Top Banner
서서서서서 서서서서서 서서서 서서 Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line
38

서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Dec 31, 2015

Download

Documents

Abraham Hart
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

서강대학교 전자공학과윤상원 교수

* “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko

10. Transmission Line

Page 2: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 2

차 례

10-1. Introduction ------------------------------------------------10-2. Transmission Lines -------------------------------------10-3. Equivalent Circuit ---------------------------------------10-4. General Transmission Line Equation ---------10-5. Lossless transmission line --------------------------10-6. Microstrip Transmission Lines --------------------10-7. Terminated Lossless line ----------------------------10-8. Standing Waves ------------------------------------------10-9. Special Termination Conditions -----------------10-10. Sourced and loaded line --------------------------10-11. Power considerations for a line ---------------

3 4 6 811142023283538

Page 3: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 3

1-1. Introduction

At RF and microwave frequencies Physical size of circuit approaches to the wave-

length - the phase of ac signal must be considered At higher frequency range For larger size of the circuits

Voltage and Current must be treated as waves Phasor notation is very convenient On the circuit board one dimensional analysis is possible

Distributed circuit approach must be used Lumped element equivalent circuit approach enable us to

use Basic Circuit Theory Impedance is very important as in the Circuit Theory

Page 4: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 4

1-2. Transmission Lines

Two wire lines

Coaxial line

Page 5: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 5

Transmission lines(2)

Microstrip lines and Striplines

Parallel-plate transmission line

Page 6: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 6

1-3. Equivalent Circuit(1)

Page 7: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 7

Equivalent circuit (2)

Page 8: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 8

1-4. General Transmission Line Equation

For a small segment of a transmission line Lumped element equivalent circuit

Apply KVL and KCL

+V(z)

-

I ( z)

+V(z+z)

-

I ( z+z)

z z+z

CzGz

Rz Lz

CjGY

LjRZ

)()()()()(

)()()()()(

zzVYzIzIzIzzI

zzIZzVzVzVzzV

Page 9: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 9

General Transmission Line Equation (2)

leads to the differential form as

or

,ZIdz

dV YV

dz

dI

022

2

Ikdz

Id,02

2

2

2

2

Vkdz

VdZYV

dz

Vd

where propagation constant k given as

jCjGLjRZYk

Page 10: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 10

General Transmission Line Equation (3)

Voltage and current waves

,)( kzkz eVeVzV kzkz eIeIzI )(

kzkzkzkz eVeVZ

eVeVZ

k

dz

dV

ZzI

0

11)(

where the characteristic impedance given as

CjG

LjR

Y

Z

I

V

I

VZ

0

Page 11: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 11

1-5. Lossless transmission line

C

L

Y

ZZ 0

jLCjZYk

0R and 0G

Propagation constant becomes

Characteristic impedance becomes

Voltage and current waves become

,)( zjzj eVeVzV zjzj eIeIzI )(

Page 12: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 12

1-6. Microstrip Transmission Lines

Microstrip Line geometry

Assume that ‘t’ is negligible compared to ‘h’ ; t/h < 0.005

→ depend only on ‘w’, ‘h’ and r.

Page 13: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 13

Microstrip Transmission Lines (2)

For a narrow lines ; w/h < 1

h

w

w

hZZ

eff

f

48ln

20

: characteristic line

impedance

8.37600 fZ

221

104.01212

1

2

1

h

w

w

hrreff

: wave impedance in

free space

: effective dielectric constant

Page 14: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 14

Microstrip Transmission Lines (3)

For a wide lines ; w/h > 1

Wavelength

444.1ln

32

393.10

hw

hw

ZZ

eff

f

: characteristic

impedance

21

1212

1

2

1

w

hrreff

: effective

dielectric constant

effeff

p c

ff

v

01

Page 15: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 15

Microstrip Transmission Lines (4)

Z0 and εeff are plotted as w/h and εr

Page 16: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 16

Microstrip Transmission Lines (5)

Assuming an infinitely thin line conductor,w/h ≤ 2 ;

w/h ≥ 2 ;

2

82

A

A

e

e

h

w

rr

rr

fZ

ZA

11.0

23.01

1

2

12 0

rr

r BBBh

w

61.0

39.01ln2

112ln1

2

r

f

Z

ZB

02

Page 17: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 17

Microstrip Transmission Lines (6)

Corrections for nonzero strip thickness t ;

twπh/wx

hwhx

t

xtwweff 22 if 2

2t 2/ if

21

Page 18: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 18

1-7. Terminated Lossless line

Voltage Reflection Coefficient ;

z=- d z=0z

Z0 Z L

Z in 0

zjzj

zjzj

zjzj

eIeI

eVeVZ

zI

eVeVzV

)0()0(

)0()0(1

)(

)0()0()(

0

djdj eZ

VdIeVdV 2

00

20 1)( , 1)(

Use standing wave concept)0(

)0(Γ0

zV

zV

Page 19: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 19

Terminated Transmission line (2)

dj

dj

ine

eZ

dI

dVZ

20

20

01

1

)(

)(

Input impedance ;

Input impedance at ;0z

0

00 1

1

)0(

)0()0(

ZI

VZZ Lin

1

1

0

00

L

L

L

L

Z

Z

ZZ

ZZ : Reflection coefficient

at load

dz

Page 20: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 20

Terminated Transmission line (3)

Reflection coeff. for various terminations ; Open line : Short circuit : Impedance matched :

For a infinite transmission line ; Phase constant :

Dispersion-free transmission line

)( LZ 10 )0( LZ 10

)( 0ZZL 00

LC

pv

f

vpSince

Page 21: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 21

1-8. Standing Waves

z=- d z=0z

Z 0

Z in 0

Shorted transmission line ;

dZ

V

eeZ

VdI

dVj

eeVdV

djdj

djdj

cos2

)(

sin2

)(

0

0

in the time domain ;

2/cossin2

sin2Re Re ),(

tdV

deVjVetdV tjtj

Page 22: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 22

Standing Waves(2)

Page 23: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 23

Standing Waves(3)

z=- d z=0z

Z 0

Z L

Z in 0

V+

V -

V+ e - jd

0V+ e - jd0V+ e - j2d

Standing wave expressions ;

dj

dj

e

eV

VVdV

2

0

20

(d)

1

)(

djeVdA

dZ

dAdI

ddAdV

)(

)(1)(

)(

)(1)()(

0

Standing wave ratio(SWR) ;

11

1SWR

0

0

min

max

min

max

I

I

V

V

Page 24: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 24

Standing Waves(4)

Page 25: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 25

Standing Waves(5)

Graphical interpretation

Voltage standing wave ratio(VSWR) or return loss used: 0log20)(log20RL d

V+

0V+

2d

resulting standing w ave

O

| |

Page 26: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 26

1-9. Special Termination Conditions

Input impedance of terminated line ;

z=- d z=0z

Z 0

Z L

Z in 0

V+

V -

V+ e - jd

0V+ e - jd0V+ e - j2d

dj

dj

ineV

eVZ

dI

dVdZ

2

0

20

01

1

)(

)()(

or

)(1

)(1)( 0 d

dZdZin

djZZ

djZZZ

eZZ

ZZ

eZZ

ZZ

ZdZL

L

dj

L

L

dj

L

L

in

tan

tan

1

1

)(0

00

2

0

0

2

0

0

0

Page 27: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 27

Special Termination Conditions(2)

Short Circuit Transmission Line

z=- d z=0z

Z 0

Z in 0=- 1

djZdZin tan)( 0

dZ

V

eeZ

VdI

dVj

eeVdV

djdj

djdj

cos2

)(

sin2

)(

0

0

00

00 tan

tan)(

LZL

Lin djZZ

djZZZdZ

Page 28: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 28

Special Termination Conditions(3)

Page 29: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 29

Special Termination Conditions(4)

Open-circuit transmission line

z=- d z=0z

Z 0

Z in 0 =1

LZL

Lin djZZ

djZZZdZ

tan

tan)(

0

00

djZdZin cot)( 0

dZ

Vj

eeZ

VdI

dV

eeVdV

djdj

djdj

sin2

)(

cos2

)(

0

0

Page 30: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 30

Special Termination Conditions(5)

Page 31: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 31

Special Termination Conditions(6)

Quarter-wave transmission line in case

In case

d

Z0

Z LZ in

),2,1 ,2/2/(2/ mmd

LL

L

L

Lin

ZjZZ

jZZZ

djZZ

djZZZdZ

tan

tan

tan

tan)

2(

0

00

0

00

),2,1 ,2/4/(4/ mmd

LL

L

L

Lin Z

Z

jZZ

jZZZ

djZZ

djZZZdZ

20

0

00

0

00 2/tan

2/tan

tan

tan)

4(

Page 32: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 32

Special Termination Conditions(7)

Quarter-wave transformer

impedance matching condition ;

d

Z in ; desired Z L ; given

Z LZ 0 = Z L Z in

Lin Z

ZdZ

20 )4/(

LinZZZ 0

Page 33: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 33

1-10. Sourced and loaded line

Phasor representation of source

Input voltage at plane AA’ ;

Z0 Z LVG

L=0

ZG

s

in out

A

A'

B

B'

Gin

inGininininin ZZ

ZVVVVV 1

Page 34: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 34

Sourced and loaded line(2)

The input reflection coeff. at plane AA’ ;

The source reflection coeff. at plane AA’ ;

The source reflection coeff. at plane BB’ ;

d

0

00

0)(ZZ

Z

ZZ

ZZd

in

in

in

inin

0

0

ZZ

ZZ

G

Gs

2jsout e

Page 35: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 35

Sourced and loaded line(3)

Transmission coefficient at plane AA’ ;

At the load end (at plane BB’) ;

0

21

ZZ

ZT

in

ininin

000

21

ZZ

ZT

L

L

Page 36: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 36

1-11. Power considerations for a line

Time averaged power

The total power at plane AA’ ; the complex input voltage : input current :

Z0 Z LVG

L=0

ZG

s

in out

A

A'

B

B'

* Re 2

1IVPav

ininin VV 1

ininin ZVI 1)/( 0

2

0

2

12

1in

inininin Z

VPPP

Page 37: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 37

Power considerations for a line(2)

In terms of generator voltage ;

The input and the generator impedances ;

The generator voltage in terms of

Gin

in

in

G

in

inin ZZ

ZVVV

11

s

sG

in

inin ZZZZ

1

1 ,

1

100

sin and

2

2

2

0

2

11

1

8

1in

ins

sGin Z

VP

Page 38: 서강대학교 전자공학과 윤상원 교수 * “RF Circuit Design: Theory and Applications”, R. Ludwig & P. Bretchko 10. Transmission Line.

Microwave & Millimeter-wave Lab. 38

Power considerations for a line(3)

or

When the impedances are matched ;

: available power

When the source is not matched ;

22022

0

2

0

2

11

1

8

1

j

js

sGin e

eZ

VP

G

GGin Z

V

Z

VP

2

0

2

8

1

8

1

2

0

2

18

1s

Gin Z

VP : available power at AA’