RF IMPEDANCE TRANSFORMATION

(WHAT THE BOOKS NEVER TELL YOU)

By Forest Cummings, W5LQU And Dave Russell, W2DMR

Transforming Turns ratio = 1 : 3 50 450 Impedance ratio = 1 : 9 Transforming with a transformer

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

SERIES = PARALLEL Rs + jXs = Rp(jXp) / (Rp + jXp) | ALGEBRA |

Rp/Rs = Q

2

+ 1

MATCH 250 TO 50 Xp -125 Rp 250 Q 2 + 1 = 250/50 = 5 Q 2 = 4 Q = 2 Xp =250/2=-125 Xs -100 Rs 50 Q = 2 Xs =50(2)=-100

200 150 100 50 XL ohms 0 XC ohms -50 -100 -150 -200 THE R-X PLANE +j 50 100 150 200 -j R ohms

150 SERIES IMPEDANCE 100 50 XL 0 XC -50 50+j50 Z A B 50 100 Z=70.7 A=45 deg Tan A=Q=1 150 200 250 R Z -100 150-j100 Z=180 B= -33.7 TanB=Q=0.67

-150

150 100 XL 50 0 XC -50 -100 -150 PARALLEL IMPEDANCE //XL 50 100 150 200 250 300 //XC R R = 250 ohms

200 150 100 XL 50 0 XC -50 -100 -125 -150 -200 SERIES = PARALLEL 250 to 50 Match 50 100 150 200 250 300 R (50-j100) SERIES = 250 // -j125 = PARALLEL

THE L NETWORK XL = 100 XL = 100 50 Xs -100 Rs 50 50 Xc -125 Equivalent series circuit Note: Series XL

NOT

L network matching 250 ohms to 50 ohms equal to shunt Xc Rp 250

MATCH 10 TO 50 Xs -20 Rs 10 Q 2 Q 2 + 1 = 50/10 = 5 = 4 Q = 2 Xs =2(10)= -20 Xp -25 Rp 50 Q = 2 Xp =50/2= -25

XL 25 ANOTHER L NETWORK Xc = -20 Xp -25 Rp 50 50 XL 25 Rs 10 Equivalent parallel circuit L network matching 10 ohms to 50 ohms NOTE: Shunt XL

NOT

equal to series Xc

Rin 50 THE Tee NETWORK (TWO L NETWORKS) XL1 = 150 XL2 = 200 Q1 XC1 -167 R 500 XC2 -250 Q2 RL 100 Q1 2 +1=500/50=10 Q1 = 3 XC1 = 500/3 = -167 XL1 = 50(3) = 150 Q2 2 +1=500/100=5 Q2 = 2 XC2 = 500/2= -250 XL2 = 100(2) = 200

Rin 50 THE Tee NETWORK (CONTINUED) XL1 = 150 1500w 1224vp, 8A 100w, 316vp, 2A XL2 = 200 XC -100 RL 100

THE PI NETWORK ALSO TWO L NETWORKS XL1 = 166 XL2 = 22 Rin 2000 Q1 XC1 -167 Q1 = 12, Q1 2 +1 = 145 Rs = 2000/145 = 13.8

XC1 = 2000/12 = -167 XL1 = 13.8(12) = 166 Rs 13.8

Q2 XC2 -31 Q2 2 Q2 = SQR(2.62) = 1.6

XL2 = 13.8(1.6) = 22 XC2 = 50/1.6 = -31 RL 50 + 1 = 50/13.8 = 3.62

THE PI NETWORK (CONTINUED) XL = 166 + 22 = 188 Rin 2000 Q1 XC1 -167 Q1 2 +1 = 145 Q1 = 12 Rs 13.8

Q2 XC2 -31 Q2 2 + 1 = 3.62

Q2 = 1.6

RL 50

JUST REMEMBER THIS !

Rp/Rs = Q

2

+ 1

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