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XL1 + XL2 = XL NEW LOAD XL1 XC1 "R" XL2 XC2 CSTRAY2 75 RL
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SOURCE RS 50 CSTRAY1
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FIGURE 346 PI network before combining calculated components
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This is so XC1 and XC(STRAY1), in parallel, will still equal the computed value of XC1 (XC(TOTAL)) 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 in Fig 347 T networks are required when two low impedances need to be matched with a high loaded Q, and must be of a higher Q than that available with the L network type Follow this procedure to match two unequal and pure resistances, as shown in the example of Fig 348 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 = RS(MALL) (Q2 + 1); R = 12(152 + 1); R = 2712 RS(MALL) is the smaller value of the two resistances, whether it is RS or RL
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SOURCE RS 50 CSTRAY1 XCNEW1 C = X pf XLNEW L = X nh XCNEW2 C = X pf CSTRAY2 75 RL LOAD
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FIGURE 347 PI matching network after combining components
Three
RS 12 15 GHz XS1 180 XP1 181 "R" 2712 XP2 401 XS2 392 58 RL (RP)
FIGURE 348 Designing a T network for use between a resistive source and load
RS 12 15 GHz 180 XL1 XTOTAL 392 XL2 58 RL
FIGURE 349 Values for a completed T network
3 Find XS1 = Q RS = 15 12 = 180 4 Find XP1 = R /Q = 2712/15 = 181 5 Find Q2 = 6 Find X P2 = 7 Find X S2 = Q2 RL = 676 58 = 392 8 XP1 and XP2 are combined by: X TOTAL = X P1 X P 2 181 401 = = 125 X P 1 + X P 2 181 + 401 " R " 2712 = = 401 676 Q2 "R" 1 = RL 2712 1 = 676 58
9 The circuit is shown completed in Fig 349 Other possible circuit configurations can be used as required (Fig 350) Figure 350a, b, and c are combined as in step 8 above, but the signs must be maintained for b and c due to the opposite reactance employed ( + for inductors and for capacitors)
Wideband Matching
Sometimes it may be necessary to design a low-loaded Q, and thus a very wideband, matching network This can be done as follows, using Fig 351a for a pure resistive load
Amplifier Design
180 SOURCE 392 LOAD SOURCE 180 392 LOAD
181
401
125
180 SOURCE 181 401 392 LOAD SOURCE LOAD
180 SOURCE 181
392 LOAD 401 SOURCE
180
392 LOAD
330
FIGURE 350
The T network and its various legal con gurations before and after combination
1896 XS1 XP1 229 "R" XP2 397 328 XS2 15 RL (Rp)
RS 50 15 GHz
a RS 15 15 GHz 33 XS1 XP1 395 19 XS2 XP 2 227 50 RL (Rp)
FIGURE 351 Two different con gurations for a wideband matching network: (a) high to low; (b) low to high
Three
that is smaller than the pure resistive source; or by employing Fig 351b 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 " = RS RL = 87 2 Solve for loaded Q: Q= 3 Complete for Fig 351a above: XP2 = "R" Q2 RS Q1 Q2 = "R" 1 = 397 RL RS 1 = 229 "R" (Q2 = 219) and X S2 = Q2 RL = 328 "R" 1 = 22 RSMALLER
X P1 =
Q1 =
(Q1 = 218) and
X S1 = Q1 " R " = 1896
4 Or complete for Fig 351b above: XP2 = RP = 227 Q "R" = 395 Q and X S2 = Q " R " = 19
X P1 =
X S1 = Q RS = 33
It is possible to match for increasingly wider bandwidths by adding sections as shown in Fig 352: 1 Maximum bandwidth is always achieved if the ratios of each of the two ensuing resistances are equal, or: R " R "1 " R "2 " R "3 = = = etc = LARGER RSMALLER " R "1 " R "2 " Rn"
XS1 XP1 "R1"
XS2 XP2 "R2"
XS3 XP 3 RL (Rp)
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