Mysteries of the Smith Chart - FARS · Mysteries of the Smith Chart Transmission Lines, Impedance...

VG – 1PSA-00527 — 10/21/2001

Pacificon 2001

Mysteries of the Smith Chart

Transmission Lines, Impedance Matching,and Little Known Facts

Stephen D. Stearns, K6OIK

Chief Technologist

TRW Firestorm Wireless Communication Products

[email protected]

VG – 2PSA-00527—10/21/2001

Pacificon 2001

Outline

Transmission Line Theory Historical development Heaviside’s rewrite of Maxwell’s theory, Telegrapher’s equations,

Impedance, reflection coefficient, SWR, phase constant, and velocityfactor

Special facts for λ/2, λ/4, and λ/8 lossless lines

The Smith Chart Bilinear complex functions

Impedance and admittance coordinates (circles, circles, and morecircles)

Impedance Matching Why match? Impedance matching vs. conjugate impedance

matching Single frequency matching Multiple-frequency and broadband matching

VG – 3PSA-00527 — 10/21/2001

Pacificon 2001

Part 1: Transmission Line Theory

VG – 4PSA-00527—10/21/2001

Pacificon 2001

Key Dates in Electrical Transmission

1830s Magnetic telegraphs - Gauss, Henry

1839 Electromagnetic telegraph - Wheatstone & Cook

1844 Telegraph in America - Morse

1850s Thousands of miles of telegraph line U.S. and Europe

1851 40-mile cable under English Channel

1855 Distributed analysis of transmission line - Lord Kelvin

1858 Transatlantic cable, project delayed by civil war

1873 Theory of electrodynamics - Maxwell

1876 Invention of telephone - Bell

1880s Vectors, vector calculus, reformulation of Maxwell’stheory, transmission line theory - Heaviside

1886 Experimental confirmation of Maxwell’s Theory - Hertz

1937 Early Smith Chart, published 1939 and 1944 - Smith

VG – 5PSA-00527—10/21/2001

Pacificon 2001

Numbers to Remember!

1.4142135623...

1.7320508075…

1.6180339887...

3.1415926535...

2.718281828459045…

2.54

299,792,458

376.7303134...

VG – 6PSA-00527—10/21/2001

Pacificon 2001

Heaviside’s Vector Formulation of Maxwell’s Theory

∇ × = −

∇ × = +

∇ ⋅ =∇ ⋅ =

==

EBt

H JDt

D

B 0

D E

B H

∂∂

∂∂

ρ

εµ

“And God said, Let there be light; and there was light.” Genesis 1:3

VG – 7PSA-00527—10/21/2001

Pacificon 2001

Frequency Domain or Phasor Form

∇ × = −∇ × = +

∇ ⋅ =∇ ⋅ =

E H

H E

E 0

H 0

j

j

ωµσ ωε( )

VG – 8PSA-00527—10/21/2001

Pacificon 2001

Heaviside’s Telegrapher’s Equations

I(x)

V(x)

dV

dxR j L I x

dI

dxG j C V x

= − +

= − +

( ) ( )

( ) ( )

ω

ω

Uniform transmission line Equivalent circuit of infinitesimal segment

R∆x L∆x

G∆x C∆x

VG – 9PSA-00527—10/21/2001

Pacificon 2001

Transmission Line SolutionTEM Waves

V x e

I xV x

Z

x

o

( ) = Voγ

( )( )=

γ α β ω ω= + = + +j R j L G j C( )( )

ZR j L

G j Co = ++

ωω

Traveling wave

Propagation constant

Characteristic impedance

VG – 10PSA-00527—10/21/2001

Pacificon 2001

NotationsReal Parameters

R = Series resistance per unit length (Ohms/meter)

L = Series inductance per unit length (Henries/meter)

G = Shunt conductance per unit length (Siemens/meter)

C = Shunt capacitance per unit length (Farads/meter)

α = Attenuation constant (nepers/meter)

β = Phase constant (radians/meter)

λ = Wavelength (meters)

vf = Velocity factor (dimensionless)

X = Reactance (Ohms)

B = Susceptance (Siemens)

s = Standing wave radio (dimensionless)

VG – 11PSA-00527—10/21/2001

Pacificon 2001

Notations (Cont’d)Complex Parameters

Z = R + jX = impedance (Ohms)

ZL = Load impedance (Ohms)

Zi = Input impedance (Ohms)

Z0 = Characteristic impedance (Ohms)

z = Z/Z0 = r + jx = normalized impedance (dimensionless)

Y = G + jB = admittance (Siemens)

y = Y/Y0 = g + jb = normalized admittance (dimensionless)

Γ = Γr + j Γi = complex reflection coefficient (dimensionless)

γ = α + jβ = propagation constant (inverse meters)

VG – 12PSA-00527—10/21/2001

Pacificon 2001

Transmission Line ParametersPhysical Dimensions and Material Properties

a a

d

dielectric(µ, ε, σ)

Parameter Coax Twinlead

R Ω/m

L H/m

G S/m

C F/m

Where skin depth is For copper

1

2

1 1

πδσ c a b+

1

π δσa c

µπ

δ2 2

1 1ln

b

a a b+ +

µπ

δ2 2

1

a

d

a+

−cosh

2πσ

lnb

a

πσ

cosh −1

2

d

a

πε

cosh−1

2

d

a

2πε

lnb

a

δπ µσ

= 1

f c

σ

δµ

c = ×

=

5 8 10

8 5

7.

.

S/m

mm at 60 Hz

6.6 m at 100 MHz

a

b

c

dielectric(µ, ε, σ)

VG – 13PSA-00527—10/21/2001

Pacificon 2001

Round Open-Wire Transmission Line Formulas

Approximate formula Widely published by ARRL and others Accurate only for large spacings: s/d > 3

or large impedances: Z0 > several hundred

Exact formula Accurate for all spacings and impedances

s

d

VG – 14PSA-00527—10/21/2001

Pacificon 2001

Comparison of Impedance FormulasRound Open-Wire Line

VG – 15PSA-00527—10/21/2001

Pacificon 2001

K6OIK Square Open-Wire Transmission Line Formula

Excellent approximation in the range of practical interest Accurate for small spacings: 1 < s/w < 3

or small impedances: 0 < Z0 < several hundred

s

w

VG – 16PSA-00527—10/21/2001

Pacificon 2001

Round vs Square Open-Wire Lines

VG – 17PSA-00527—10/21/2001

Pacificon 2001

Optimal Characteristic ImpedancesCoax

For minimum loss Zo = 77Ω

For maximum breakdown voltage Zo = 30Ω

For minimum temperature rise Zo = 60Ω

Zo = 50Ω has no special significance

VG – 18PSA-00527—10/21/2001

Pacificon 2001

ΖOΖLΓL

TerminalPlane

Reflection Coefficient and Impedance Relationat a Terminal Plane

For every terminal plane, the complex load impedance andcomplex reflection coefficient seen to the right give the sameinformation for that terminal plane

Question: How do Γ and z change as the terminal planemoves?

Definition

Inverse

Γ =−+

= −+

Z Z

Z Z

z

zL o

L o

1

1

z = +−

1

1

ΓΓ

VG – 19PSA-00527—10/21/2001

Pacificon 2001

Relations Between Two Terminal Planes

ΖOΖLΓL

OutputTerminal

Plane

InputTerminal

Plane

ΖiΓ i

Impedance relation

zz j l

jz liL

L

=+

+tan

tan

ββ1

Reflection coefficient relation

Γ Γi Lj le= − 2β

Cross relations

ze

e

ze

e

iL

j l

Lj l

Li

j l

ij l

=+−

=+−

−

−

1

1

1

1

2

2

2

2

ΓΓ

ΓΓ

β

β

β

β

VG – 20PSA-00527—10/21/2001

Pacificon 2001

Velocity Factor

λ

λ

free space

actual

c

f

v

f

=

=

Velocity factor

vv

cfactual

free space

= =λ

λ

Wavelength

VG – 21PSA-00527—10/21/2001

Pacificon 2001

How To Measure Velocity Factor of a Line(One Way To Do It)

vfl

c Z

Z

fopen

short

=−−

2 1

1

π

cot

AntennaAnalyzer

AntennaAnalyzer

Known length

Same length

opencircuit

shortcircuit

VG – 22PSA-00527—10/21/2001

Pacificon 2001

Phase Constant

Phase constant β and velocity factor vf give equivalentinformation

Both can be calculated from line dimensions and materialproperties

Best to measure!

β πλ

π= =2 2

actual f

f

v c radians/meter

β ω ω= + +Im ( )( )R j L G j C

VG – 23PSA-00527—10/21/2001

Pacificon 2001

Geometric mean of two complex numbers

Calculation is trivial in polar form on Smith Chart

How to Measure Complex Zo of A Line(One Way to Do It)

AntennaAnalyzer

AntennaAnalyzer

Unknown orarbitrary length

Same length

opencircuit

shortcircuit

Z Z Zo open short= ×

VG – 24PSA-00527—10/21/2001

Pacificon 2001

What Special Lengths of Lossless Line Do

Z Zi L=

ZZ

Zio

L

=2

Z Z Z Zi o L o= if and are real (resistive)

Half wavelength, l = _/2

Quarter wavelength, l = _/4

Eighth wavelength, l = _/8

VG – 25PSA-00527—10/21/2001

Pacificon 2001

Standing Wave Ratio

s

s

s

=+−

= −+

1

1

1

1

ΓΓ

Γ

z

z

z

= +−

= −+

1

1

1

1

ΓΓ

Γ

Easy to remember from

VG – 26PSA-00527 — 10/21/2001

Pacificon 2001

Part 2: The Smith Chart

VG – 27PSA-00527 — 10/21/2001

Pacificon 2001

0.10.1

0.1

0.20.2

0.2

0.30.3

0.3

0.40.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.03.0

3.0

4.04.0

4.0

5.05.0

5.0

1010

10

2020

20

5050

50

0.20.2

0.20.2

0.40.4

0.40.4

0.60.6

0.60.6

0.80.8

0.80.8

1.01.0

1.01.0

20-20

30-30

40-40

50-50

60-60

70-70

80-80

90-90

100-100

110-110

120-120

130-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40-40

35-35

30-30

25-25

20-20

15-15

10-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.080.09

0.090.1

0.10.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.320.32

0.330.33

0.340.34

0.350.35

0.360.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.430.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFL

EC

TIO

N C

OE

FFICIEN

T IN

DEG

REES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O

R CAPACITIVE SUSCEPTANCE (+jB/Yo)

CAPACITIVE REACTANCE COMPONENT (-jX

/Zo), O

R IND

UCTI

VE

SUSC

EPTA

NC

E (-

jB/Y

o)

RESISTANCE COMPONENT (R/Zo), OR CONDUCTANCE COMPONENT (G/Yo)

VG – 28PSA-00527—10/21/2001

Pacificon 2001

Complex Functions

Basic types of complex functions Global Properties

– Linear – lines map to lines

– Bilinear – circles map to circles Local Properties

– Conformal – right angles map to right angles

z = x + jy

Complex Number

zi

(x, y)

x

y

wi

(u, v)

u

v

wr

w = u + jv

Complex Number

f( )zr

VG – 29PSA-00527—10/21/2001

Pacificon 2001

Mathematical Basis of the Smith Chart

Γ = −+

z

z

u jvr jx

r jx

1

1

1

1+ =

( - ) +

( + ) +

A bilinear conformal complex function

Right HalfZ Plane

r

x

Interior Unit CircleΓ Plane

v

u

VG – 30PSA-00527—10/21/2001

Pacificon 2001

Smith Chart: Impedance Coordinates

r S

erie

s R

esis

tanc

e

Γr

Γi

∞0

x=1

r=0

x=-1

x=0r=1

r=2

x Series Reactance

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.160.17

0.170.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE

OF

TRA

NSM

ISSION

CO

EFFIC

IENT

IND

EGR

EES

AN

GLE

OF

REFLE

CT

ION

CO

EFFIC

IENT

IND

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

DG

ENER

ATO

R—

><—

WA

VEL

ENG

THS

TOW

AR

DLO

AD

<—

IND

UC

TIV

ER

EAC

TAN

CE

COM

PON

ENT

(+jX

/Zo), OR

CAPACITIVE SUSCEPTANCE (+jB/Yo)

CAPACITIVEREACTANCECOMPONENT(-jX/Zo)

,OR

IND

UCTI

VE

SUSC

EPTA

NC

E(-

jB/Y

o)


InductiveReactance(Positive)

CapacitiveReactance(Negative)

x=0

x=1r=1

r=2

x=-1

r=0

VG – 31PSA-00527—10/21/2001

Pacificon 2001

Smith Chart: Admittance Coordinates

Shu

nt C

ondu

ctan

ce

Γr

Γi

∞ 0

b=1

g=0

b=-1

b=0g=1

g=2

Shunt Susceptance

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.60.6

0.6

0.70.7

0.7

0.80.8

0.80.9

0.9

0.9

1.01.0

1.0

1.21.2

1.2

1.41.4

1.4

1.61.6

1.6

1.81.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-2

0

30-3

0

40-4

0

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120130

-130

140-140

150-150

160-160

170-170

180±

90-90

85-85

80-80

75-75

70-70

65-65

60-60

55-55

50-50

45-45

40

-40

35

-35

30

-3025

-2520

-2015

-1510

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.19

0.19

0.2

0.2

0.21

0.21

0.22

0.22

0.23

0.23

0.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.410.42

0.420.43

0.43

0.440.44

0.450.45

0.460.46

0.47

0.470.48

0.480.49

0.49

0.0

0.0

AN

GLE

OF

TRA

NSM

ISSI

ON

CO

EFF

ICIE

NT

IND

EGR

EES

AN

GLE

OF

REF

LEC

TIO

NC

OE

FFIC

IEN

TIN

DEG

REE

S

—>

WA

VELEN

GTH

STO

WA

RD

GEN

ERA

TOR

—>

<—W

AV

ELENG

THS

TOW

AR

DLO

AD

<—

IND

UC

TIVE

REA

CTA

NC

ECO

MPO

NEN

T(+jX/Zo),OR

CAPACITIVESUSCEPTANCE(+jB/Yo)

CAPACITIVE REACTANCE COMPONENT (-jX/Zo), ORIN

DU

CTIVE

SUSC

EPTAN

CE

(-jB/Yo)


b

gb=0

b=1

g=1

g=2

b=-1

g=0

InductiveSusceptance

(Negative)

CapacitiveSusceptance

(Positive)

VG – 32PSA-00527—10/21/2001

Pacificon 2001

Smith Chart: Constant SWR Circles

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-100.

04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE

OF

TRA

NSM

ISSION

CO

EFFIC

IENT

IND

EGR

EES

AN

GLE

OF

REFLE

CT

ION

CO

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IENT

IND

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—>

WA

VEL

ENG

THS

TOW

AR

DG

ENER

ATO

R—

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WA

VEL

ENG

THS

TOW

AR

DLO

AD

<—

IND

UC

TIV

ER

EAC

TAN

CE

COM

PON

ENT

(+jX

/Zo), OR



,OR

IND

UCTI

VE

SUSC

EPTA

NC

E(-

jB/Y

o)

RESISTANCE COMPONENT (R/Zo), OR CONDUCTANCE COMPONENT (G/Yo) 2 3 41.5Γr

Γ i

VG – 33PSA-00527—10/21/2001

Pacificon 2001

Smith Chart: Constant Impedance Magnitude Circles

Γr

Γ i

x

r0.5

12

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.160.17

0.170.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE

OF

TRA

NSM

ISSION

CO

EFFIC

IENT

IND

EGR

EES

AN

GLE

OF

REFLEC

TIO

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DEG

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ENG

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AR

DG

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UC

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TAN

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PON

ENT

(+jX

/Zo), OR



,OR

IND

UCTI

VE

SUSC

EPTA

NC

E(-

jB/Y

o)


0.5 2

1

VG – 34PSA-00527—10/21/2001

Pacificon 2001

Smith Chart: Constant Impedance Phase Angle Circles

Γr

Γ i

x

90°

45°

0°

315°

270°22

5°

180°

135° 0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.40.

4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE

OF

TRA

NSM

ISSION

CO

EFFIC

IENT

IND

EGR

EES

AN

GLE

OF

REFLEC

TIO

NC

OE

FFICIEN

TIN

DEG

REES

—>

WA

VEL

ENG

THS

TOW

AR

DG

ENER

ATO

R—

><—

WA

VEL

ENG

THS

TOW

AR

DLO

AD

<—

IND

UC

TIV

ER

EAC

TAN

CE

COM

PON

ENT

(+jX

/Zo), OR



,OR

IND

UCTI

VE

SUSC

EPTA

NC

E(-

jB/Y

o)


0°

45°

315°

VG – 35PSA-00527—10/21/2001

Pacificon 2001

Smith Chart: Multiplication, Division, Squares, andSquare Roots

Unary Operatorssquares a2

square rootstangents tan θcotangents cot θinverse tangents tan-1 aInverse cotangents cot-1 a

Binary Operatorsmultiplication X a • bdivision ÷ c/a

geometric mean

a

ab

VG – 36PSA-00527—10/21/2001

Pacificon 2001

Smith Chart: A Nomogram for Math Calculations

Γr

Γi

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-100.

04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE

OF

TRA

NSM

ISSION

CO

EFFIC

IENT

IND

EGR

EES

AN

GLE

OF

REFLEC

TIO

NC

OE

FFICIEN

TIN

DEG

REES

—>

WA

VEL

ENG

THS

TOW

AR

DG

ENER

ATO

R—

><—

WA

VEL

ENG

THS

TOW

AR

DLO

AD

<—

IND

UC

TIV

ER

EAC

TAN

CE

COM

PON

ENT

(+jX

/Zo), OR



,OR

IND

UCTI

VE

SUSC

EPTA

NC

E(-

jB/Y

o)


√c=1.414

a=4

c=2

b=0.5

-√2

VG – 37PSA-00527 — 10/21/2001

Pacificon 2001

Part 3: Impedance Matching

VG – 38PSA-00527—10/21/2001

Pacificon 2001

Impedance Matching Categories

Single frequency matching Manual synthesis using Smith Chart Eight canonical networks

Lumped elements Series and parallel stubs Transmission line sections

Multiple frequency matching Ladder networks Multiple stubs Multiple line sections

Broadband matching Maximize SWR bandwidth

Software for computer-aided manual design Software for network optimization Smith Chart used for visualization only

VG – 39PSA-00527—10/21/2001

Pacificon 2001

Bandwidth Classifications

Narrowband < 10%

Moderate band 10% to 50%

Broadband > 50%

Fractional Bandwidth

VG – 40PSA-00527—10/21/2001

Pacificon 2001

Two Kinds of Matching

Conjugate Matching

Best use at source(transmitter)

Maximizes power delivery tothe load

Does not minimize reflectionsunless Zs is real

Normally done by thetransmitter manufacturer at thecircuit design level

Ideally Zs (ext) = 50 Ω

Load Matching

Best used at ends of transmissionlines

Minimizes reflections

Does not maximize deliveredpower unless Z0 is real

ΖS

∼+

-

ΖLΖO ΖL

Zs = ZL* ZL = ZO

VG – 41PSA-00527—10/21/2001

Pacificon 2001

Where Should Matching Network Go?

Poor Setup

Good Setup

Best Setup

Tx

High toLow SWR

AntennaTuner

High SWR

Long Transmission Line

Tx MatchingNetwork

Low SWR Low SWR

Tx AntennaTuner

MatchingNetwork

Perfect 1:1 Low SWR

Very Low-Loss Line

Low SWR

Insertion Loss x dB

VG – 42PSA-00527—10/21/2001

Pacificon 2001

Necessary Test Equipment

Antenna analyzer Autek CIA MFJ

Noise bridge (less accurate)

Network analyzer (more accurate) Hewlett-Packard

VG – 43PSA-00527—10/21/2001

Pacificon 2001

Matching Network Design Recipe

1. Measure transmission line parameters Zo, vf

2. Measure antenna feedpoint impedance across band(s) of interest

3. Measure or calculate impedance across band(s) of interest at networkinsertion point

4. Narrowband match: Select appropriate lossless L network, 2 or 4 choices Select lumped elements vs stubs Calculate component values Calculate SWR and SWR bandwidth Build and test

5. Broadband match: Use design software - winSMITH or equivalent Design n-stage lossless ladder network Select lumped elements vs stubs Calculate component values Calculate SWR and SWR bandwidth

VG – 44PSA-00527—10/21/2001

Pacificon 2001

How to Measure Antenna Feedpoint Impedance

Measure impedance through known line

Divide measure impedance by Zo

Plot impedance point on Smith Chart

Move counter clockwise on chart by electrical length of line

Read coordinate values from chart

Multiply result by Zo

VG – 45PSA-00527—10/21/2001

Pacificon 2001

Smith Chart: Effect of Adding Series Reactances orShunt Susceptances

Γ

Γi

r

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLEC

TIO

N C

OE

FFICIEN

T IN

DEG

REES

> W

AV

ELEN

GTH

S TO

WA

RD

GEN

ERA

TOR

>

< W

AV

ELEN

GTH

S TO

WA

RD

LO

AD

<

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O


CAPACITIVE REACTANCE COMPONENT (-

jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


+b

+x

-b

-x

VG – 46PSA-00527 — 10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110120

-120130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-3530

-3025

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.380.39

0.390.4

0.40.41

0.410.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFL

EC

TIO

N C

OE

FFICIE

NT

IN D

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


Z

(a)

0 Z

Forbidden Area

VG – 47PSA-00527 — 10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110120

-120130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-3530

-3025

-2520

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.390.4

0.40.41

0.410.42

0.420.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFL

EC

TIO

N C

OE

FFICIE

NT

IN D

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


Forbidden Area

Z

(b)

0 Z

VG – 48PSA-00527 — 10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110120

-120130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-3530

-3025

-2520

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.390.4

0.40.41

0.410.42

0.420.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLE

CT

ION

CO

EFFIC

IENT

IN D

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


Forbidden Area

Z

(c)

0 Z

VG – 49PSA-00527 — 10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110120

-120130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-3530

-3025

-2520

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.390.4

0.40.41

0.410.42

0.420.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLE

CT

ION

CO

EFFIC

IENT

IN D

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


Forbidden Area

(d)

Z 0 Z

VG – 50PSA-00527 — 10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110120

-120130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-3530

-3025

-2520

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.390.4

0.40.41

0.410.42

0.420.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLE

CT

ION

CO

EFFIC

IENT

IN D

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


Forbidden Area

(e)

Z 0 Z

VG – 51PSA-00527 — 10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110120

-120130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-3530

-3025

-2520

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.390.4

0.40.41

0.410.42

0.420.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLE

CT

ION

CO

EFFIC

IENT

IN D

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


Forbidden Area

(f)

Z 0 Z

VG – 52PSA-00527 — 10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110120

-120130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-3530

-3025

-2520

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.390.4

0.40.41

0.410.42

0.420.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLE

CT

ION

CO

EFFIC

IENT

IN D

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


Forbidden Area

Z 0 Z

(g)

VG – 53PSA-00527 — 10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110120

-120130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-3530

-3025

-2520

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.390.4

0.40.41

0.410.42

0.420.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLE

CT

ION

CO

EFFIC

IENT

IN D

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

D G

ENER

ATO

R —

><—

WA

VEL

ENG

THS

TOW

AR

D L

OA

D <

—

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


Forbidden Area

Z 0 Z

(h)

VG – 54PSA-00527—10/21/2001

Pacificon 2001

Matching: Four L-Networks Using Lumped Elements

Γ

Γi

r

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLE

CT

ION

CO

EFFIC

IEN

T IN

DEG

REES

> W

AV

ELEN

GTH

S TO

WA

RD

GEN

ERA

TOR

>

< W

AV

ELEN

GTH

S TO

WA

RD

LO

AD

<

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


ZL

ZL

ZL

ZL

Start

Finish

VG – 55PSA-00527—10/21/2001

Pacificon 2001

Matching: Four L-Networks Using Stubs

Γ

Γi

r0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE O

F TRA

NSM

ISSION

CO

EFFIC

IENT IN

DEG

REES

AN

GLE O

F REFLE

CT

ION

CO

EFFIC

IENT

IN D

EGR

EES

> W

AV

ELEN

GTH

S TO

WA

RD

GEN

ERA

TOR

>

< W

AV

ELEN

GTH

S TO

WA

RD

LO

AD

<

IND

UC

TIV

E R

EAC

TAN

CE

COM

PON

ENT (+

jX/Zo), O



jX/Zo)

, OR IN

DU

CTIV

E SU

SCEP

TAN

CE

(-jB

/Yo)


ZL

ZL

ZL

ZL

Start

Finish

VG – 56PSA-00527—10/21/2001

Pacificon 2001

Reactance & Susceptance of Lumped Elements

Inductors

Capacitors

X fLL = 2π BfLL = −1

2π

B fCC = 2πXfCC = −1

2π

VG – 57PSA-00527—10/21/2001

Pacificon 2001

X Zlf

v cshorted of

=

tan

2π B

Zlf

v c

shorted

of

= −

1

2tan

π

BZ

lf

v copeno f

=

1 2

tanπ

XZ

lf

v c

openo

f

= −

tan

2π

Reactance & Susceptance of Stubs

Assuming Zo is real, then

Shorted Stubs

Open Stubs

VG – 58PSA-00527—10/21/2001

Pacificon 2001

Broadband Matching Network Design RecipeUsing 4-Element π-Resonant and T-Resonant Networks

Putting network insertion point close to load (antenna) givesgreatest SWR bandwidth

Step 1: Using an L-network, move the midband impedancepoint to prime point A or B. Bandwidth will be maximized ifthe minimum reactance or susceptance L-network is chosenin this step.

Step 2: Wrap the impedance locus into the SWR circle byadding a series or parallel resonant circuit as required tocomplete the π-resonant or T-resonant network

VG – 59PSA-00527—10/21/2001

Pacificon 2001

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE

OF

TRA

NSM

ISSION

CO

EFFIC

IENT

IND

EGR

EES

AN

GLE

OF

REFLEC

TIO

NC

OE

FFICIEN

TIN

DEG

REES

—>

WA

VEL

ENG

THS

TOW

AR

DG

ENER

ATO

R—

><—

WA

VEL

ENG

THS

TOW

AR

DLO

AD

<—

IND

UC

TIV

ER

EAC

TAN

CE

COM

PON

ENT

(+jX

/Zo), OR



,OR

IND

UCTI

VE

SUSC

EPTA

NC

E(-

jB/Y

o)


A B

SWR = 1.5

fl

fmid

fu

Γr

Γi

ZL

ZL

ZL

ZL

ZL

ZL

ZL

ZL

∏-Resonant and T-Resonant NetworkFor Moderate and Broadband Matching

VG – 60PSA-00527—10/21/2001

Pacificon 2001

Caron’s Example 10: VHF Folded Blade Antenna

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-50

60

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-100.

04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.15

0.16

0.16

0.17

0.17

0.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

0.0

AN

GLE

OF

TRA

NSM

ISSION

CO

EFFIC

IENT

IND

EGR

EES

AN

GLE

OF

REFLE

CT

ION

CO

EFFIC

IENT

IND

EGR

EES

—>

WA

VEL

ENG

THS

TOW

AR

DG

ENER

ATO

R—

><—

WA

VEL

ENG

THS

TOW

AR

DLO

AD

<—

IND

UC

TIV

ER

EAC

TAN

CE

COM

PON

ENT

(+jX

/Zo), OR



,OR

IND

UCTI

VE

SUSC

EPTA

NC

E(-

jB/Y

o)


160

150

140

130

120110

105

100

VG – 61PSA-00527—10/21/2001

Pacificon 2001

Caron’s Matching Solution

0.1

0.1

0.1

0.2

0.2

0.2

0.3

0.3

0.3

0.4

0.4

0.4

0.50.5

0.5

0.6

0.6

0.6

0.7

0.7

0.7

0.8

0.8

0.8

0.9

0.9

0.9

1.0

1.0

1.0

1.2

1.2

1.2

1.4

1.4

1.4

1.6

1.6

1.6

1.8

1.8

1.8

2.02.0

2.0

3.0

3.0

3.0

4.0

4.0

4.0

5.0

5.0

5.0

10

10

10

20

20

20

50

50

50

0.2

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1.0

1.0

1.01.0

20-20

30-30

40-40

50

-5060

-60

70

-70

80

-80

90

-90

100

-100

110

-110

120

-120

130

-130

140

-140

150

-150

160

-160

170

-170

180

±

90-9

085

-85

80-8

0

75-7

5

70-7

0

65-6

5

60-6

0

55-5

5

50-5

0

45-45

40

-40

35

-35

30

-30

25

-25

20

-20

15

-15

10

-10

0.04

0.04

0.05

0.05

0.06

0.06

0.07

0.07

0.08

0.08

0.09

0.09

0.1

0.1

0.11

0.11

0.12

0.12

0.13

0.13

0.14

0.14

0.15

0.150.16

0.160.17

0.170.18

0.18

0.190.19

0.20.2

0.210.21

0.22

0.220.23

0.230.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.3

0.3

0.31

0.31

0.32

0.32

0.33

0.33

0.34

0.34

0.35

0.35

0.36

0.36

0.37

0.37

0.38

0.38

0.39

0.39

0.4

0.4

0.41

0.41

0.42

0.42

0.43

0.43

0.44

0.44

0.45

0.45

0.46

0.46

0.47

0.47

0.48

0.48

0.49

0.49

0.0

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160

150 140

130

120110

105

100

Max VSWR=1.67

VG – 62PSA-00527—10/21/2001

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WinSmith Display

Max VSWR=1.59

VG – 63PSA-00527—10/21/2001

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ARRL Radio Designer

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ARRL Radio Designer

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Caron’s Example 11: Long Wire Receiving Antenna

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Caron’s Solution

Max VSWR=6.2

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Caron’s Solution

Max VSWR=6.2

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Eagleware’s Solution 1

Max VSWR=5.05

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Max VSWR=4.77

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Max VSWR=6.59

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Eagleware’s Solution 4: Fano Limit

Max VSWR=3.42

VG – 72PSA-00527—10/21/2001

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GM3HAT 4-Band Dipole of Delight

VG – 73PSA-00527—10/21/2001

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GM3HAT Feedpoint ImpedanceAt Five Harmonic Frequencies

VSWR=11.02

VSWR=1.62

VG – 74PSA-00527—10/21/2001

Pacificon 2001

K6OIK 80m Suboctave Band Matching Network

150Ω89°@ 3.5 MHz

5.9 µH18.8 µH

25Ω91°@ 3.5 MHz

Zant

VG – 75PSA-00527—10/21/2001

Pacificon 2001

K6OIK’s Multiband Match Performance

VSWR=1.46

VG – 76PSA-00527—10/21/2001

Pacificon 2001

Software for Smith Charting and Network Design

Smith Chart Analysis & Display MicroSmith 2.3, ARRL, 1992, $39

A primitive DOS program.

winSMITH 2.0, Noble Publishing, 1995, $79Written by Eagleware. Easy to use. Restricted to ladder networks.Doesn’t have series stubs. Lacks an optimizer.

Matching Network Optimization & Synthesis ARRL Radio Designer 1.5, ARRL, 1995, $150

No longer sold. ARD’s optimizer works with Serenade netlists andhandles more variables than Serenade SV’s optimizer.

Serenade SV (student version), Ansoft, 2000, $0 (free)Download (about 20 Mbytes) from:http://www.ansoft.com/about/academics/sersv/index.cfm

Advanced Automated Smith Chart 3.0, Artech House, 1998, $395 =MATCH=, Eagleware, $699 (requires GENESYS Basic, $1997) Harmonica Linear Design Suite, Ansoft, 2000, $6900

VG – 77PSA-00527—10/21/2001

Pacificon 2001

References: Articles

Robert L. Thomas, “Broadband Impedance Matching in High-QNetworks,” EDN, pp. 62–69, December 20, 1973.

Neal C. Silence, “The Smith Chart and Its Usage in RF Design,”RF Design, pp. 85–88, April 1992.

Thomas R. Cuthbert, Jr., “Broadband Impedance Matching Methods,”RF Design, pp. 64–91, August 1994.

Thomas R. Cuthbert, Jr., “Broadband Impedance Matching - Fast andSimple,” RF Design, pp. 38–50, November 1994.

William E. Sabin, “Broadband HF Matching with ARRL RadioDesigner,” QST, pp. 33–36, August 1995.

William E. Sabin, “ARRL Radio Designer and the Circles Utility, Part 1:Smith Chart Basics,” QEX, pp. 3–9, Sept/Oct 1998.

William E. Sabin, “ARRL Radio Designer and the Circles Utility, Part 2:Small-Signal Amplifier Design,” QEX, pp. 3–11, Nov/Dec 1998.

VG – 78PSA-00527—10/21/2001

Pacificon 2001

References: Articles (Cont’d)

Steve Sparks, “A Practical Amateur Application of the Smith Chart,”Communications Quarterly, pp. 102–106, Summer 1999.

This article contains serious Smith charting errors. See the comments by GarryShapiro, NI6T, Communications Quarterly, p. 3, Fall 1999.

K.C. Chan and A. Harter, “Impedance Matching and the Smith Chart –The Fundamentals,” RF Design, pp. 52–66, July 2000.

VG – 79PSA-00527—10/21/2001

Pacificon 2001

References: Books

Robert A. Chipman, Transmission Lines, Schaum Outline Series,McGraw-Hill, 1968.

Basic, mathematical. A classic, but out-of-print.

Robert L. Thomas, A Practical Introduction to Impedance Matching,Artech House, 1976, ISBN 0890060509.

Intermediate, mathematical. A nice treatment of 4-element networks for widebandmatching.

Pieter L. D. Abrie, The Design of Impedance-Matching Networks forRadio-Frequency and Microwave Amplifiers, Artech House, 1985,ISBN 0890061726.

Advanced, mathematical.

Wilfred Caron, Antenna Impedance Matching, ARRL, 1989,ISBN 0872592200.

Intermediate, non-mathematical. Caron illustrates manual Smith chart methods attheir best, but which nonetheless have been completely replaced by computer-aided network design.

Brian C. Wadell, Transmission Line Design Handbook, Artech House,1991, ISBN 0890064369.

Analysis and formulas for many transmission lines. Comparable to M.A.R. Gunstonor K.C. Gupta, et al., below.

VG – 80PSA-00527—10/21/2001

Pacificon 2001

References: Books (Cont’d)

Phillip H. Smith, Electronic Applications of the Smith Chart inWaveguide Circuit, and Component Analysis, 2nd edition, NoblePublishing, 1995, ISBN 1884932398.

Originally published by McGraw-Hill, 1969, and reprinted by Krieger, 1983.Intermediate, mathematical.

K.C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines andSlotlines, 2nd ed., Artech House, 1996, ISBN 089006766X.

Analysis and formulas for many transmission lines.

M.A.R. Gunston, Microwave Transmission-Line Impedance Data,Noble Publishing, 1997, ISBN 1884932576.

Originally published by Van Nostrand Reinhold, 1972. Analysis and formulasfor many transmission lines. Comparable to B. Wadell above.

ARRL Antenna Book, 18th edition, chapters 24-28, ARRL, 1997,ISBN 0872596133.

Elementary, non-mathematical.

M. Walter Maxwell, W2DU, Reflections II: Transmission Lines andAntennas, 2nd ed., Worldradio Books, 2001, ISBN 0970520603.

A non-mathematical treatment of transmission lines and matching thatexamines and corrects common misunderstandings.

VG – 81PSA-00527—10/21/2001

Pacificon 2001

References: Application Notes, Videos, and Web Sites

Application Notes Times Microwave’s Complete Coaxial Cable Catalog & Handbook

Download from:http://www.timesmicrowave.com/products/military/TL14/TL14.htm

Videos Glenn Parker, Introduction to the Smith Chart, Noble Publishing,

1996. 50 minutes, $99.

Useful Web Sites http://www.timesmicrowave.com/calculators/index.htm http://www.sss-mag.com/smith.html http://www.ee.surrey.ac.uk/Personal/D.Jefferies/smith.html http://www.scott-inc.com/html/smith.htm

This Presentation is at http://www.fars.k6ya.org/docs/smithchart.html

Mysteries of the Smith Chart - FARS · Mysteries of the Smith Chart Transmission Lines, Impedance...

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