project report of phase shifter

7/31/2019 Project Report of Phase Shifter

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PHASE SHIFTING ANTENNA DESIGN BY

USING PIN DIODE

FOR ELE 401-402

Hacettepe University

Department of Electrical and Electronics Engineering

Prepared For: PROF. Birsen SAKA

Prepared By: Mmin ZPOLAT

Spring 2012


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ii

ABSTRACTThis report contains considerations for pin diode phase shifters used for phased array antenna

control. The categories are areas in which ferrite and diode phase shifters differ.The structure

and usage areas of pin diode are presented.Switched line phase shifter, loaded line phase

shifter and reflection type phase shifter circuits examined in terms of phase shift, insertion

loss, bandwidth especially from 500 MHZ to 8 GHZ.Mathematical derivations and

simulations of these phase shifters are evaluated and presented to clarify working principle of

phase shifting circuits.


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iii

ACKNOWLEDGEMENTS

Many thanks are due my project advisor, Professor Birsen Saka, for her guidance,

encouragement and mentorship.Especially, her understanding attitude during my difficult

times is very important and memorable to me. I should also appreciate my gratitude to

Metehan Bulut for his helpful attitude, guidance and contribitions for realizing circuit.Also

special thanks is necessary to Burhan Erdemli who helped me to obtain pin diodes.


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iv

TABLE OF CONTENTS

ABSTRACT ......................................................................................................................... ii

ACKNOWLEDGEMENTS................................................................................................ iii

TABLE OF CONTENTS ................................................................................................... iv

TABLE OF FIGURES ...................................................................................................... vii

ABSTRACT .................................................................................................................................................... iiACKNOWLEDGEMENTS ........................................................................................................................... iiiTABLE OF CONTENTS ............................................................................................................................... ivTABLE OF FIGURES ................................................................................................................................... vi1.INTRODUCTION........................................................................................................................................ 1

1.1 Phased Array Antenna System ................................................................................................................. 11.1.1 Linear Array .................................................................................................................................... 11.1.2 Planar Array .................................................................................................................................... 21.1.3 Frequency Scanning Array ............................................................................................................... 2

2.PHASE SHIFTERS...................................................................................................................................... 32.1 Overview of Phase Shifters................................................................................................................. 32.2 Phase Shifters: Related Design Issues ...................................................... ............................................... 52.3 Pin Diode ............................................................................................................................................... 62.4 S Parameters .......................................................................................................................................... 72.5 Microstrip Calculations .......................................................................................................................... 92.6 Digital Phase Shifter ............................................................................................................................. 112.7 Switched Line Phase Shifter .................................................................................................................. 11

2.7.1 Mathematical Derivation ................................................................................................................ 122.7.2 Simulations .................................................................................................................................... 15

2.8 Loaded Line Phase Shifter..................................................................................................................... 302.8.1 Mathematical Derivation ................................................................................................................ 312.8.2 Simulations .................................................................................................................................... 33

2.9 Reflection Type Phase Shifter ................................................................................................................ 402.9.1 Mathematical Derivation: ............................................................................................................... 41


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2.9.2 Simulations .................................................................................................................................... 442.10 Implemented Circuit ............................................................................................................................ 46

3.CONCLUSION .................................................................... ...................................................................... 504.REFERENCES .......................................................................................................................................... 515.APPENDICES ............................................................................................................................................ 52

Datasheet of Pin Diode ............................................................................................................................... 52


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vi

TABLE OF FIGURES

Figure Page

1.1 Linear phased array ........................................................................................................2

1.2 Planar array....................................................................................................................2

2.1 Stucture of pin diode ......................................................................................................6

2.2 Pin diode current vs ressistance ......................................................................................7

2.3 S parameters ..................................................................................................................7

2.4 Microstrip calculation .................................................................................................. 10

2.5 Digital phase shifter ..................................................................................................... 11

2.6 Switched line phase shifter ........................................................................................... 12

2.7 Switched line phase shifter circuit diagram at ADS ...................................................... 14

2.8 22.5 degree phase shift at 500 MHZ ............................................................................. 15

2.9 45 degree phase shift at 500 MHZ ................................................................................ 16

2.10 22.5 degree phase shift at 750 MHZ ........................................................................... 17

2.11 45 degree phase shift at 750 MHZ .............................................................................. 19

2.12 22.5 degree phase shift at 1 GHZ ............................................................................... 19

2.13 45 degree phase shift at 1 GHZ ................................................................................... 21





2.18 Phase shift vs frequency for 22.5 degree switched line phase shifter ........................... 26

2.19 Phase shift vs frequency for 45 degree switched line phase shifter .............................. 262.20 Insertion loss for 22.5 degree phase shift ..................................................................... 27

2.21 Insertion loss for 45 degree phase shift ....................................................................... 27

2.22 Reflection coefficients vs frequency for 22.5 degree phase shift .................................. 27

2.23 Reflection coefficients vs frequency for 45 degree phase shift ..................................... 27

2.24 Input return loss vs frequency for 22.5 degree phase shift ........................................... 28

2.25 Input return loss vs frequency for 45 degree phase shift .............................................. 28

2.26 Two bit application ..................................................................................................... 28


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2.27 45 degree phase shift at 750 MHZ ............................................................................... 29

2.28 Loaded line phase shifter ............................................................................................ 31

2.29 Loaded line phase shifter-ABCD matrix...................................................................... 31

2.30 Main line mounted ...................................................................................................... 32

2.31 Loaded line phase shifter state 1 ............................................................................... 33

2.32 Loaded line phase shifter - state 2 ............................................................................... 33


2.34 23 degree phase shift at 500 MHZ ............................................................................... 35




2.38 Reflection type phase shifter ....................................................................................... 39

2.39 Lange coupler geometry .............................................................................................. 42

2.40 Reflection type phase shifter ADS simulation state 1 .................................................. 44

2.41 Reflection type phase shifter ADS simulation state 2 .................................................. 44


2.43 Incremential line phase shifter..................................................................................... 46

2.44 Implemented circuit .................................................................................................... 47

2.45 Graph of phase shift .................................................................................................... 482.46 Graph of S21............................................................................................................... 48


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Figure 1.1: Linear phased array

1.1.2 Planar Array

These antenna arrays completely consist of singles radiating elements and each of it gets an

own phase shifter. The elements are ordered in a

matrix array. The planar arrangement of all

elements forms the complete phased-array

antenna.

Advantages: Beam steering in two planes or

even the digital beamforming is possible.

Disadvantage: Complicated arrangement and

more electronically controlled phase shifter

needed .

1.1.3 Frequency Scanning Array

Frequency scanning is a special case of the phased array antenna where the main beam

steering occurs by the frequency scanning of the exciter. The beam stearing is a function of

the transmitted frequency. This type of antenna is called a frequency scanning array. The

normal arrangement is to feed the different radiating elements from one folded waveguide.

The frequency scanning array is a special case of serial feeding type of a phased array

antenna and is based on a particular property of wave propagation in waveguides. The phase

difference between two radiating elements is n360 at the normal frequency.

Figure 1.2: Planar array
http://www.radartutorial.eu/06.antennas/an51.en.htmlhttp://www.radartutorial.eu/06.antennas/an51.en.html


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By changing the frequency, the angle s between the axis of the main beam and the normal

on the array antenna changes. Height information is generated using the following

philosophy:

If the transmitted frequency rises then the beam travels up the face of the antenna;

If the transmitted frequency falls then the beam travels down the face of the antenna.

As frequency is varied, the beam axis will change, and scanning can be accomplished in

elevation. The radar set is designed so that it keeps track of the frequencies as they are

transmitted and then detects and converts the returned frequencies into 3D display data.

2.PHASE SHIFTERS

2.1 Overview of Phase Shifters

The three basic techniques for electronic beam steering are (1) frequency scanning, (2) beam

switching, and (3) phase scanning with phase shifters. Of the three techniques, the use of

phase shifters is by far the most popular, and considerable effort has gone into the

development of a variety of phase shifters. Phase shifters can be separated into two

categories: reciprocal and nonreciprocal. The reciprocal phase shifter is not directionally

sensitive. That is, the phase shift in one direction (e.g., transmit) is the same as the phase shift

in the opposite direction (e.g., receive). Therefore, if reciprocal phase shifters are used, it is

not necessary to switch phase states between transmit and receive. With a nonreciprocal phase

shifter, it is necessary to switch the phase shifter (i.e., change phase state) between transmit

and receive.

All diode phase shifters are reciprocal along with certain types of ferrite phase shifters. It is

worth noting that, owing to losses associated with their magnetic properties, ferrite phase

shifters are almost never used at frequencies below 3 GHz. Diode phase shifters, in contrast,

improve as the frequency gets lower.

There are three basic types of phase shifters that typically compete for use in a phased array.

They are (1) the diode phase shifter, (2) the nonreciprocal ferrite phase shifter, and (3) the

reciprocal (dual-mode) ferrite phase shifter. Each has its strengths, and the choice of which to

use is highly dependent on the radar requirements. Each will be discussed in turn. For solid-

state systems, diodes are used and can be switched in a fraction of a microsecond.


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Diode Phase Shifters: Diode phase shifters are typically designed by using one of three

techniques: (1) switched-line, (2) hybrid-coupled, and (3) loaded-line. The switched-line

technique simply switches in lengths of line in binary increments (e.g., 180, 90, and 45)

and requires a set of diodes for each bit. The diodes are used as switches to control which bits

are activated to achieve a particular phase state.

The hybrid-coupled technique uses a microwave hybrid and effectively changes the distance

at which the reflection takes place. This technique is usually used in binary increments, and

an additional set of diodes is required for each phase state.

The diode phase shifters described above are limited in their ability to handle high peak

power. Depending on their size and frequency, they are normally restricted to power levels of

less than 1 kW. For higher power levels, the loaded-line technique is used. The diodes are

used to switch in increments of capacitance and inductance that provide small changes in

phase. Because the diodes are decoupled from the main transmission line, they need to handle

only modest amounts of power in each diode. Very high power (i.e., kilowatt) configurations

are possible. The technique does require many diodes, and the phase shifters are typically

large and bulky as compared with the switched-line and hybrid-coupled techniques.

Diode phase shifters have the advantage of being small and light in weight (except for high-

power devices). They are suitable for stripline, microstrip, and monolithic configurations. The

main disadvantage of the diode phase shifter is that an additional set of diodes is normally

required for each additional bit. As lower-sidelobe antennas are required, the number of bits

increases. For low sidelobe antennas, 5, 6, or 7 bits may be required. As the number of bits

increases, both cost and loss of the diode phase shifters are also increased. For active arrays,

the phase shifter losses are not of significance because they occur prior to the power amplifier

on transmit and after the low-noise amplifier on receive. This is not the case with most ferrite

devices.

Ferrite Phase Shifters: Most ferrite phase shifters are nonreciprocal,and their early versions

used discrete lengths of ferrite (as shown in Figure 13.35) to implement each of the bits

(180, 90, 45, etc.). In this configuration, a current pulse is passed through each bit, and the

ferrite toroid is saturated. When the current is removed, the ferrite toroid is said to belatched

and retains its magnetization owing to its hysteresis properties. If the current is in a forward

direction, the ferrite is latched with a particular phase (e.g., 180). The ferrite maintains thephase until a current pulse in the opposite direction is applied. The ferrite phase shifter is then


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latched to the reference phase (0). This change in phase with a change in current direction is

due to the nonreciprocal nature of the device.Other phase shifters use a single toroid and a

single driver. In this configuration, the phase shifter is latched on a minor hysteresis loop by

only partially magnetizing the ferrite. The distinct advantage of this technique is that any

number of bits may be implemented while using only a single toroid. They have the

advantage of low loss and relatively high power operation. Devices that handle up to 100 kW

of peak power have been built. They are amenable to waveguide construction and are heavier

and bulkier than comparable diode devices.

In summary, diodes and nonreciprocal ferrite phase shifters are viable competitors. At L band

and lower, diode phase shifters are an obvious choice. At S band and higher, ferrites should

continue to hold an edge in higher-power systems and where additional bits are needed forthe low phase errors required for low-sidelobe antennas. These comments do not apply for

the solid-state systems described below. Ferrite phase shifters are more temperature-sensitive

than diodes, and the phase will change with a change in temperature. This can be controlled

by keeping the temperature constant (within a few degrees) across the array. A more common

technique is to sense the temperature at several locations in the array and then correct the

phase commands to the phase shifters[3].

2.2 Phase Shifters: Related Design Issues

One of the essential components of a phased array system is the phase shifter. It can be

implemented by various means, but the performance of phase shifters is mainly judged by the

following factors:

a. Frequency range

b. Insertion loss

c. Input return loss

d. Output return loss

e. Phase error

f. Linearity

g. Control voltage-current. [4]


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2.3 Pin Diode

A PIN diode is a semiconductor device that operates as a variable resistor at RF and

microwave frequencies. The resistance value of the PIN diode is determined only by the

forward biased dc current. In switch and attenuator applications, the PIN diode should ideally

control the RF signal level without introducing distortion which might change the shape of the

RF signal.An important additional feature of the PIN diode is its ability to control large RF

signals while using much smaller levels of dc excitation. When the forward bias control

current of the PIN diode is varied continuously, it can be used for attenuating, leveling, and

amplitud modulating an RF signal. When the control current is switched on and off, or in

discrete steps, the device can be used for switching, pulse modulating, and phase shifting an

RF signal. In addition, the PIN diode has the ability to control large RF signal power while

using much smaller levels of control power.

Figure 2.1: Stucture of pin diode

A drawing of a PIN diode chip is shown in Figure. The performance characteristics of the PIN

diode depend mainly on the chip geometry and the processed semiconductor material in the

intrinsic or I -region, of the finished diode. When the diode is forward biased, holes and

electrons are injected into the I-region. This charge does not recombine instantaneously, but

has a finite lifetime ( t ) in the I-region. If the PIN diode is reverse biased , there is no stored

charge in the I-region and the device behaves like a Capacitance (CT) shunted by a parallel

resistance (RP). If the d-c voltage across the PIN diode is zero, there remains some finite


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charge stored in the I-region, but it is not mobile. If operated at zero volts dc, any PIN diode

behaves as a somewhat lossy Capacitor. Some small dc Voltage (called the "punch-through"

Voltage) must be applied to the I-region to sweep out this remaining fixed charge. The

forward biased PIN diode behaves as a current controlled resistor that presents a linear

resistance to the flow of RF current through the diode. This is the property of a PIN diode that

enables the device to be used as the RF power control element in linear attenuators and

modulators. [5]

Figure 2.2: Pin diode current vs ressistance

2.4 S Parameters

In Advanced Design System (ADS) , simulation results are showed in terms of s parameters

so it is necessary to review of formulas of s parameters.However it is possible to show phase

shift in time domain, it is not possible to measure phase shift, insertion loss etc.So it is

necessary to be familiar with S parameters.


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Figure 2.3: S parameters

Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix)

describe the electrical behavior oflinear electrical networks when undergoing various steady

statestimuli by electrical signals.

1 111 12

21 222 2

b aS SS Sb a

=

1 111

1 1

b VS

a V

+= =

and

2 221

1 1

b VS

a V

+= =

1 112

2 2

b VS

a V

+= =

and

2 222

2 2

b VS

a V

+= =

Scalar Logarithmic Gain

The scalar logarithmic (decibel or dB) expression for gain (g) is

2120 log | |g S= dB (0.1)

This is more commonly used than scalar linear gain and a positive quantity is normally

understood as simply a 'gain'. A negative quantity can be expressed as a 'negative gain' or

more usually as a 'loss' equivalent to its magnitude in dB. For example, a 10 m length of cablemay have a gain of - 1 dB at 100 MHz or a loss of 1 dB at 100 MHz.

Insertion Loss

In case the two measurement ports use the same reference impedance, the insertion loss (IL)

is the dB expression of the transmission coefficient21| |S . It is thus given by:

2120 log | |IL S= dB (0.2)

It is the extra loss produced by the introduction of the DUT between the 2 reference planes of

the measurement. Notice that the extra loss can be introduced by intrinsic loss in the DUT

and/or mismatch. In case of extra loss the insertion loss is defined to be positive.
http://en.wikipedia.org/wiki/Linearhttp://en.wikipedia.org/wiki/Electrical_networkhttp://en.wikipedia.org/wiki/Steady_statehttp://en.wikipedia.org/wiki/Steady_statehttp://en.wikipedia.org/wiki/Steady_statehttp://en.wikipedia.org/wiki/Steady_statehttp://en.wikipedia.org/wiki/Electrical_networkhttp://en.wikipedia.org/wiki/Linear


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Input Return Loss

Input return loss (inRL ) is a scalar measure of how close the actual input impedance of the

network is to the nominal system impedance value and, expressed in logarithmic magnitude,is given by

21| 20 log | ||inRL S= dB (0.3)

By definition, return loss is a positive scalar quantity implying the 2 pairs of magnitude (|)

symbols. The linear part, |11 |S is equivalent to the reflected voltage magnitude divided by the

incident voltage magnitude.

Voltage Reflection Coefficient

The voltage reflection coefficient at the input port (in

) or at the output port ( out ) are

equivalent to11S and 22S respectively, so 11in S = and 22out S =

As11S and 22S are complex quantities, so are in and out .

2.5 Microstrip Calculations

It is neccesary to learn how to specify and design microstrip properties so formulas used

which is shared below.The microstrip is a very simple yet useful way to create a transmission

line with a PCB. There are some advantages to using a microstrip transmission line over other

alternatives. Modeling approximation can be used to design the microstrip trace. By

understanding the microstrip transmission line, designers can properly build these structures

to meet their needs. A microstrip is constructed with a flat conductor suspended over a ground

plane. The conductor and ground plane are seperated by a dielectric. The suface microstrip

transmission line also has free space (air) as the dielectric above the conductor. This structure

can be built in materials other than printed circuit boards, but will always consist of a

conductor seperted from a ground plane by some dielectric material.

Microstrip Design Equations:

1 1 1

2 21 12

r reff

d

W

+ = +

+


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( )

0

60 8ln for W/d 1

4

120for W/d 1

/ 1.393 0.667ln / 1.444

r

r

d W

W dZ

W d W d

+

=

+ + +

2

2

0

8for W/d < 2

2

12 0.611 ln(2 1) ln( 1) 0.39 for W/d > 2

2

where

1 1

60 2

A

A

r

r r

r r

r

e

eW

dB B B

ZA

= + +

+ = +

0

0.110.23

1

377

2

r

r

BZ

+

+

=

But for calculation convenience, it is useful to use websites which is designed for this purpose

like:

http://www1.sphere.ne.jp/i-lab/ilab/tool/ms_line_e.htm

Figure 2.4: Microstrip calculation
http://www1.sphere.ne.jp/i-lab/ilab/tool/ms_line_e.htmhttp://www1.sphere.ne.jp/i-lab/ilab/tool/ms_line_e.htm


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2.6 Digital Phase Shifter

Digital phase shifter creates different phase shift according to different input control bits.

Normally, a binary array of phase shift bits is used to be compatible with computer control

requirements and give the greatest selection of phase states with the lowest number of

elements. Each bit is half of the size of the bit preceding it. Figure shows a phase shifter

architecture which can come to any multiples of 22.5.

Figure 2.5: Digital phase shifter

2.7 Switched Line Phase Shifter

The switched-line phase shifter is dependent only on the lengths of line used. Also, the

switched-line phase shifter is simple in both principle and design. One of the two lines is

labeled as a "reference" line, and the other as a "delay" line. An important advantage of this

circuit is that the phase shift will be approximately a linear function of frequency. This

enables the circuit to operate at a broader frequency range. Also, the phase shift created by the

switched-line phase shifters is dependent on transmission line lengths only, and they are

therefore very stable over time and temperature. The PIN diodes of this phase shifter may

suffer from parameter drift, but this usually provides degradation in the insertion loss of the

circuit and not the phase shift. For the switched-line phase shifter, both the peak power

capability and the insertion losses are independent of the phase shift.

The conventional switched-line phase shifter is comprised of two line segments of different

length selectively connected to the transmission line. The different path lengths between thetwo line segments determines the amount of phase shift to be introduced. The transmission

line is switched over from one line segment of the phase shifter to the other when the phase

shift is removed. Figure illustrates the schematic of the conventional switched-line phase

shifter with RF input 1, RF output 2, four PIN diodes D1, D2, D3, and D4, and two

transmission lines L1 and L2. Only one arm should be ON at a time. When the PIN diodes D1

and D3 are ON while PIN diodes D2 and D4 are OFF, the reference delay line L1 is in the

circuit. When the PIN diodes D2 and D4 are ON while PIN diodes D1 and D3 are OFF, the


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delay line L2 is in the circuit[6]. By switching the signal between two lines L1 and L2 of differ-

ent lengths, it is possible to realize a specific phase shift :2 L

= (2.4)

The advantages are the following.The diode contribution to insertionloss is practically constant in both bias positions (loss

variation is due to the length difference of the switched paths).The circuit "center conductor"

can be fabricated in one plane (especially suited for microstrip).The circuit is compact,

especially for small bits since only transmission line lengths on the order of the required

phase shift need be used.

The disadvantages are the following.

Four diodes are needed per bit.Complementary bias signals are required for each bit ("on" and

"off" paths).Phase shift tends to be proportional to frequency unless a frequency dispersive

switched path is used All bits have as much diode loss as the 180 bit [7]

2.7.1 Mathematical Derivation

Exact analysis can be done on a circuit shown in figure below. Superposition theorem can be

used to solve the phase shifter problem. All impedances are normalized to the generatorimpedance, which is also equal to the transmission line characteristic impedance. For even

excitation, both voltage generators have V/2 input with the same phase. Open circuit

termination can be replaced at the plane of symmetry.

Figure 2.6 Switched line phase shifter


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For odd excitation, both voltage generators have V/2 input with 180 phase difference. The

short circuit termination can be replaced at the plane of symmetry. For even excitation, the

normalized admittance looking at point B is

1 2

1 1

cot( ) cot( )2 2

e

B

f r

yl l

Z j Z j

= +

fZ

is normalized switch impedance when switch is forward biased;

rZ

is normalized

switch impedance when switch is reverse biased. For odd excitation,

1 2

1 1

tan( ) tan( )2 2

o

B

f r

yl l

Z j Z j

= +

+ +

In both modes, voltage at point B,BV is

0

2(1 )

e

B e

B

VV

y=

+

The transmission coefficient21

S is defined by adding the voltage for even and odd

excitation and divided by the voltage associated with maximum delivered power V/2. After

superposition, the left voltage generator generates full voltage and the right voltage

generator generates nothing.

21

0

1 1

/ 2 1 1

e o

B B

e o

B B

V VS

V y y

+= =

+ +

21

1 2 1 2

1 1

1 1 1 11 1

cot( ) cot( ) tan( ) tan( )

2 2 2 2f r f r

S

l l l lZ j Z j Z j Z j

= + + + +

+ +

1

21 21| |jS S e =

Generally switch impedance under forward bias can be neglected. Assume the switch is

ON in the upper path,21

S can be simplified.

2

21 211

2 1 2

1 1| |

1 1 11 tan( ) 1

2cot( ) tan( ) tan( )

2 2 2

j

r r

S S el

jl l l

Z j j Z j

= =+ + + +

+


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The differential phase shift is given by

2 1 =

Design and Simulation Issues:

The calculation steps to desing switched line phase shifter as follows:

22.5 degree phase shifter at 500 MHZ for 6.6 diaelectric constant =>

2 1( )L L =

Where

2 / Vp = and Vp=1

eff

22.5 degree=>0.392 rad

At 500 MHZair

=c/f=0.6 m

0.60.234

6.56

air

g

eff

= = =

L=g

/(2)=14.60 mm

The difference of two microstrip line must be 14.60 mm at these conditions.Calculation isshowed to clarify and reinforce design formulas.


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2.7.2 Simulations

AT 500 MHZ

Figure 2.7: Switched line phase shifter circuit diagram at ADS


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Figure 2.8: 22.5 degree phase shift at 500 MHZ

Phase shift, input output reflection coefficient,scalar gain ,insertion loss and return loss can

be seen respectively.


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Figure 2.9: 45 degree phase shift at 500 MHZ

Phase shift, input output reflection coefficient,scalar gain ,insertion loss and input return loss

can be seen respectively.


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AT 750 MHZ

Figure 2.10: 22.5 degree phase shift at 750 MHZ




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AT 1 GHZ

Figure 2.12: 22.5 degree phase shift at 1 GHZ

Phase shift, input output reflection coefficient, scalar gain , insertion loss and input return

loss can be seen respectively.


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Figure 2.13: 45 degree phase shift at 1 GHZ

Phase shift, input output reflection coefficient, scalar gain, insertion loss and input return loss



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AT 2 GHZ





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Phase shift, input output reflection coefficient,scalar gain, insertion loss and input return loss



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AT 4 GHZ


Phase shift, input output reflection coefficient,scalar gain , insertion loss and input return



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Phase shift, input output reflection coefficient, scalar gain, insertion loss and input return



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The graphs of phase shift, insertion loss, reflection coefficient, input return loss vs frequency

are obtained by using Matlab curve fitting property.

Figure 2.18: Phase shift vs frequency for 22.5 degree switched line phase shifter

It is obvious that we obtained best phase shift around 750 MHZ in switched line phase

shifter.

Figure 2.19: Phase shift vs frequency for 45 degree switched line phase shifter

Best performance obtained about 1.5 GHZ for switched line phase shifter.


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Figure 2.20: Insertion loss for 22.5 degree phase shift

Insertion loss is pretty good at around 1 GHZ for 22.5 degree phase shifter.

Figure 2.21: Insertion loss for 45 degree phase shift

Insertion loss is pretty good at around 2 GHZ for 45 degree phase shifter.

Figure 2.22: Reflection coefficients vs frequency for 22.5 degree phase shift

Figure 2.23: Reflection coefficients vs frequency for 45 degree phase shift


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Figure 2.24: Input return loss vs frequency for 22.5 degree phase shift

Figure 2.25: Input return loss vs frequency for 45 degree phase shift

Two bit circuit is formed for switched line phase shifter for 22.5 degree at 750 MHZ.

Figure 2.26: Two bit application


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44.9 degree phase shift is observed .However insertion loss increased.


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2.8 Loaded Line Phase Shifter

The two element transmission diode phase shifterwas first realized by placing diode

controlled switched reactances about a quarter wavelength apart on a transmission line, asshown in Fig. below. The basis for this phase- shifter design arises from two factors. First,

any symmetric pair of quarter-wavelength spaced shunt susceptances (or series reactances)

will have mutually canceling reflections provided their normalized susceptances (or

reactances, if mounted in series with the line) are small compared with unity. This feature

imbues the phase shifter section with good match in both control states, regardless of the

susceptance sign or value, provided the magnitude is small. The second factor is that shunt

capacitance elements electrically lengthen a transmission line while inductive elementsshorten it. Thus switching from inductive to capacitive elements produces an increase in

electrical length with a corresponding phase shift. The phase shift (in radians) provided by a

pair of line shunting susceptances is approximately equal to the algebraic normalized suscep

tance change of one of them. An equivalent circuit consisting of a uniform length of line with

characteristic impedance Z0' is useful for evaluating the maximum input VSWR when several

sections are cascaded to form a complete phase shifter. Because of the use of cascaded

identical sections, this circuit is sometimes called the "iterated" phase shifter. By duality, the

phase shift of a pair of series reactances can be obtained substituting F0 for Z and Xfor B.

However, the shunt circuit is more frequently used because diodes can be heat sunk to the

circuit housing more readily.

It is a fundamental tenet of Foster's reactance theorem that all susceptances and reactances

realizable with passive circuitry have a positive slope with frequency. However, since the

phase shift produced by a transmission phase shifter is proportional to the difference in

switched shunt susceptances, it is possible over a 10-20 percent bandwidth to have phase shift

increase, be relatively constant, or decrease with frequency, according to the specific design

of the susceptance elements.


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Obviously, this circuit is limited in the amount of phase shift it can provide by the fact that

susceptance magnitudes must be kept small for a good match. Usually, only up to about 45

of phase shift per pair of elements is practical. For very high power phase shifters, this limit

on the amount of phase shift obtainable per diode is no disadvantage since many diodes are

needed to control the power. In fact, distributing the diodes along the transmission line has

the advantage of insuring that they share equally in the phase-shifting task and the further ad-

vantage that the heat dissipated in the diodes is also distributed. However, except where

either high power or very little phase-shift operation is required, this circuit is less practical

than the hybrid coupler circuit which uses only two diodes per bit, regardless of the amount

of phase shift required.[7]

2.8.1 Mathematical Derivation

If we model loaded line phase shifter and normalize all values, we can obtain phase shift

formula by using ABCD matrix.

Figure 2.29: Loaded line phase shifter-ABCD matrix

Figure 2.28: Loaded line phase shifter


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1

(2 ) 1

A B bx jx

C D jb bx bx

=

1 2

1 2

1

(2 ) 1

V Vbx jx

I jb bx bx I

=

1 2 2

1 2 2

1 2

(1 ) ( )

| | (|1 |) | |

V AV I B

V bx V I jx

V bx jx V

=

=

= +

|1 | 1bx jx + = ==> for best performance

2

2

1

bx

b=

+

2arg( / ) arg( )oV V A B = = +

2

2arctan( )

1

b

b =

(2.5)

Design steps and calculations of loaded line:

Figure 2.30: Main line mounted

N= characteristic impedance

For 22.5 degree phase shift at 4 GHZ=>

If we choose B as 10 and -10 for inductance and capacitance respectively,

0

10 / 50 0.2

10 / 50 0.2

on

ff

b

b

= =

= =

1

2

2tan ( )

1

2* * *

2* * *

s e

j

b

b

L L L

NL

f B

BC

f N

=

= +

=

=


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1

2

2*0.2tan ( ) 22.6

0.2 1 = =

9

509.96

2* *4*10 *0.2L

= = nH

9.96 2.3 7.66eL = =

9

0.20.159

2* *4*10 *50jC

= = pF

2.8.2 Simulations

AT 4 GHZ

Figure 2.31: Loaded line phase shifter state 1

Figure 2.32: Loaded line phase shifter - state 2


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In ADS, switching property of pin diode is not working properly, so it is necessary to draw

two circuit, the one at the left shows when the pin diodes are on and the one at the right shows

when the pin diodes are off.


102.5-79.5=23 degree phase shift between on and off states.


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AT 500 MHZ


102.9-79.6=23.3 degree phase shift at 500 MHZ.


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AT 1 GHZ


103.11-79.66=23.45 degree phase shift.


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AT 2 GHZ


103.16-79.76=23.56 degree phase shift at 2 GHZ.


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In theoritical loaded line phase shifter is not good at greater than 45 degree phase shift

applications.

For 53 degree phase shift at 2 GHZ=>

If we choose B as 25 and -25 for inductance and capacitance respectively,

0

25 / 50 0.5

25 / 50 0.5

on

ff

b

b

= =

= =

arctan(0.5*2/ (0.25 1) 53 = =

9

507.96

2* *2*10 *0.5L

= = nH

9

0.50.8

2* *2*10 *50j

C

= = pF

7.96 2.3 5.66eL = =


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121.83-61.82=60.01 degree phase shift.It is foresaw a quite error in phase shift and according

to ADS (60-53=7) 7 degree phase error ocurred.Loaded line phase shifter is not suitable for

greater than 45 degree phase shift.In the aspect of insertion loss, loaded line phase shifter has

shown pretty good performance in simulation.


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2.9 Reflection Type Phase Shifter

To illustrate behaviour of a reflection type phase shifter,we use a specific example.Consider a

grounded variable capacitor C seen from a reference line of characteristic impedance0Z .The

reflection coefficient :

^

^

1

1

jjw C e

jwC

= =+ (2.6)

^12 tan ( )wC = (2.7)

is unitary in amplitude and a has a phase depending on the normalized capacitance

^

0C CZ= difference between the reflected and the incident waves can therefore vary from 0

degree for zero capacitane( thus when the load is an open circuit) to -180 degree in the limit

when the capacitance becomes infinite for seperating the incident from the reflected as shown

in the schematic.The direct and coupled port of the coupler are terminated with two identical

reactances.If such reactances can be variad simultaneously by a control signal , a tunnable

phase shifter is obtained.The signal incident on port 1 is split between to port 2( direct port )

and port 3 ( coupled port) with equal amplitudes and 90 degree phase shift.As a consequence,

the signals reflected back into the hybrid junction by two equal loads at ports 2 and 3 will

cancel at port 1( since they are there 180 degree out of phase) while they sum at port 4 (where

they arrive in phase).Depending on the values of the reactances, thus on their reflection

coeffiecients the output signal (port 4 of hybrid junction) undergoes a phase shift. [8]

Figure 2.38: Reflection type phase shifter


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2.9.1 Mathematical Derivation:

Reflection-type phase shifters shown in Fig. 2.9 are also called time delay phase shifters.

Assuming a perfect switch having an infinite admittance when closed, it shows +j for any

lengths of line behind it. When the switch is open, the admittance seen at switch is that of the

length of line behind it, l/2. The normalized admittance can be written as:

0

/ 2cot(2 ( )) cot( )

2

Y lj j

Y

= =

The equivalent reflection coefficient is given by

0

0

Y Y

Y Y

=

+

Since the line is terminated by a susceptance

2 2

0 0 0

2 2

0 0

( ) 2

Y jB

Y Y Y B jBY

Y Y Y B

=

= =

+ +

the angle of the reflection coefficient is

0

2

0 0

2 /arctan( ) 2arctan( )

1 ( / )

B Y B

B Y Y

= =

The normalized diode admittance under conduction and reverse bias is:

0

0

DCY Z

jY wL

= diode in conduction

0

0

DCY

jwCZY = diode reverse biased

For diode under conduction state,

02arctan( cot( ))2

c

Zj j

wL

=

For a reverse biased diode,


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02arctan( cot( ))2

cjwCZ j

=

The phase shift is:

= C R

If the diode is not perfect, the inductive reactance of forward-biased diode reducesC and

thus reduces . On the other hand, the capacitive reactance of reverse-biased diode reduces

C and thus increases . With careful design, the error can be cancelled each other. [4]

Lange Coupler:The Lange coupler is a four port, interdigitated structure developed by Dr.

Julius Lange around 1969. The couplers are widely used as power combiners and splitters

in RF amplifiers as well as in mixers and modulators. The coupling is derived from closely

spaced transmission lines, such as microstrip lines. Typically the number of conductors or

fingers (N) is even. The geometry for N = 4 is shown at below.

Isolated Port (3) Direct Port (4)

Figure 2.39: Lange coupler geometry


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The length of the fingers (L) is set by the desired center frequency (fo) of the filter. The

device is relatively broadband, with flat frequency response around fo. The finger length isequal to the quarter wavelength ( s) of fo in the substrate, i.e.

L = s / 4 (2.8)

0*

s

eff

c

f

= (2.9)

Simulation of Reflection Type Phase Shifter Using Lange Coupler

For 45 degree phase shift at 8 GHZ=>

Lange coupler calculation:

8

9

9.6

7.1

3*1014.07

8 *10 * 7.1

r

eff

s

=

=

= =

L = 14.07/ 4 =3.52 mm

Phase calculation:

1

2

2 1

| |

| |

j

ON ON

jOFF OFF

e

e

=

= =

For best return loss operation

*

ON OFF =

2 1

1

2

22.52

22.52

22.5 ( 22.5) 45

=

= =

= =

= =


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2.9.2 Simulations

Figure 2.40: Reflection type phase shifter ADS simulation state 1

Figure 2.41: Reflection type phase shifter ADS simulation state 2


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60-14=46 degree phase shift is obtained in simulation at 8 GHZ for reflection type phase

shifter.


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2.10 Implemented Circuit

Figure 2.43: Incremential line phase shifter

The circuit is taken from Foundations of Microwave Engineering, Robert E. Collin.This

circuit has some advantages in the implementation phase.Tranmission lines are used instead

of inductors and capacitors to bias pin diodes which is easier in the aspect of realization

circuit.Circuit has two main branch shorter one is reference line and longer one is delay

line.If it is wanted to activate reference line, negative bias is added to the upper part of the

circuit and positvely bias is added to lower part and to activate delay line it is necessary to

invert biasing.The difference between two situation gives phase shift.The tranmission lineswhich are added parallelly and grounded is used to complete biasing of pin diodes.
http://eu.wiley.com/WileyCDA/Section/id-302479.html?query=Robert+E.+Collinhttp://eu.wiley.com/WileyCDA/Section/id-302479.html?query=Robert+E.+Collin


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Necessary values and calculations:

Since pin diodes are basically current controlled resistors, it is necessary to generate current at

the branch of pin diodes.100 ohms resistors are added which yields to 5V/100=50mA.According to datasheet of pin diode, 50 mA current causes about 1 ohm.

Pin diode: Cj=0.4 pF, Rj=0.01 ohm, Rs=0.01 ohm, Ls=2.5 nH, Cp=0.13 pF

Msub: H=1.524 mm, Er=3.38

Generator and Load impedance: 50ohm

2 12 ( ) / L L =

At 2.4 GHZ

76.88g

= mm

2 (25 45) / 77 = =-93 degree phase shift is expected.

Figure 2.44: Implemented circuit


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Figure 2.45: Graph of phase shift

When the reference line is activated , -13 degree phase obtained and when the delay line is

activated 74 degree phase is obtained. 13 74 87 = = degree phase shift is obtained in

real.Even though the implementation is circuit is not very achiveful, obtained phase shift is

relatively satisfactory.


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Figure 2.46: Graph of S 21

When reference line is activated, 21S is about 6 dB and when the delay line is activated 21S

is about 2.1 dB.Since we lived diffuculites when realizing the circuit.The difference is caused

from distorted transmission line.


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3.CONCLUSION

In this project, the design concept and application of various type of phase shifters at different

frequencies are discussed.Switched line phase shifter is examined more than the other phase

shifters because of design and implementation process is simpler than the others.Switched line

phase shifter has a linear relationship with frequency so phase shift is frequency

dependent.Other main disadvantage of this phase shifter is, it has great insertion loss for two

or more bits application since pin diodes are serially connected to circuit.On the other hand, in

the implemented circuit even though it is not in a good shape, acquired phase shift is pretty

satisfactory. Loaded line phase shifter is another concept which is examined but it can not be

used where if it is necessary more than 45 degree phase shift.Loaded line phase shifter has

less insertion loss since pin diodes are connected parallely to the circuit and it is more suitable

for multiple bit application. Theoretically, reflection type phase shifter has best phase shift

and insertion loss performance and it has wider frequency range too.For future work, by using

phase shifters introduced in this project, designing and implementing phase array radar is

proposed.


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4.REFERENCES

[1] Federal Standard 1037C. Definition of Phase Array

[2] White, J. F. 2005. Microwave Phase Shifters. Encyclopedia of RF and MicrowaveEngineering.

[3] Skolnik M., 2008, Radar Handbook, pp 13.51-13.53, The McGraw-Hill

[4] Xu J., 2008, X-band Phase Shifters for Phased Array, UNIVERSITY OF CINCINNATI

[5] W. E. DOHERTY and JR. R. D. JOOS, 1992, The pin diode circuit designers

Handbook, pp 3-6, Microsemi-Watertown

[6] MALORATSKY L.G., Electrically Tunable Switched-Line Diode Phase Shifters Part 1:

Design Procedure, Aerospace Electronics Co.

[7] White, J.F.; , "Diode Phase Shifters for Array Antennas,"Microwave Theory and

Techniques, IEEE Transactions on , vol.22, no.6, pp. 658- 674, Jun 1974

doi: 10.1109/TMTT.1974.1128309[8] Sorrentino R. and Bianchi G., 2009, Microwave and RF Engineering,pp 193-195,Wiley

Tutorial:

Encyclopedia of RF and Microwave Engineering

Phase Shifter Design Tutorial

Odd /Even Mode Analysis

Agilent, Lange Coupler Design

Agilent ADS Tutorial

Agilent, Lange Coupler DesignSoftware:

Advanced Design System

Matlab
http://eu.wiley.com/WileyCDA/Section/id-302479.html?query=R.+Sorrentinohttp://eu.wiley.com/WileyCDA/Section/id-302479.html?query=R.+Sorrentinohttp://eu.wiley.com/WileyCDA/Section/id-302479.html?query=Giovanni+Bianchihttp://eu.wiley.com/WileyCDA/Section/id-302479.html?query=Giovanni+Bianchihttp://eu.wiley.com/WileyCDA/Section/id-302479.html?query=R.+Sorrentinohttp://eu.wiley.com/WileyCDA/Section/id-302479.html?query=R.+Sorrentino


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5.APPENDICES

Datasheet of Pin Diode

PHASE SHIFTING ANTENNA DESIGN BY

USING PIN DIODE

Mmin ZPOLAT

Hacettepe University

Department of Electrical and Electronics Engineering

Instructor: PROF. Birsen SAKA

Spring 2012

project report of phase shifter

Documents