RF IMPEDANCE TRANSFORMATION

By

Forest Cummings, W5LQU

And

Dave Russell, W2DMR

(WHAT THE BOOKS NEVER TELL YOU)

Transforming

50 450

Turns ratio = 1 : 3

Impedance ratio = 1 : 9

Transforming with a transformer

DEFINITION OF Q

Q = Rp/XpQ = Xs/Rs

Xp RpXs

Rs

SERIES = PARALLEL

= Rp(jXp) / (Rp + jXp)

ALGEBRA

Rp/Rs =

|

|

Q2 + 1

Rs + jXs

MATCH 250 TO 50

250

50

Q2 + 1 = 250/50 = 5Q2 = 4Q = 2Xp =250/2=-125

RpXp

-125 Rs

Xs-100

Q = 2Xs =50(2)=-100

50

100

150

200

0

-50

-100

-150

-200

50 100 150 200R ohms

XC ohms

XL ohms

THE R-X PLANE

+j

-j

50

100

150

0

-50

-100

-150

50 100 150 200 250R

XC

XL

50+j50

150-j100

ZA

Z=70.7 A=45 deg Tan A=Q=1

SERIES IMPEDANCE

Z

B

Z=180 B= -33.7 TanB=Q=0.67

50

100

150

0

-50

-100

-150

50 100 150 200 250 300XC

XL

PARALLEL IMPEDANCE

R = 250 ohms

//XL

//XC

R

50

100

200

0

-5050 100 150 200 250 300

RXC

XL

-125

= 250 // -j125 (50-j100)

-100

-150

-200

150

SERIES = PARALLEL250 to 50 Match

SERIES = PARALLEL

THE L NETWORK

50

Rs

Xs-100

250

RpXc

-125

XL = 100 XL = 100

Equivalentseries circuit

L network matching250 ohms to 50 ohms

Note: Series XL NOT equal to shunt Xc

5050

MATCH 10 TO 50

Rs10

Rp50

Xp-25

Q2 + 1 = 50/10 = 5Q2 = 4Q = 2Xs =2(10)= -20

Q = 2Xp =50/2= -25

Xs-20

ANOTHER L NETWORK

Rp50

Xp-25

10Rs

Xc = -20

Equivalent parallelcircuit

L network matching10 ohms to 50 ohms

XL25

XL25

NOTE: Shunt XL NOT equal to series Xc

50

THE Tee NETWORK(TWO L NETWORKS)

Q2Q1

XC2-250

XC1-167

RL100

Rin50

R500

Q22+1=500/100=5Q2 = 2XC2 = 500/2= -250XL2 = 100(2) = 200

XL2 = 200

Q12+1=500/50=10Q1 = 3XC1 = 500/3 = -167XL1 = 50(3) = 150

XL1 = 150

THE Tee NETWORK(CONTINUED)

XC-100

RL100

Rin50

XL1 = 150 XL2 = 200

100w, 316vp, 2A

1500w1224vp, 8A

THE PI NETWORKALSO TWO L NETWORKS

RL50

Q1 Q2Rin2000

Rs13.8

Q1 = 12, Q12+1 = 145Rs = 2000/145 = 13.8XC1 = 2000/12 = -167XL1 = 13.8(12) = 166

XL1 = 166

XC1-167

Q22 + 1 = 50/13.8 = 3.62Q2 = SQR(2.62) = 1.6XL2 = 13.8(1.6) = 22XC2 = 50/1.6 = -31

XL2 = 22

XC2 -31

THE PI NETWORK(CONTINUED)

RL50

Q1 Q2Rin2000 Rs

13.8XC1-167

Q22 + 1 = 3.62Q2 = 1.6

XC2-31

XL = 166 + 22 = 188

Q12+1 = 145Q1 = 12

JUST REMEMBER THIS !

Rp/Rs =

Q2 + 1

SIMPLE ANTENNA COUPLER

50

45 FOOTLONG WIRE

500 pF

10 uH

GROUND

TUNES 40M – 10M