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RF IMPEDANCE TRANSFORMATION By Forest Cummings, W5LQU And Dave Russell, W2DMR (WHAT THE BOOKS NEVER TELL YOU)
Transforming Turns ratio = 1 : 3 Impedance ratio = 1 : 9 Transforming with a transformer
DEFINITION OF Q Q = Rp/XpQ = Xs/Rs Xp Rp Xs Rs
SERIES = PARALLEL = Rp(jXp) / (Rp + jXp) ALGEBRA Rp/Rs = | | Q Rs + jXs
MATCH 250 TO Q = 250/50 = 5 Q 2 = 4 Q = 2 Xp =250/2=-125 RpXp -125 Rs Xs -100 Q = 2 Xs =50(2)=-100
R ohms XC ohms XL ohms THE R-X PLANE +j -j
R XC XL 50+j j100 Z A Z=70.7 A=45 deg Tan A=Q=1 SERIES IMPEDANCE Z B Z=180 B= TanB=Q=0.67
XC XL PARALLEL IMPEDANCE R = 250 ohms //XL //XC R
R XC XL -125 = 250 // -j125 (50-j100) SERIES = PARALLEL 250 to 50 Match SERIES = PARALLEL
THE L NETWORK 50 Rs Xs Rp Xc -125 XL = 100 Equivalent series circuit L network matching 250 ohms to 50 ohms Note: Series XL NOT equal to shunt Xc 50
MATCH 10 TO 50 Rs 10 Rp 50 Xp -25 Q = 50/10 = 5 Q 2 = 4 Q = 2 Xs =2(10)= -20 Q = 2 Xp =50/2= -25 Xs -20
ANOTHER L NETWORK Rp 50 Xp Rs Xc = -20 Equivalent parallel circuit L network matching 10 ohms to 50 ohms XL 25 XL 25 NOTE: Shunt XL NOT equal to series Xc 50
THE Tee NETWORK (TWO L NETWORKS) Q2Q1 XC XC RL 100 Rin 50 R 500 Q2 2 +1=500/100=5 Q2 = 2 XC2 = 500/2= -250 XL2 = 100(2) = 200 XL2 = 200 Q1 2 +1=500/50=10 Q1 = 3 XC1 = 500/3 = -167 XL1 = 50(3) = 150 XL1 = 150
THE Tee NETWORK (CONTINUED) XC -100 RL 100 Rin 50 XL1 = 150XL2 = w, 316vp, 2A 1500w 1224vp, 8A
THE PI NETWORK ALSO TWO L NETWORKS RL 50 Q1Q2 Rin 2000 Rs 13.8 Q1 = 12, Q = 145 Rs = 2000/145 = 13.8 XC1 = 2000/12 = -167 XL1 = 13.8(12) = 166 XL1 = 166 XC Q = 50/13.8 = 3.62 Q2 = SQR(2.62) = 1.6 XL2 = 13.8(1.6) = 22 XC2 = 50/1.6 = -31 XL2 = 22 XC2 -31
THE PI NETWORK (CONTINUED) RL 50 Q1 Q2 Rin 2000 Rs 13.8 XC Q = 3.62 Q2 = 1.6 XC2 -31 XL = = 188 Q = 145 Q1 = 12
JUST REMEMBER THIS ! Rp/Rs = Q 2 + 1
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