Fourier-Based Transmission Line Ultra-wideband Wilkinson Power Divider for

EARS Applications

ByK. Shamaileh, M. Almalkawi,

V. Devabhaktuni, N. Dib, B. Henin, A. Abbosh

NSF EARS Award 1247946Program Director George Haddad

1

Outline• Motivation and Challenges• Research on Power Dividers• Wilkinson Power Divider Design

• Conventional Vs Proposed Ultra-wideband Schematics

• Simulation and Experimental Results• Summary• Acknowledgment

2

Motivation and Challenges• Most of the frequency spectrum is allocated to different

wireless services

• Typically, some of these assigned bands remain idlesome of the time

• Cognitive Radios (CRs) are gaining attention as anattractive solution to maximizing bandwidth utilizationand channel capacity

3

Motivation and Challenges• In CR, the temporarily unallocated frequencies are loaned to

secondary users as long as the “legitimate/primary” usersare not receiving/transmitting data

• The concept of CR enhances access to the radio spectrum

However

• To bring this concept to reality, we require front-endmicrowave components that support CR operation overwide frequency range (e.g. spectrum sensing)

4

CR Framework

Cognitive Radio

Front-end components

DSP/internetworking

Input/output interface

FiltersDividersAntennas

...

5

Examples of Front-end Components

Antenna array

Power divider

6

Ultra-wideband Spectrum• The frequency spectrum ranges between 3.1 GHz and

10.6 GHz• Approved for commercial applications (FCC, 2002)• Most widely used in medical treatments, tactical and

strategic communication, through-the-wall imaging,high data rate transmission, etc.

Different approaches have been recently reported:

7

Research on Power Dividers

Multilayer substrate Stubs based

Increasedfabrication cost

Largercircuit area

Larger circuit area,difficulty in cascading

Tapered lines

Each uniform impedance branch in the power divider is replaced bya single non-uniform transmission line (NTL) transformer

Proposed UWB Wilkinson Power Divider

8

Single Frequency Proposed UWB

9

Design Objectives

• Objective 1: NTL that matches a source impedance Zs

to a load impedance Zl

Even Mode Analysis

• Objective 2: Achieve optimum output ports isolationand matching conditions

Odd Mode Analysis

Even Mode Analysis

10

32R2

2R1

2R

deinZ• Accomplished by enforcing

the magnitude of thereflection coefficient |Γ| tobe zero (or close to zero)over UWB frequency range

• |Γ| at the input port can beexpressed in terms of Ze

in

• Zein is calculated from ABCD parameters of NTL

• B and C values are calculated in terms of a truncated Fourier series

• Optimum values of the Fourier coefficients are obtained by minimizing anerror function in MATLAB

where

1 1

1 1,i i K K

i i K K

A B A B A BA BC D C D C DC D

1, 2, ...i K

01

( ) 2 2ln cos sinN

n nc n

Z z nz nza bZ d d

c

in in inin 1

Error max( , ... ... )f f fj mE E E

j je ljin

j jl

A f Z B fZ f

C f Z D f

2in

jinf jE f

ej sin

jin ej sin

Z f Zf

Z f Z

11

Even Mode Analysis

• ABCD matrix of the network is calculated as follows:

• Carried out to obtain theresistor values R1, R2 and R3

for achieving the optimumoutput ports isolation andmatching conditions

3 2Total2 2

12

1st Section

2nd Section 3rd Section

.

.

. .

.

R R

R

ABCD ABCD ABCD ABCD

ABCD ABCD ABCD

12

32R2

2R1

2R

3d

3d

3d

oinZ

Odd Mode Analysis

• Finally, we have:

• Setting V2 to zero, and solving for , we obtain:

• For perfect output ports matching over the UWB range, the below errorneeds to be minimized over the R1, R2, R3 design space

1 2

1 2Total

V VA BI IC D

11

VI

11

oin

V BZ

I D

out out outout 1

Error max( , ... ... ),f f fj mE E E 2out

joutf jE f

13

Odd Mode Analysis

Simulation and Experimental Results

• Characteristic impedance of 50Ω

• Rogers RO4003C substrate withrelative permittivity of 3.55,thickness of 0.813 mm, and losstangent of 0.0027 is employed

• Length of each NTL arm of theproposed WPD is set to 10 mm

14

• Input and output ports matching parameters S11 and S22, respectively, andthe isolation parameter S23 are below -10 dB over the UWB range.

• S21 is in the range -3.2 dB to -4.2 dB over the UWB frequency range.

3 4 5 6 7 8 9 10 11-50

-40

-30

-20

-10

0

Frequency (GHz)

S-P

aram

eter

s (d

B)

S11: Simulated

S11: Measured

S21: Simulated

S21: Measured

S22: Simulated

S22: Measured

S23: Simulated

S23: Measured

15

S-Parameters

• The measured phase imbalance is less than ± 10o over the entire designfrequency range

• The obtained amplitude imbalance is around ± 0.1 dB over the entireUWB range

-0.5

-0.25

0

0.25

0.5

|S21

| - |S

31| (

dB)

3 4 5 6 7 8 9 10 11-30

-20

-10

0

10

20

30

Frequency (GHz)

S

21 -

S31

(Deg

ree)

16

Imbalance

Simulated and measured group delay are: Almost flat over the UWB range Less than 0.2 ns

3 4 5 6 7 8 9 10 110

0.1

0.2

0.3

0.4

Frequency (GHz)

Gro

up D

elay

(ns)

SimulatedMeasured

17

Group Delay

3-D IIR Digital Beam Filters for Space-Time White Space Detection in Cognitive Radio

• Four sub-systems areproposed for space-timewhite space detection (Univ.of Akron Contribution)

• A power divider is essentialin feeding the antenna arrayin S-1! (Univ. of ToledoContribution)

18

• After S-4, an algorithm to solve the link scheduling androuting problem efficiently utilizing 3D sensinginformation is required (Univ. of Norfolk Contribution)

Summary• For the first time, a CAD method for the design of an

UWB WPD based on Fourier impedance profiles hasbeen presented.

• The design optimizes both cost and real estate!

• The proposed WPD has been fabricated. There is aclose match between simulations and measurements.

• The proposed WPD can serve as a front-end modulein realizing EARS hardware.

19

Acknowledgment

• This research is supported in part by NSF EARS Award 1247946(Collaborators – Norfolk State, Ohio Northern, University of Akron)

• The authors gratefully acknowledge the motivation and support fromNSF EARS Program Director Dr. George Haddad

Thank You