RF Communication Circuits - PowerPoint Presentation

Slide1

RF Communication Circuits

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Ali Fotowat-AhmadySlide2

RF Communication Circuits

Dr. Fotowat-AhmadySharif University of TechnologyFall-1391Prepared by: Siavash Kananian & Alireza Zabetian

Lecture 2: Transmission LinesSlide3

A

wave guiding structure is one that carries a signal (or power) from one point to another. There are three common types: Transmission lines Fiber-optic guides WaveguidesWaveguiding Structures3Slide4

Transmission Line

Has two conductors running parallel Can propagate a signal at any frequency (in theory) Becomes lossy at high frequency Can handle low or moderate amounts of power Does not have signal distortion, unless there is loss May or may not be immune to interference Does not have Ez or Hz components of the fields (TEMz) PropertiesCoaxial cable (coax)

Twin lead (shown connected to a 4:1 impedance-transforming balun)

4Slide5

Transmission Line (cont.)

CAT 5 cable(twisted pair)The two wires of the transmission line are twisted to reduce interference and radiation from discontinuities. 5Slide6

Transmission Line (cont.)

Microstriph

w

e

r

e

r

w

Stripline

h

Transmission lines commonly met on printed-circuit boards

Coplanar strips

h

e

r

w

w

Coplanar waveguide (CPW)

h

e

r

w

6Slide7

Transmission Line (cont.)

Transmission lines are commonly met on printed-circuit boards.A microwave integrated circuitMicrostrip line7Slide8

Fiber-Optic Guide

Properties Uses a dielectric rod Can propagate a signal at any frequency (in theory) Can be made very low loss Has minimal signal distortion Very immune to interference Not suitable for high power Has both Ez and Hz components of the fields8Slide9

Fiber-Optic Guide (cont.)

Two types of fiber-optic guides:1) Single-mode fiber2) Multi-mode fiberCarries a single mode, as with the mode on a transmission line or waveguide. Requires the fiber diameter to be small relative to a wavelength. Has a fiber diameter that is large relative to a wavelength. It operates on the principle of total internal reflection (critical angle effect).9Slide10

Fiber-Optic Guide (cont.)

http://en.wikipedia.org/wiki/Optical_fiberHigher index core region10Slide11

Waveguides

Has a single hollow metal pipe Can propagate a signal only at high frequency:  > c The width must be at least one-half of a wavelength Has signal distortion, even in the lossless case Immune to interference Can handle large amounts of power Has low loss (compared with a transmission line) Has either E

z or H

z component of the fields (TMz

or TEz

) Properties

http://en.wikipedia.org/wiki/Waveguide_(electromagnetism)

11Slide12

Lumped circuits: resistors, capacitors, inductors neglect time delays (phase)account for propagation and time delays (phase change)Transmission-Line Theory Distributed circuit elements: transmission linesWe need transmission-line theory whenever the length of a line is significant compared with a wavelength.12Slide13

Transmission Line

2 conductors

4 per-unit-length parameters:

C

= capacitance/length [

F/m

]

L

= inductance/length [

H/m

]

R

= resistance/length [



/m

]

G

= conductance/length [

/

m or S/m

]



D

z

13Slide14

Transmission Line (cont.)

+ + + + + + +- - - - - - - - - -

x

x

x

B

14

R

D

z

L

D

z

G

D

z

C

D

z

z

v

(

z

+



z

,

t

)

+

-

v

(

z

,

t

)

+

-

i

(

z

,

t

)

i

(

z

+



z

,

t

)Slide15

Transmission Line (cont.)

15

R

D

z

L

D

z

G

D

z

C

D

z

z

v

(

z

+



z

,

t

)

+

-

v

(

z

,

t

)

+

-

i

(

z

,

t

)

i

(

z

+



z

,

t

)Slide16

Hence

Now let Dz  0:“Telegrapher’sEquations”

TEM Transmission Line (cont.)

16Slide17

To combine these, take the derivative of the first one with respect to

z:Switch the order of the derivatives.TEM Transmission Line (cont.)17Slide18

The same equation also holds for

i.Hence, we have:TEM Transmission Line (cont.)18Slide19

TEM Transmission Line (cont.)

Time-Harmonic Waves:19Slide20

Note that

= series impedance/length= parallel admittance/lengthThen we can write:TEM Transmission Line (cont.)

20Slide21

Let

Convention:Solution:ThenTEM Transmission Line (cont.)



is called the "propagation constant."

21Slide22

TEM Transmission Line (cont.)

Forward travelling wave (a wave traveling in the positive z direction):

The wave “repeats” when:

Hence:

22Slide23

Phase Velocity

Track the velocity of a fixed point on the wave (a point of constant phase), e.g., the crest.

v

p

(

phase velocity

)

23Slide24

Phase Velocity (cont.)

SetHenceIn expanded form:24Slide25

Characteristic Impedance

Z0so+ V+(z

)-

I+

(z)

z

A wave is traveling in the

positive z direction

.(

Z

0

is a number, not a function of

z

.)

25Slide26

Use Telegrapher’s Equation:

soHenceCharacteristic Impedance Z0 (cont.) 26Slide27

From this we have:

UsingWe haveCharacteristic Impedance Z0 (cont.) Note: The principal branch of the square root is chosen, so that Re (Z0) > 0

.

27Slide28

Note:

wave in +z directionwave in -z direction

General Case (Waves in Both Directions)

28Slide29

Backward-Traveling Wave

so+ V -(z)- I - (

z)

z

A wave is traveling in the negative

z

direction.

Note: The reference directions for voltage and current are the same as for the forward wave.

29Slide30

General Case

A general superposition of forward and backward traveling waves:Most general case:Note: The reference directions for voltage and current are the same for forward and backward waves. 30

+ V

(z)-

I

(z)

zSlide31

guided wavelength

 gphase velocity  vpSummary of Basic TL formulas

31Slide32

Lossless Case

so

(

indep

. of freq.)

(real and

indep. of freq.)32Slide33

Lossless Case (cont.)

In the medium between the two conductors is homogeneous (uniform) and is characterized by (, ), then we have that The speed of light in a dielectric medium isHence, we have that The phase velocity does not depend on the frequency, and it is always the speed of light (in the material).

(proof given later)

33Slide34

Where do we assign

z = 0?The usual choice is at the load.Terminating impedance (load)Ampl. of voltage wave propagating in negative z

direction at z

= 0.Ampl. of voltage wave propagating in positive

z direction at z = 0.

Terminated Transmission Line

Note: The length

l

measures distance from the load:

34Slide35

What if we know

Terminated Transmission Line (cont.)HenceCan we use z = - l

as a reference plane?

Terminating impedance (load)

35Slide36

Terminated Transmission Line (cont.)

Compare:Note: This is simply a change of reference plane, from z = 0 to z = -l.Terminating impedance (load)

36Slide37

What is

V(-l )?propagating forwardspropagating backwardsTerminated Transmission Line (cont.)

l

 distance away from load

The current at z = -

l is then

Terminating impedance (load)

37Slide38

Total volt. at distance

l from the loadAmpl. of volt. wave prop. towards load, at the load position (z = 0).

Similarly,

Ampl. of volt. wave prop. away from load, at the load position (z

= 0).





L

 Load reflection coefficient

Terminated Transmission Line (cont.)





l

 Reflection coefficient at

z

= -

l

38Slide39

Input impedance seen “looking” towards load at

z = -l .Terminated Transmission Line (cont.)39Slide40

At the load

(l = 0):Thus,Terminated Transmission Line (cont.)Recall40Slide41

Simplifying, we have

Terminated Transmission Line (cont.)Hence, we have41Slide42

Impedance is periodic with period

g/2Terminated Lossless Transmission LineNote:tan repeats when

42Slide43

For the remainder of our transmission line discussion we will assume that the transmission line is lossless.

Terminated Lossless Transmission Line43Slide44

Matched load:

(ZL=Z0)For any l No reflection from the load A

Matched Load

44Slide45

Short circuit load: (

ZL = 0)Always imaginary!Note:B

S.C. can become an O.C. with a

g/4

trans. line

Short-Circuit Load

45Slide46

Using Transmission Lines to Synthesize Loads

A microwave filter constructed from microstrip.This is very useful is microwave engineering.46Slide47

Example

Find the voltage at any point on the line.47Slide48

Note:

At l = d :HenceExample (cont.)

48Slide49

Some algebra:

Example (cont.) 49Slide50

where

Example (cont.) Therefore, we have the following alternative form for the result:Hence, we have50Slide51

Example (cont.)

Voltage wave that would exist if there were no reflections from the load (a semi-infinite transmission line or a matched load). 51Slide52

Example (cont.)

Wave-bounce method (illustrated for l = d ):52Slide53

Example (cont.)

Geometric series: 53Slide54

Example (cont.)

orThis agrees with the previous result (setting l = d ).Note: This is a very tedious method – not recommended. Hence54Slide55

At a distance

l from the load:If Z0  real (low-loss transmission line)Time- Average Power FlowNote:

55Slide56

Low-loss

lineLossless line ( = 0)Time- Average Power Flow56Slide57

Quarter-Wave Transformer

soHenceThis requires ZL to be real.

Z

L

Z

0

Z

0T

Z

in

57Slide58

Voltage Standing Wave Ratio

58Slide59

Coaxial Cable

Here we present a “case study” of one particular transmission line, the coaxial cable.

a

b

Find

C, L, G, R

We will assume no variation in the

z

direction, and take a length of one meter in the

z

direction in order top calculate the per-unit-length parameters.

59

For a

TEM

z

mode, the shape of the fields is independent of frequency, and hence we can perform the calculation using electrostatics and

magnetostatics

. Slide60

Coaxial Cable (cont.)

-l0l0

a

b

Find

C

(capacitance / length)

C

oaxial cable

h

= 1

[

m

]

From Gauss’s law:

60Slide61

-

l0l0a

b

C

oaxial

cable

h = 1 [m

]

Hence

We then have

Coaxial Cable (cont.)

61Slide62

Find

L (inductance / length)From Ampere’s law: Coaxial cableh = 1 [m]

I

S

h

I

I

z

center conductor

Magnetic flux:

Coaxial Cable (cont.)

62

Note: We ignore “internal inductance” here, and only look at the magnetic field

between

the two conductors (accurate for high frequency.Slide63

C

oaxial cableh = 1 [m]

I

Hence

Coaxial Cable (cont.)

63Slide64

Observation:

This result actually holds for any transmission line.Coaxial Cable (cont.)64Slide65

For a lossless cable:

Coaxial Cable (cont.)65Slide66

-

l0l0a

b

Find

G

(conductance / length)

C

oaxial cable

h = 1

[

m

]

From Gauss’s law:

Coaxial Cable (cont.)

66Slide67

-

l0l0a

b

We then have

or

Coaxial Cable (cont.)

67Slide68

Observation:

This result actually holds for any transmission line.Coaxial Cable (cont.)68Slide69

To be more general:

Note: It is the loss tangent that is usually (approximately) constant for a material, over a wide range of frequencies.Coaxial Cable (cont.)As just derived,The loss tangent actually arises from both conductivity loss and polarization loss (molecular friction loss), ingeneral.69

This is the loss tangent that would arise from conductivity effects.Slide70

General expression for loss tangent:

Effective permittivity that accounts for conductivityLoss due to molecular frictionLoss due to conductivityCoaxial Cable (cont.)70Slide71

Find

R (resistance / length)Coaxial cableh = 1 [m]

Coaxial Cable (cont.)

a

b

R

s

=

surface resistance of metal

71Slide72

General Transmission Line Formulas

(1)(2)(3)Equations (1) and (2) can be used to find L and C if we know the material properties and the characteristic impedance of the lossless line. Equation (3) can be used to find

G if we know the material loss tangent.

(4)

Equation (4) can be used to find

R (discussed later).

72Slide73

General Transmission Line Formulas (cont.)

Al four per-unit-length parameters can be found from73Slide74

Common Transmission Lines

CoaxTwin-lead

a

b

h

a

a

74Slide75

Common Transmission Lines (cont.)

Microstrip

h

w

e

r

t

75Slide76

Common Transmission Lines (cont.)

Microstrip

h

w

e

r

t

76Slide77

At high frequency,

discontinuity effects can become important. Limitations of Transmission-Line TheoryBend

incident

reflectedtransmitted

The simple TL model does not account for the bend.

ZTH

ZL

Z

0

+

-

77Slide78

At high frequency,

radiation effects can become important. When will radiation occur?We want energy to travel from the generator to the load, without radiating. Limitations of Transmission-Line Theory (cont.)ZTHZL

Z

0

+

-

78Slide79

a

b

z

The coaxial cable is a perfectly shielded system – there is never any radiation at any frequency, or under any circumstances.

The fields are confined to the region between the two conductors.

Limitations of Transmission-Line Theory (cont.)

79Slide80

The twin lead is an open type of transmission line – the fields extend out to infinity.

The extended fields may cause interference with nearby objects. (This may be improved by using “twisted pair.”)

+

-

Limitations of Transmission-Line Theory (cont.)

Having fields that extend to infinity is not the same thing as having radiation, however.

80Slide81

The

infinite twin lead will not radiate by itself, regardless of how far apart the lines are.h

incident

reflected

The incident and reflected waves represent an exact solution to Maxwell’s equations on the infinite line, at any frequency.

S

Limitations of Transmission-Line Theory (cont.)

No attenuation on an infinite lossless line

81Slide82

A

discontinuity on the twin lead will cause radiation to occur.Note: Radiation effects increase as the frequency increases.Limitations of Transmission-Line Theory (cont.)hIncident wave

pipe

obstacle

Reflected wave

bend

h

Incident wave

bend

Reflected wave

82Slide83

To reduce radiation effects of the twin lead at discontinuities:

hReduce the separation distance h (keep h << ).Twist the lines (twisted pair).

Limitations of Transmission-Line Theory (cont.)

CAT 5 cable

(twisted pair)

83