21

CHAPTER 2

DESIGN AND DEVELOPMENT OF LOADED LINE PHASE

SHIFTER FOR WIRELESS APPLICATION

2.1 PREAMBLE

The demand for phased array systems for performing continuous

scanning has created the need for phase shifters capable of providing, smaller

scan angles with fewer blind spots. The loaded line phase shifters are the most

preferred choice for such applications owing to their smaller phase shifting

property with comparatively low insertion loss (Koul and Bhat 1991 b).

Loaded line phase shifters with semiconductor diode control have

been reported in the literature. A p-i-n diode controlled loaded line phase

shifter for L and S band suitable for beam steering array application is

proposed (White 1965). A reduced size 4-bit 90° phase shifter employing

single-section and a 4 bit 360° network employing 45° section as a basic

building block are reported (Opp and Hoffman 1968). A 75° separation

between the loading susceptances is shown to give better performance than

for 90° separation in Voltage Standing Wave Ratio (VSWR), return loss and

phase shift (Yahara 1972). Design figures for different types of phase shifters

including loaded line are reported (Garver 1972). The design equations for a

loaded line phase shifter for arbitrary susceptance spacing and maximum

bandwidth are obtained (Davis 1974). The diode phase shifter circuits

including loaded line phase shifter and the performance of p-i-n diodes and

requirements of a driver are reported (White 1974).

22

The RF performance of micro strip semiconductor phase shifters

operating at S band and Ultra High Frequency (UHF) are described (Burns

et al 1974). A series loaded line S band phase shifter for small phase shifts

(11.25° and 22.5°) has been proposed. A p-i-n diode based 3 bit F-band phase

shifter for high power applications is reported (Swartz et al 1978). Practical

design of C band 4 bit p-i-n phase shifter is presented (Katsumi and Susumu

1979). The design of loaded-line p-i-n diode digital phase shifter circuits for

main line mounted, stub mounted and switchable stub length conditions is

reported. Starting from the p-i-n diode parameters, optimum designs of these

circuits for obtaining minimum insertion loss, maximum bandwidth and

minimum size have been discussed (Bahl and Gupta 1980).

The circuit design procedures for the loaded-line phase shifter are

presented. The effect of losses in the loading elements on the circuit

parameters and the design factors affecting their bandwidth are discussed

(Atwater 1985). The loaded line phase shifter that incorporated both lossy and

imperfectly matched diodes is reported (Manuel 1990).

Simple closed- form expressions for the admittances separated by a

quarter-wavelength transmission line in a loaded line phase shifter are

presented (Bartolucci et al 1995). Single switch configuration of loaded line

phase shifter is reported. This structure exhibited interesting properties,

leading to reduction in size and the number of semiconductor switches

used(Bartolucci 1996). The low cost phase shifters for L-band phased array

antennas is reported. The performance is enhanced by including extra

compensation circuits in biasing networks of the p-i-n diodes that tuned out

the parasitic elements(Nemai 1997).

First, three bits of the four bit hybrid MIC phase shifter are realized

with the loaded line phase shifter with special tuning elements for the fine

tuning of the required phase shift and is reported (Jan 1998). The least

23

significant bit of 5 bit phase shifter is realized with simplified loaded line

configuration for good matching and is reported (Stanimir 2003). The four

bits of a Ku band six bit phase shifter is realized with loaded line phase shifter

with special tuning elements for the fine tuning of the required phase shift and

is described (Wang et al 2007). A loaded line phase shifter with enlarged

phase shift range and bandwidth is presented (Xinyi and Koenraad 2010 a).

2.2 LOADED LINE PHASE SHIFTER

2.2.1 The Structure

Conventional loaded-line phase shifter circuit as shown in

Figure 2.1 consists of two two-state switchable susceptance (jBi) connected in

shunt with a line which has a section of characteristic impedance Z0 and

electrical length , where i=1, 2 refers to the two states of the switches.

Figure 2.1 Loaded line phase shifter

A loaded line phase shifter with single susceptance element is also

possible. But, two susceptance elements separated by quarter wave length

spacing offers, wider bandwidth (Pozar 1998,Koul and Bhat 1991). A

symmetric pair of quarter-wavelength spaced shunt susceptances that are

small (or series reactance) mutually cancels reflections. These features

provide the phase-shifter section a good match in both the control states,

regardless of the susceptance sign or value.

Input Output

Y0

Yi

Yi

24

The shunt capacitance elements lengthen a transmission line

electrically while inductive elements shorten it. Thus, switching from

inductive to capacitive elements produces an increase in electrical length with

a corresponding phase shift. The phase shifts provided by a pair of shunt

susceptance is equal to the normalized susceptance change of one of them.

Each section of a loaded line phase shifter shown in Figure 2.2 (a) and(b

)consists of a /4 transmission line symmetrically loaded at its ends by small

susceptance which are controlled by semiconductor switches such as p-i-n

diodes. Desired phase shift is obtained by changing electrical length of lines

through switching p-i-n diodes.

Figure 2.2(a) Loaded line phase shifter loaded with lumped susceptance

Figure 2.2(b) Loaded line single bit phase shifter with transmission line

and p-i-n diodes

jBn jBn-jBn -jB

25

2.2.2 Design of Loaded Line Phase Shifter

The design of a phase shifter involves the representation of phase

shifter in its equivalent circuit form (Opp and Hoffman 1968) as shown in

Figure 2.3(a)

Figure 2.3 (a) Electrical equivalent (b) Shunt Susceptance arm of loaded

line phase shifter

Figure 2.3(b) shows the shunt susceptance arm of loaded line phase

shifter along with another similar arm at a distance /4, connected through

main transmission line which decides the susceptance B required to produce

the necessary phase shift. The single arm consists of a /4 line with

characteristic impedance Zt, short transmission line of electrical length l,

with characteristic impedance Z0 = 50 and a diode connected in series with

its cathode ground. The /4 line and short transmission line acts as a matching

network to the diode impedances in ON and OFF conditions, with the main

transmission line with characteristic impedance Zc.

The ABCD matrix of the phase shifter shown in Figure 2.1, under

lossless condition, is given by

A B

C D= [P] [Q] [R] (2.1)

'

Yc’

26

where [P] and [R] are the ABCD matrices of the shunt arms of the phase

shifter and is given by

(P) =i

1 0

jB 1 (2.2)

(R) =1 0

jBi 1 (2.3)

where i = (1, 2) representing diode ON/OFF condition and [Q] is the ABCD

matrix of the main transmission line and is given by (Pozar 1998).

[Q] =c

c

cos jZ sin

jsin / Z cos (2.4)

Hence

[P] [Q] [R] =c

c

cos jZ sin1 0 1 0

jsin / Z cosjBi 1 jBi 1= [M1] (2.5)

By performing matrix multiplication,

c i c

1 2

i c i c c i

cos Z B sin jZ sin[M ]

2jB cos jZ B sin jsin / Z cos Z B sin (2.6)

The ABCD parameters of phase shifter circuit shown in Figure 2.3a

is

c

2

c

cos ' jsin '/ Y '[M ]

jY ' sin ' cos ' (2.7)

27

Since Figure 2.3a is an equivalent circuit of Figure 2.1 matrices M1

and M2 are equivalent, and comparing the ABCD parameters

1

c i' cos (cos Z B sin ) (2.8)

1/22

i ic c

c c

B BY' Y 1 2 cot

Y Y (2.9)

From the ABCD parameters, S parameters are obtained as

(Atwater 1985)

m o m o11 22

m m o m o

B Y C ZS S

2A B Y C Z (2.10)

21 12

m m o m o

2S S

2A B Y C Z (2.11)

where Zo = 1/Yo is the characteristics impedance of the circuit into which the

phase shifter is connected, where subscripts m are used on the matrix

elements.

Under input matched condition S11 = 0, and this leads to

m o m oB Y C Z (2.12)

By substituting this in the expression for transmission coefficient

(S21),equation 2.11

21

m m o c i c o

1 1S

A B Y (cos Z B sin ) jZ Y sin ) (2.13)

28

In the input matched lossless case, magnitude of S21 is unity.

Hence,

c i c o(cos Z B sin ) jZ Y sin 1 (2.14)

Thus,

c icos cos Z B sin (2.15)

c osin Z Y sin (2.16)

where is the phase angle of S21

In complex conjugate mode, the phase is switched symmetrically

about 90 by increments of ± / 2 by loading the line with the diode

operating ON and OFF respectively.

The phase shifter is designed to operate in complex conjugate mode

and the phase is switched symmetrically about 90 by increments of ± /2 by

loading the line with the diode operating ON and OFF respectively.

Substituting the value of = 90 ± /2 in equations (2.15) and (2.16) yields

c o

cos2

Z Zsin

(2.17)

i

o

B costan

Y 2cos

2

(2.18)

where Z0 is characteristic impedance of the circuit, = l is electrical length

of the main transmission line and is phase shift.

29

Calculation of Zt and l

A portion of the shunt susceptance of a loaded line phase shifter is

shown in Figure 2.4. When the diode is in ON condition from Figure 2.4a

DON 0SON 0

0 DON

Z jZ tan lZ Z

Z jZ tan l (2.19)

Using quarter wave transmission line Figure 2.5a

2

tin ON

s OFF

ZZ

Z (2.20)

(a) (b)

Figure 2.4 A portion of shunt susceptance of a loaded line phase shifter

with diode a) ON and b)OFF condition

(a) (b)

Figure 2.5 One arm of shunt susceptance of a loaded line phase shifter

with diode a) ON and b) OFF condition

OnOff

30

As the loaded line phase shifter is designed to operate in complex

conjugate mode, the impedance of one arm is (Atwater 1985)

in ON

i

jZ

B (2.21)

where Bi is the susceptance of one arm.

similarly, when diode is in OFF state, from Figure 2.4 b

DOFF 0SOFF 0

0 DOFF

Z jZ tan lZ Z

Z jZ tan l (2.22)

From Figure 2.5b and using the quarter wave transmission line equation,

2

tin OFF

s ON

ZZ

Z (2.23)

in OFF

i

jZ

B (2.24)

By substituting = 90 in Equation (2.18)

i oB Y tan2

(2.25)

By solving equations (2.20), (2.21), (2.23) and (2.24), Zt and l can

be calculated.

All these design parameters and the derived formulae for the

conventional loaded line phase shifters and are listed in Table 2.1.

31

Table 2.1 Design parameter expressions of loaded line phase shifter

Sl.

NoParameter Expression

1. S,ONZ DON 0SON 0

0 DON

Z jZ tan lZ Z

Z jZ tan l

2. S,OFFZ DOFF 0SOFF 0

0 DOFF

Z jZ tan lZ Z

Z jZ tan l

3. ZC

sin

2cos

ocZZ

4. in ,ONZ in ON

i

jZ

B

5. in,OFFZ in ,OFF

i

jZ

B

6. B1ON o

cosB Y tan

2cos

2

7. B2OFF o

cosB Y tan

2cos

2

8. Zt2 2

t in ,ON S,OFFZ Z Z ;2

t in OFF sONz z z

2.2.3 Issues in Loaded Line Phase Shifters

A loaded line phase shifter consists of periodically loaded

reactances separated by a minimum distance of /4 which increases the total

length of the phase shifter. Also, the loading of the reactance are done by

shunt quarter wave transformers which increases the width of the phase

shifters also. As a result of the above, the total size of the phase shifter

32

increases because of the reactive loading of the transmission line, the Q of the

phase shifter increases and hence, the operating bandwidth of the phase shifter

decreases. To circumvent this problem of size, a novel fractal based phase

shifter is attempted. Since, miniaturization of phase shifter becomes an

important issue in the design of wireless RF systems, this thesis addresses the

issue of miniaturization using the concept of KOCH fractal geometry.

2.3 FRACTAL BASED LOADED LINE PHASE SHIFTER

2.3.1 Preamble

Fractals are fragmented space-filling containers used to pack

electrically large features efficiently into small physical areas efficiently.

Among the well known KOCH, Sierpenski, and Minkowski fractals used for

RF applications, KOCH has been an ideal fractal for phase shifter applications

due to its simplicity for analysis and easiness for fabrication. KOCH fractals

are characterized by iteration factor and iteration order. Iteration factor

represents the construction law of fractal geometry, and iteration order depicts

how many iteration processes are to be carried out. Generation law of KOCH

curve facilitates to begin with a specified initiator.

2.3.2 Generation of KOCH Fractal Geometry

As shown in Figure 2.6, the length of the original microstrip line is

l, the length of the microstrip line K1 is 2W+2L/3 (Chen and Wang 2008) and

the length of the microstrip line K2 is 6W+4L/9. If the line width W L/6,

then the length of the KOCH shaped microstrip lines decreases as the iteration

order increases, and also the occupied circuit area of the KOCH curves

decreased as the iteration order increased. Thus, the space filling property is

provided.

33

(a) K0, zeroth iteration order

(b) K1, first iteration order

(c) K2, second iteration order

Figure 2.6 KOCH fractal shaped micro strip lines whose iteration factor

is 1/5

2.3.3 Construction of Single Bit 22.5 KOCH Loaded Line Phase

Shifter

For a straight microstrip line of /4 electrical length, Figure 2.6

shows generation process of a KOCH-shaped microstrip line with iteration

factor of 1/5. The condition that must be satisfied to get a reduced size micro

strip line by applying KOCH fractal curve is as

LineLengthLine Width

6(2.26)

34

KOCH fractals are applied to shunt quarter wave transmission line

and bias line of conventional loaded line phase shifter with 0.2 iteration factor

with iteration order of one. The resulting layout is shown in Figure 2.7.

Figure 2.7 Layout of single bit miniaturized loaded line phase shifter

2.3.4 Equivalent Circuit Model of KOCH based Fractal Loaded Line

Phase Shifter

For the detailed understanding of operation of the KOCH based

fractal loaded line phase shifter, the equivalent circuit analysis is made. The

equivalent circuit of the KOCH based fractal loaded line phase shifter is sub

divided into four smaller sections

i. Transmission line

ii. Diode section

iii. Bias Network

iv. Stub shunt(KOCH fractal)

i. Transmission Line

The 50 transmission line has two end coupled gaps. The layout

and its corresponding equivalent circuit is shown in Figure 2.8 (a).

35

Figure 2.8(a) Equivalent circuit of transmission lines

ii. Diode

The equivalent circuit model of the chosen diode namely

MA4P789-287 p-i-n Diode for OFF and ON condition of the diode are shown

in Figure 2.8(c) and (d) respectively.

Figure 2.8(b) Equivalent circuit of p-i-n diode

Figure 2.8(c) Equivalent circuit of diode OFF condition

36

Figure 2.8(d) Equivalent circuit of diode ON condition

iii. Bias Network

The open circuited quarter wave transmission lines in biasing

network are represented as series LC resonator and the KOCH is represented

in equivalent circuit form.

Figure 2.8(e) Equivalent circuit of Bias network

37

iv. Fractal structure

Figure 2.8(f) Microstrip Bend

Figure 2.8(g) Equivalent circuit of Bend

Figure 2.8 (h) Equivalent circuit of single KOCH fractal

38

The design equations for the equivalent circuit are tabulated in

Table 2.2. Using the design equations, the component values are estimated.

Table 2.2 Design equations for equivalent circuit of transmission lines

Structure Characteristics and Uses Equation

High impedance series

line

Equivalent to series

inductanceoX Z tan( l)

Low impedance series

line

Equivalent to series

inductanceoB Y tan( l)

Quarter wave open

circuit stub

Equivalent to a LC series

Resonator

o

o

ZL

4

2

o

1C

L

The L and C values of micro strip bed are calculated using equation 2.27 and

2.28

L w100 4 4.21 nH / m

h h (2.27)

bend r rC (14 12.5)w / h (1.83 2.25)pF / m

w w

h

(2.28)

The conventional and reduced size KOCH fractal single bit phase

shifters are the basic building blocks of n bit phase shifters. The issues in

single bit phase shifters are limited to practical applicability as they can

provide only fixed beam tilt. In order to get varied beam scanning in the

desired direction, a n-bit phase shifter is required. Hence, a 3 bit phase shifter

design is attempted purposely in this research.

39

2.4 THREE BIT CONVENTIONAL LOADED LINE PHASE

SHIFTER

2.4.1 Structure of 3 Bit Conventional Loaded Line Phase Shifter

Three bit loaded line phase shifter can be constructed by cascading

of 22.5 , 45 and 90 sections of loaded line phase shifters. It can provide 8

different phase shifts from 0 to 157.5 with an increment of 22.5 . The

different phase shift can be obtained by providing bias to the appropriate

phase shifter sections. The line sketch of the conventional 3 bit loaded

line phase shifter showing the three sections in cascaded form is shown in

Figure 2.9.

Figure 2.9 Line Sketch of Conventional 3 bit loaded line phase shifter

2.5 RESULTS AND DISCUSSION

2.5.1 Design and Simulation of Single Bit 22.5 Conventional Loaded

Line Phase Shifter Section for WLAN Application

Specifications

Frequency of operation (f) = 2.45 GHz

Desired Phase shift is ( ) = 22.5

Bandwidth = 80MHz (2.4 - 2.48GHz)

Z0 =50 and = 90

40

For this specification Microwave associates MA4P789-287 p-i-n

diode is selected due to its low series resistance. The ON state impedance of

the diode was calculated as ZDON=1.639+j21.75 and the OFF state

impedance ZDOFF =-j108.22 . Substituting ZDON and ZDOFF in equation

(2.17), the calculated design data are tabulated in Table 2.3.

Table 2.3 Design parameter values of loaded line phase shifter

Sl. No Parameter Values

1. ZC 49

2. Zt 121

3. l 33.5º

4. ZDON 1.6+j22

5. ZDOFF -j108.75

6. ZINON j250

7. ZINOFF -j250

8. BON 0.004mho

9. BOFF -0.004mho

The simulated layout is shown in Figure 2.10 and the simulation is

done using Advanced Design System (ADS).

VSWR

VSWR2VSWR2=vswr(S22)

VSWR

conven225

conven225_1ModelType=RF

V_DCSRC1

Vdc=1.5 V

PIN_diode

PinDiode2

PIN_diode

PinDiode1

TermTerm2

Z=50 Ohm

Num=2

CAPP2

C13

Term

Term1

Z=50 Ohm

Num=1

VSWR

VSWR3VSWR1=vswr(S11)

VSWR

CAPP2

C11

MSUB

MSub1

Rough=0 um

TanD=0.011

T=0.045 mmHu=1.0e+036 um

Cond=1.0E+50

Mur=1

Er=4.6

H=1.6 mm

MSub

DC

DC1

DC

S_Param

SP1

Step=5 MHz

Stop=3 GHz

Start=2 GHz

S-PARAMETERS

Figure 2.10 Simulated layout of single bit 22.5 conventional loaded line

phase shifter

41

Figure 2.11 (a) shows the simulation results of single bit 22.5

conventional loaded line phase shifter. The plot shows the frequency vs. S

parameters for ON and OFF condition of diode. It is observed from the plot

that the insertion loss is less than -1 dB for the chosen frequency band of 2.2-

2.6 GHz and the return loss is less than -15 dB for the same bandwidth

considering the lossy FR-4 substrate with loss tangent 0.011.

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-30

-25

-20

-15

-10

-5

0

S-P

ara

me

ter

(dB

)

Frequency (GHz)

S11

ON

S11

OFF

S21

ON

S21

OFF

Figure 2.11(a) Simulated S parameter of single bit 22.5 conventional

loaded line phase shifter

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-180.0

-157.5

-135.0

-112.5

-90.0

-67.5

-45.0

-22.5

0.0

22.5

45.0

67.5

90.0

112.5

135.0

157.5

180.0

Ph

ase

(d

eg

)

Frequency (GHz)

S21

OFF

S21

ON

Figure 2.11(b) Simulated phase plot of single bit 22.5 conventional

loaded line phase shifter

42

Figure 2.11(b) shows the simulated phase plot of single bit 22.5

conventional loaded line phase shifter for on and off condition of the diodes.

The plot shows the phase shift of 23.2 at 2.45 GHz with ± 2 band width of

100MHz from 2.4 to 2.6GHz.

Table 2.4 Simulation results of single bit 22.5 conventional loaded line

phase shifter

Diode

state

S11

(dB)

S21

(dB)

S21

(degrees)

(on phase-off phase)

Simulated DesiredPhase

Error

ON -22.28 -0.85 131.4-23.2 -22.5 -0.7

OFF -27.42 -0.65 154.6

Table 2.4 shows the simulated results of 22.5 conventional loaded

line phase shifter. At the designed frequency of 2.45 GHz the return loss is

less than -22 dB, insertion loss is less than -0.85 dB and the phase error is

0.7 .

2.5.2 Design of single bit 22.5° KOCH Loaded Line Phase Shifter

For the reduced size KOCH Fractal based single bit loaded line

phase shifter, the calculated design parameters are as shown in Table 2.3 for

the same specifications of conventional loaded line 22.5° phase shifter.

2.5.2.1 Simulation of Single Bit 22.5 KOCH Loaded Line Phase shifter

In the KOCH phase shifter layout, blocking capacitors and p-i-n

diodes are added and simulation is done for the ON and OFF condition

of the diodes as shown in Figure 2.12. These capacitors block the DC power

entering into the measuring equipment. The length of the short transmission

lines is tuned to obtain desired phase shift.

43

V_DCSRC1

Vdc=1.5 V

PinDiode2finalkochmergedfinalkochmerged_1ModelType=RF

PinDiode1

C12

TermTerm2

Z=50 OhmNum=2

Term

Term1

Z=50 Ohm

Num=1

S_Param

SP1

Step=5 MHzStop=3 GHz

Start=2 GHz

S-PARAMET ERS

C11

MSUBMSub1

Rough=0 umTanD=0.011

T=0.045 mmHu=1.0e+036 um

Cond=1.0E+50Mur=1Er=4.6

H=1.6 mm

MSub

Figure 2.12 Simulation of single bit 22.5 KOCH loaded line phase shifter

Figure 2.13 (a) shows that the insertion loss is less than -0.88 dB

for a frequency band of 2.2-2.6 GHz and return loss is less than -14 dB for the

same bandwidth for both ON and OFF condition of diode.

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-30

-28

-26

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

S-p

ara

mete

r (

dB

)

Frequency (GHz)

S11

ON

S11

OFF

S21

ON

S21

OFF

Figure 2.13(a) Simulated return loss and insertion loss of single bit 22.5

KOCH loaded line phase shifter

Figure 2.13(b) shows the simulated phase plot of single bit

22.5 KOCH loaded line phase shifter for on and off condition of the diodes.

44

The plot shows that the phase shift of 22.53 at 2.45 GHz with ± 2 band width

of 81.5MHz is achieved.

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-180.0

-157.5

-135.0

-112.5

-90.0

-67.5

-45.0

-22.5

0.0

22.5

45.0

67.5

90.0

112.5

135.0

157.5

180.0S

21(d

eg)

Frequency (GHz)

S21

OFF

S21

ON

Figure 2.13(b) Simulated phase plot of single bit 22.5 KOCH loaded line

phase shifter

Table 2.5 shows the simulated results of 22.5 KOCH loaded line

phase shifter. At the designed frequency of 2.45 GHz, the return loss is more

than 21 dB, insertion loss is less than 0.74 dB and the phase error is 0.03 .

Table 2.5 Simulation results of single bit 22.5 KOCH loaded line phase

shifter

Diode

state

S11

(dB)

S21

(dB)

S21

(degrees)

(ON phase-OFF phase)

Simulated Desired Phase Error

ON-

21.31

-

0.743122.8

-22.53 -22.5 -0.03

OFF-

25.91

-

0.628145.4

45

2.5.2.2 Design and simulation of equivalent circuit model of single bit

22.5 KOCH loaded line phase shifter

The equivalent circuit model for the KOCH loaded line phase

shifter is shown in Figure 2.14. The calculated equivalent circuit model

parameters of the KOCH fractal loaded line phase shifter are tabulated in

Table 2.6.

The circuit is simulated with all distributed components that are

represented in terms of their equivalent circuit form. A bias voltage of 1.5 V

is provided for diode ON condition whereas -20V for diode OFF condition.

The equivalent circuit is simulated in ADS Schematic simulator and the

results are shown in Figure 2.15 (a) and 2.15 (b).

Table 2.6 Component values of Equivalent circuit

Sl. No. Parameter Values

1 C1,C6 470pF

2 C3,C7 .32pF

3 C4 5.5pF

4 C8 .13pF

5 C9 .01pF

6 C10 .013pF

7 C11 .015pF

8 C13 .35pF

9 C12 .05pF

10 C16,C18,C20,C22 2.1pF

11 C14 3.3pF

12 L1 .65nH

13 L2 .7nH

14 L3 1.28nH

15 L5,L7,L8,L9,L10,L11,L12 2.1nH

16 L13,L14,L15 2.8nH

46

CC71

C=c4 pF

C

C7C=420 pF

CC51

C=c4 pF

C

C48

C=c4 pF

C

C64

C=c4 pF

CC65

C=c4 pF

CC74

C=c4 pF

C

C73

C=c4 pF

C

C72

C=c4 pF

L

L38

R=

L=l3 nH

L

L26

R=

L=l4 nH

S_Param

SP1

Step=3 MHz

Stop=2.8 GHzStart=2.2 GHz

S-PARAM ETERS

C

C8

C=420 pF

C

C3C=2.4188 pF {t}

L

L40

R=

L=l3 nH

L

L34

R=L=l3 nH

LL35

R=

L=l3 nH

L

L36

R=L=l3 nH

LL37

R=

L=l3 nH

L

L39

R=L=l3 nH

LL41

R=

L=l3 nH

L

L42

R=

L=l3 nH

L

L43

R=L=l3 nH

VAR

VAR1

c4=2.1

l4=2.1

l3=4.05

E q nV a r

L

L24

R=

L=l4 nH

LL25

R=

L=l4 nH

L

L22

R=L=l4 nH

L

L23

R=L=l4 nH

L

L20

R=

L=l4 nH

LL21

R=

L=l4 nHL

L18

R=L=l4 nH

L

L19

R=L=l4 nH

LL27

R=

L=l4 nH

L

L29

R=

L=l4 nH

L

L28

R=

L=l4 nH

LL31

R=

L=l4 nH

L

L30

R=L=l4 nH

L

L33

R=L=l4 nH

L

L32

R=L=l4 nH

C

C24

C=0.05 pF

C

C23C=0.05 pF

C

C20C=0.35 pF

C

C22

C=0.35 pF

V_DC

SRC1Vdc=-20 V

TermTerm2

Z=50 Ohm

Num=2TermTerm1

Z=50 Ohm

Num=1

L

L6

R=

L=26 nH {t}

C

C9C=1.269 pF {-t}

C

C10

C=1.269 pF {-t}

CC6

C=3.32 pF

CC12

C=0.13 pF

C

C13

C=0.1 pF

C

C14C=0.013 pF

C

C16

C=.013 pF

C

C17

C=0.1 pF

L

L12

R=L=0.7 nH

C

C18

C=.013 pF LL14

R=

L=0.7 nH

DCDC1

DC

L

L11

R=L=0.65 nH

L

L13

R=

L=0.65 nH

C

C15C=0.15 pF C

C19

C=0.15 pF

C

C11C=36.50027 pF {t}

C

C2

C=36.50027 pF {t}

Figure 2.14 Equivalent circuit of single bit 22.5 KOCH loaded line phase shifter

Diode

KOCH

Equivalent

Bias

Network

KOCH

Equivalent

Diode

47

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

S2

1(d

B)

Frequency (GHz)

S21

OFF

S21

ON

Figure 2.15(a) Simulated insertion loss of equivalent circuit model of

single bit 22.5 KOCH loaded line phase shifter

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-50

-40

-30

-20

-10

0

S1

1(d

B)

Frequency (GHz)

S11

OFF

S11

ON

Figure 2.15(b) Simulated return loss of equivalent circuit model of single

bit 22.5 KOCH loaded line phase shifter

The OFF state insertion loss is -0.6dB and ON state insertion loss is

about -1.6 dB .The return loss is less than -15 dB for ON state but for OFF

state it ranges from -10 dB to -40dB in the frequency range of 2.4-2.48GHz.

48

2.5.2.3 Fabrication of Single Bit 22.5 KOCH Loaded Line Phase

shifter

To validate the simulation results, a single bit 22.5° KOCH loaded

line phase shifter is fabricated on a FR-4 substrate (thickness of 1.6 mm;

dielectric constant r of 4.6 and loss tangent of 0.011) using a copper etching

process. Two p-i-n diodes (MA4P789-287 with SOT-23 package), capacitors

and SMA connectors are used in the circuit. The p-i-n diodes are ground

through holes by PTH. The phase shifter RF performance is measured using

Agilent ENA series E5062A vector network analyzer. The fabricated single

bit 22.5 KOCH loaded line phase shifter is shown in Figure 2.16.

Figure 2.16 Prototype of single bit 22.5 KOCH loaded line phase shifter

Figure 2.17(a) shows measursed S parameter performance. The

return loss is less than -13 dB for the entire band of 2.4-2.5GHz and insertion

loss ranges from -2.1 to -2.4 dB for ON and OFF condition. Figure 2.17 (b)

shows the measured phase plot of single bit 22.5 KOCH loaded line phase

shifter for ON and OFF condition of the diodes. The plot shows a phase shift

of 22.35 at 2.45 GHz with ±2 band width of 100MHz.

49

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-30

-28

-26

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

S-p

ara

met

er (

dB

)

Frequency (GHz)

S11

ON

S11

OFF

S21

ON

S21

OFF

Figure 2.17(a) Measured return loss and insertion loss of single bit

22.5 KOCH loaded line phase shifter

2.40 2.41 2 .42 2.43 2.44 2.45 2.46 2.47 2 .48 2.49 2.50

-200

-150

-100

-50

0

50

100

150

200

S2

1 (

deg

)

Frequency (G H z)

S21

O N

S21

OFF

Figure 2.17(b) Measured phase of single bit 22.5 KOCH loaded line

phase shifter

50

Table 2.7 Measured results of single bit 22.5 KOCH loaded line phase

shifter at 2.45GHz

Diode

state

S11

(dB)

S21

(dB)

S21

(degrees)

(on phase-off phase)

Simulated DesiredPhase

Error

ON -17.74 -2.206 -75.119-22.35 -22.5 0.15

OFF -21.70 -2.126 -52.765

The Table 2.7 shows the Measured results of 22.5 KOCH loaded

line phase shifter. At the designed frequency 2.45 GHz, the return loss is less

than -17 dB, insertion loss is less than -2.2 dB and the phase error is 0.15 .

2.6 DESIGN OF 3 BIT CONVENTIONAL LOADED LINE

PHASE SHIFTER

Specifications

Frequency of operation (f) = 2.45 GHz

Desired Phase shift ( ) = 22.5 ,45 ,67.5 ,90 ,112.5 ,135 ,157.5

Bandwidth = 80MHz (2.4 - 2.48GHz)

Z0 =50 and = 90

A 3 bit conventional loaded line phase shifter layout for the above

stated specification is designed as per the design parameter stated in Table

2.1.and using ADS(Advanced design suit) software. The layout is shown in

Figure 2.18.

51

Figure 2.18 Layout of 3 bit conventional loaded line phase shifter.

2.7 DESIGN AND SIMULATION OF 3 BIT KOCH LOADED

LINE PHASE SHIFTER

KOCH fractals are applied to shunt quarter wave transmission line

and bias line of different sections (22.5 , 45 and 90 ) of conventional loaded

line Phase shifter layout with 0.2 iteration factor. The iteration order of two is

applied to 22.5 phase shifter section and iteration order of one is applied to

45 and 90 phase shifter sections. Simulation layout of 3 bit KOCH loaded

line Phase shifter is shown in Figure 2.19 .

Figure 2.19 Simulation of 3 bit KOCH loaded line phase shifter

52

2.7.1 Simulation of 3 Bit KOCH Loaded Line Phase Shifter

Figure 2.20(a) shows the simulated performance of return loss. It

shows return loss for all the phase bits are less than -15dB for the desired

frequency band 2.4 – 2.48 GHz.

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50-30

-25

-20

-15

S11

(000)

S11

(001)

S11

(010)

S11

(011)

S11

(100)

S11

(101)

S11

(110)

S11

(111)

S11 (

dB

)

F requency (G H z)

Figure 2.20(a) Simulated return loss of 3 bit KOCH loaded line phase

shifter

2 .40 2 .41 2 .42 2 .43 2 .44 2 .45 2 .46 2 .47 2 .48 2 .49 2 .50-2 .00

-1 .75

-1 .50

S21

(d

B)

F requ ency (G H z)

S2 1

(0 0 0 )

S2 1

(0 0 1 )

S2 1

(0 1 0 )

S2 1

(0 1 1 )

S2 1

(1 0 0 )

S2 1

(1 0 1 )

S2 1

(1 1 0 )

S2 1

(1 1 1 )

Figure 2.20(b) Simulated insertion loss of 3 bit KOCH loaded line phase

shifter

53

Figure 2.20 (b) shows the simulated insertion loss performance of 3

bit KOCH loaded line phase shifter. It shows a variation of insertion loss from

-1.68 dB to -2dB for various phase bits in the desired band of 2.4GHz to

2.48GHz.

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-200

-150

-100

-50

0

50

100

150

200

S2

1 (

deg

)

Frequency (GHz)

S21

(000)

S21

(001)

S21

(010)

S21

(011)

S21

(100)

S21

(101)

S21

(110)

S21

(111)

Figure 2.20 (c) Simulated phase plot of 3 bit KOCH loaded line phase

shifter

Figure 2.20(c) shows the simulated phase performance of 3 bit

KOCH loaded line phase shifter. All the phase bits are linear in the desired

band width of 2.4GHz to 2.48GHz. It also shows that least significant bits

22.5 and 45 bits are linear over 2.2 to 2.8GHz.

Table 2.8 shows the simulated results of 3 bit KOCH loaded line

phase shifter. At the designed frequency of 2.45 GHz, the return loss is more

than 19.5 dB, insertion loss is less than 1.95 dB and a maximum phase error is

1.35 for 111 phase bit.

Phase shift = 126.594 -(-76.779 )=203.373

= 360 -203.373 = 156.627

54

Table 2.8 Simulated results of three bit KOCH loaded line phase shifter

at 2.45 GHz

Bit

InputS11 (dB) S21 (dB)

S21

(degrees)

(ON phase-OFF phase)

Obtained DesiredPhase

Error

000 -23.384 -1.658 -77.243 - - -

001 -26.206 -1.673 -99.733 22.49 22.5 .01

010 -22.129 -1.749 -121.51 44.274 45 0.726

011 -25.048 -1.762 -143.92 66.68 67.5 0.8

100 -19.870 -1.851 -167.31 90.071 90 0.071

101 -21.515 -1.867 170.301 112.45 112.5 0.05

110 -19.551 -1.951 148.965 133.79 135 1.21

111 -23.244 -1.954 126.606 156.15 157.5 1.35

2.7.2 Fabrication and Testing of 3 bit KOCH Loaded Line Phase

Shifter

The simulation results are validated by fabricating the circuits on a

commercially available low cost FR-4 substrate using wet etching process.

The mask necessary for the fabrication is directly generated by the simulator.

Blocking capacitors, p-i-n diodes and SMA connectors are hand soldered.

The RF performance of the fabricated Phase shifter is measured

using Agilent ENA series E5062A Vector network analyzer. The fabricated

prototype of the 3-bit KOCH loaded line phase shifter is shown in

Figure 2.21.

55

Figure 2.21 Fabricated prototype of 3 bit KOCH loaded line phase shifter

2.7.3 Measured Results of 3 Bit KOCH Loaded Line Phase Shifter

Figure 2.22(a) shows the performance of return loss .The return

loss is -10dB for 100 phase bit and less than -10dB for other phase bits in the

band of 2.4 to 2.48GHz.

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-40

-35

-30

-25

-20

-15

-10

S1

1(d

B)

Frequency (GHz)

S11

(000)

S11

(001)

S11

(010)

S11

(011)

S11

(100)

S11

(101)

S11

(110)

S11

(111)

Figure 2.22(a) Measured return loss of 3 bit KOCH loaded line phase

shifter

56

Figure 2.22(b) shows the performance of insertion loss. Minimum

insertion loss for the desired band is -1.45dB for 000 and 001phase bit and

maximum is -3.28 dB for 110 phase bits.

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50-3.5

-3.0

-2.5

-2.0

-1.5

-1.0 S

21(000)

S21

(001)

S21

(010)

S21

(011)

S21

(100)

S21

(101)

S21

(110)

S21

(111)

S21(d

B)

Frequency (GHz)

Figure 2.22(b) Measured Insertion loss of 3 bit KOCH loaded line phase

shifter

Figure 2.22 (c) shows the performance of S21 phase of 3 bit KOCH

loaded line phase shifter. It shows that all the phase bits are linear for the

desired band width 2.4 -2.48 GHz. It is also observed that phase shifts of LSB

phase bits are more linear than that of the MSB phase bits.

Figure 2.22 (d) shows the phase shift performance of 3 bit KOCH

loaded line phase shifter. The ±2 band width is satisfied for all phase bits

except 110 and 111 phase bits. ± 5 band width is satisfied for 110 and 111

phase bit.

57

2.2 2.4 2.6 2.8

-180.0

-157.5

-135.0

-112.5

-90.0

-67.5

-45.0

-22.5

0.0

22.5

45.0

67.5

90.0

112.5

135.0

157.5

180.0S

21

(d

eg

)

Frequency (GHz)

S21

(000)

S21

(001)

S21

(010)

S21

(011)

S21

(100)

S21

(101)

S21

(110)

S21

(111)

Figure 2.22(c) Measured phase plot of 3 bit KOCH loaded line phase

shifter

2.2 2.3 2.4 2.5 2.6 2.7 2.8-180.0

-157.5

-135.0

-112.5

-90.0

-67.5

-45.0

-22.5

0.0

22.5

45.0

67.5

90.0

112.5

135.0

157.5

180.0

Ph

ase

sh

ift

(deg

)

Frequency (GHz)

S21

(001)

S21

(010)

S21

(011)

S21

(100)

S21

(101)

S21

(110)

S21

(111)

Figure 2.22(d) Measured phase shift of 3 bit KOCH loaded line phase

shifter

58

Table 2.9 shows the measured values of 3 bit KOCH loaded line

phase shifter at the design frequency of 2.45 GHz. It shows that minimum

phase error is 0.2° for 101 phase bit and maximum phase error is 2.16° for

111 phase bit.

Table 2.9 Measured results of three bit KOCH loaded line phase shifter

at 2.45GHz

Bit

Input

S11

(dB)

S21

(dB)

S21

(deg)

(ON phase-OFF

phase)Phase error

Obtained Desired

000 -21.38 -1.45 39.47 - - -

001 -36.20 -2.14 16.10 -22.37 -22.5 0.87

010 -13 -2.5 -7.46 -46.94 -45 1.94

011 -11.42 -2.62 -29.3 -68.79 -67.5 1.29

100 -10.33 -2.96 -51.96 -91.44 -90 1.44

101 -10.95 -2.95 -73.22 -112.7 112.5 0.2

110 -11.65 -3.12 -93.93 -133.42 -135 1.58

111 -10.09 -2.90 -115.85 -155.34 -157.5 2.16

2.8 RF PERFORMANCE COMPARISON OF SINGLE BIT

CONVENTIONAL AND SINGLE BIT KOCH LOADED LINE

PHASE SHIFTERS

The layout simulation, equivalent circuit model simulation and

measured responses of the single bit KOCH 22.5 phase shifter are depicted in

Figure 2.23(a) and (b). The return loss for all condition ranges from -10 dB to

-45 dB. The variation in return loss is due to substrate parameter ( r, h, tan )

variations. The simulated insertion loss for on and off condition is less than -

0.68dB whereas the measured one is less than -2.4dB. This variation of -1.7 dB in

59

the ON and OFF condition is due to soldering, connector losses, and deviation

in substrate loss between the simulated and practical one.

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-50

-40

-30

-20

-10

0

S1

1(d

B)

Frequency (GHz)

S11

ON(Equivalent circuit model)

S11

OFF(Equivalent circuit model)

S11

ON(Measurement)

S11

OFF(Measurement)

S11

ON(Simulation)

S11

OFF(Simulation)

Figure 2.23(a) Simulated, equivalent circuit model and measured return

loss of single bit 22.5 KOCH loaded line phase shifter

2.40 2.42 2.44 2.46 2.48 2.50

-5

-4

-3

-2

-1

0

S2

1(d

B)

Frequency (GHz)

S21

ON(simulation)

S21

OFF(Simulation)

S21

ON(Maesurement)

S21

OFF(Measurement)

S_21offeqS21

ON(Equivqlent circuit model)

S_21offeqS21

OFF(Equivqlent circuit model)

Figure 2.23(b) Simulated, equivalent circuit model and measured

insertion loss of single bit 22.5 KOCH loaded line phase

shifter

60

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-33.75

-22.50

-11.25

0.00

Ph

ase

sh

ift

(deg

)

Frequency (GHz)

Equivqlent circuit model

Measurement

Simulation

Figure 2.23(c) Comparison of Phase shift of single bit KOCH 22.5 phase

shifter

The phase shift performance of layout simulation, equivalent circuit

model and measured ones are compared in Figure 2.22(c). The performances

are within the tolerance range of ±2 in the desired band of 2.4 to 2.48 GHz.

2.9 RF PERFORMANCE OF 3 BIT KOCH LOADED LINE

PHASE SHIFTERS

Figure 2.24(a) and (b) shows the comparison between simulated

and measured performance of return and insertion losses respectively. The

simulated return loss varied between -15dB and -30dB for all eight states

where as the measured one varied between -10dB and -15dB except two LSB

states. This is due to parameter variation of the substrate between simulated

and actual values. The simulated insertion loss varied between -1.5dB and -

2dB where as measured ones varied between -1.5dB and -3.25dB. This is due

to tangent loss variation between the values used in simulation and actual

values and radiation losses.

61

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-40

-30

-20

-10

S1

1(d

B)

Frequency (GHz)

000_Simulated

001_Simulated

010_Simulated

100_Simulated

111_Simulated

000_Measured

001_Measured

010_Measured

100_Measured

111_Measured

Figure 2.24(a) Simulated and measured return loss of the 8 states of

3 bit KOCH loaded line phase shifter

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

S21(d

B)

Frequency (GHz)

000_Simulated

001_Simulated

010_Simulated

100_Simulated

111_Simulated

000_Measured

001_Measured

010_Measured

100_Measured

111_Measured

Figure 2.24(b) Simulated and measured insertion loss of the 8 states of 3

bit KOCH loaded line phase shifter

62

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-180.0

-157.5

-135.0

-112.5

-90.0

-67.5

-45.0

-22.5

0.0

Ph

ase

sh

ift

(deg

)

Frequency (GHz)

Simulation

Measurement

Figure 2.24(c) Simulated and measured phase shift of the 8 states of 3

bit KOCH loaded line phase shifter

Comparison of simulated and measured phase shift values of 3 bit

KOCH loaded line phase shifter for the desired band 2.4 to 2.48 GHz is shown in

Figure 2.24 (c).The plot shows that there is good agreement between the two.

Simulated and measured phase errors for KOCH phase shifter are minimal.

2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50

-180.0

-157.5

-135.0

-112.5

-90.0

-67.5

-45.0

-22.5

0.0

Ph

ase

sh

ift

(deg

)

Frequency (GHz)

Koch

Conventional

Figure 2.25 Measured phase shift comparison between KOCH and

conventional loaded line phase shifter for all the 8 states

63

Figure 2.25 shows that the KOCH phase shifter performance is

better than the conventional one in all the phase states.

Figure 2.26 Comparison of Conventional and KOCH three bit loaded

line phase shifters

By applying KOCH, the electrical length in the transverse direction

is reduced. Thus, a miniaturization of 41.88% for single bit and 44% for 3-bit

phase shifter shown in Figure 2.26 is achieved. By using KOCH, a Band

width increase of 19.75 MHz achieved for single bit 22.5 phase bit.

The lower phase bits like 22.5 and 45 are generally realized with

loaded line phase shifter because it offers low insertion loss for these phase

bits. The lower phase bits are investigated for the band 2.3-2.8 GHz to find

out the phase error bandwidth and return loss bandwidth simultaneously

(Xinyi and Koenraad 2010 b). The bandwidth is calculated for ±2 phase error

and -10dB return loss for 22.5 phase bit and 45 phase bit of 3 bit

conventional and KOCH phase shifter.

64

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-6

-5

-4

-3

-2

-1

0

1

2

3

Phase Error

Return Loss

Frequency (GHz)

Ph

ase

Err

or

(deg

)

-40

-35

-30

-25

-20

-15

-10

-5

0

S11

(dB

)

Figure 2.27(a) Relationship between phase error, return loss and

frequency of 22.5° phase bit for conventional three bit

phase shifter

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-8

-6

-4

-2

0

2

4

Phase Error

Return Loss

Frequency (GHz)

Ph

ase

Err

or

(deg

)

-40

-35

-30

-25

-20

-15

-10

-5

0

S11(d

B)

Figure 2.27(b) Relationship between phase error, return loss and

frequency of 22.5° phase bit for KOCH three bit phase

shifter

65

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

Phase Error

Return Loss

Frequency (GHz)

Ph

ase

Err

or

(deg

)

-30

-25

-20

-15

-10

-5

0

S11

(dB

)

Figure 2.27(c) Relationship between phase error, return loss and

frequency for 45° phase bit of conventional three bit

phase shifter

2.2 2.3 2.4 2.5 2.6 2.7 2.8

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

Phase Error

return Loss

Frequency (GHz)

Ph

ase

Err

or

(deg

)

-30

-25

-20

-15

-10

-5

0

S11

(dB

)

Figure 2.27(d) Relationship between phase error, return loss and

frequency of 45° phase bit for KOCH three bit phase

shifter

66

From Figure 2.27(a), (b), (c) and (d) the bandwidth is calculated

and tabulated in Table 2.10.

Table 2.10 Bandwidth comparison of conventional and KOCH 22.5º

and 45º phase bits of 3 Bit loaded line phase shifter

Phase Bit

(in degrees)

Band width (MHz)

Conventional KOCH % increased

22.5 300 348 16

45 180 203 12.8

2.10 CONCLUSION

In this chapter the issue of miniaturization has been addressed using

the concept of fractal geometry. To start with single bit KOCH fractal based

loaded line phase shifter is designed and developed. The simulation results at

2.45GHz show an insertion of - 0.743dB, return loss of -21.3dB and a phase

error of -0.03°.The measured results at 2.45GHz show an insertion loss of -

2.2dB, return loss of -21.7 dB and a phase error 0.15°.While comparing the

simulation and measurement results the return loss remains same in both the

cases.The increase in insertion loss and phase error may be due to loss

tangent variation of dielectric material used.

Next a the 3 bit KOCH fractal based loaded line phase shifter is

designed and developed. The simulation results at 2.45GHz show an average

insertion loss of -1.81 dB for all the 8 phase states. A worst case return loss of

-19.55dB and maximum phase error of -1.35° when all diodes are in ON state.

The measured results show an average insertion loss of -2.58 dB , a worst

case return loss of -10.09dB and a phase error of 2.16° when all diodes are in

ON state. The deviation in the insertion loss and phase error is due to loss

67

tangent variation of the FR-4 substrate and variation in the return loss may be

due to discontinuities arising out of the manufacturing tolerances. However

the RF performance of the 3 bit KOCH loaded line phase shifter is found to

be feasible for the WLAN applications.

KOCH fractal based 3 bit loaded line phase shifter offers a size

reduction of 44%(miniaturization) and band width increment of 16% and

12.8% for 22.5° and 45° phase bits respectively. It is observed that the size

reduction (miniaturization)has been achieved without sacrificing the RF

performance 3 bit KOCH fractal based loaded line phase shifter.