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**RF IMPEDANCE TRANSFORMATION**

(WHAT THE BOOKS NEVER TELL YOU) By Forest Cummings, W5LQU And Dave Russell, W2DMR

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**Transforming Transforming with a transformer Turns ratio = 1 : 3 50**

450 Impedance ratio = 1 : 9 Transforming with a transformer

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DEFINITION OF Q Xs Rp Xp Rs Q = Xs/Rs Q = Rp/Xp

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**Rp/Rs = Q2 + 1 SERIES = PARALLEL Rs + jXs = Rp(jXp) / (Rp + jXp) |**

ALGEBRA | Rp/Rs = Q2 + 1

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**MATCH 250 TO 50 Xs -100 Xp Rp 250 Rs -125 50 Q = 2 Q2 + 1 = 250/50 = 5**

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**THE R-X PLANE 200 150 100 +j 50 XL ohms R ohms 100 150 200 XC ohms 50**

R ohms 100 150 200 XC ohms 50 -50 -j -100 -150 -200

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**SERIES IMPEDANCE 150 100 50+j50 50 Z=70.7 A=45 deg Tan A=Q=1 Z XL A R**

R B 50 100 150 200 250 XC -50 Z 150-j100 -100 Z=180 B= TanB=Q=0.67 -150

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**PARALLEL IMPEDANCE //XL //XC R = 250 ohms 150 100 50 XL R 50 100 150**

R 50 100 150 200 250 300 XC -50 //XC -100 R = 250 ohms -150

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**SERIES = PARALLEL 250 to 50 Match**

200 150 100 50 XL R 50 XC 100 150 200 250 300 -50 -100 -125 -150 (50-j100) = 250 // -j125 SERIES = PARALLEL -200

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**THE L NETWORK XL = 100 XL = 100 Xs -100 Rp 50 50 Xc Rs 250 -125 50**

Equivalent series circuit L network matching 250 ohms to 50 ohms Note: Series XL NOT equal to shunt Xc

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**MATCH 10 TO 50 Xs -20 Xp -25 Rp 50 Rs 10 Q = 2 Xp =50/2= -25**

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**ANOTHER L NETWORK Xc = -20 Xp -25 XL 25 Rp 50 XL 25 Rs 50 10**

L network matching 10 ohms to 50 ohms Equivalent parallel circuit NOTE: Shunt XL NOT equal to series Xc

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**THE Tee NETWORK (TWO L NETWORKS)**

XL1 = 150 XL2 = 200 Q1 Q2 Rin 50 R 500 XC1 -167 XC2 -250 RL 100 Q12+1=500/50=10 Q1 = 3 XC1 = 500/3 = -167 XL1 = 50(3) = 150 Q22+1=500/100=5 Q2 = 2 XC2 = 500/2= -250 XL2 = 100(2) = 200

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**THE Tee NETWORK (CONTINUED)**

1224vp, 8A XL1 = 150 XL2 = 200 100w, 316vp, 2A Rin 50 XC -100 RL 100

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**THE PI NETWORK ALSO TWO L NETWORKS**

XL1 = 166 XL2 = 22 Q1 Q2 Rin 2000 Rs 13.8 RL 50 XC2 -31 XC1 -167 Q1 = 12, Q12+1 = 145 Rs = 2000/145 = 13.8 XC1 = 2000/12 = -167 XL1 = 13.8(12) = 166 Q = 50/13.8 = 3.62 Q2 = SQR(2.62) = 1.6 XL2 = 13.8(1.6) = 22 XC2 = 50/1.6 = -31

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**THE PI NETWORK (CONTINUED)**

XL = = 188 Q2 Q1 Rin 2000 RL 50 Rs 13.8 XC2 -31 XC1 -167 Q12+1 = 145 Q1 = 12 Q = 3.62 Q2 = 1.6

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JUST REMEMBER THIS ! Rp/Rs = Q2 + 1

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**SIMPLE ANTENNA COUPLER**

TUNES 40M – 10M 45 FOOT LONG WIRE 10 uH 50 500 pF GROUND

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