is the smaller value of the two resistances, whether it is RS or RL 3 Find XS1 4 Find XP1 5 Find: "R" RL 2712 58 QRS R /Q 15 12 2712/15 180 ohms 181 ohms
Q2 6 Find: XP2 7 Find: XS2
"R" Q2
2712 676
401 ohms
Q2RL
676 58
392 ohms
8 XP1 and XP2 are combined by: XP1XP2 XP1 XP2 181 401 181 401
XTOTAL
125 ohms
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Amplifier Design
Amplifier Design
Figure 340 Designing a T network for use between a resistive source and load
9 The circuit is shown completed in Fig 341 Other possible circuit configurations can be used as required (Fig 342) Figure 342a, b, and c are combined as in step 8 above, but the signs must be maintained for b and c because of the opposite reactance employed ( for inductors and for capacitors)
Wideband matching Sometimes it may be necessary to design a low-Q, very
wideband matching network This can be done as follows, by using Fig 343a for a pure resistive load that is smaller than the pure resistive source or by employing Fig 343b for a pure resistive load that is larger than the pure resistive source XS1 and XP1 can be considered as a separate L network from XS2 and XP2, so each L may be oriented any way that is convenient For instance, XS1 may be an inductor, so XP1 must then be a capacitor; however, XS2 may be the capacitor, with XP2 being the inductor: 1 Solve for R : "R" 2 Solve for loaded Q: Q 3 Complete for Fig 343a: XP2 "R" |Q2 Q2 "R" RL 1 397 ohms (Q2 219) XS2 XP1 RS |Q1 Q1 RS "R" 1 229 ohms (Q1 XS1 Q2RL and 328 ohms and 1896 ohms "R" RSMALLER 1 22 RS RL 87 ohms
218) Q1"R"
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Amplifier Design
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Figure 341 Values for a completed T network
4 Or complete for Fig 343b: XP2 XP1 RP Q "R" Q 227 ohms 395 ohms and and XS2 XS1 Q"R" QRS 19 ohms 33 ohms
It is possible to match for increasingly wider bandwidths by adding sections as shown in Fig 344: 1 Maximum bandwidth is always achieved if the ratios of each of the two ensuing resistances are equal, or: "R"1 RSMALLER "R"2 "R"1 "R"3 "R"2 R LARGER "R"n RS, or adopt the Fig 343a RS
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