Lec.12 Wilkinson Divider and Ring Coupler

RF & Microwave EngineeringBETE-Spring 2009

Department of Electrical EngineeringAir University

Types of Dividers and Couplers

Basic 3 & 4 port Networks

Lecture No. 12

RF & Microwave EngineeringBETE-Fall 2009

Basit Ali ZebDepartment of Electrical Engineering, AU

Topics of Discussion

• T-junction Divider

• Wilkinson Power Divider

• Couplers

–900 Hybrid Coupler

–1800 Ring Coupler



T- Junction Divider (Lossless)

Two basic requirements to be fulfilled:

• Feed line should be matched.

• Input time average power Pin should be divided between ports 2 and 3 in a desired ratio.



T- Junction Split Ratio

For Example:



Time Average Power

Referring to the figure:As port 1 is matched:



Practical Issues

1. Junction Effects

2. Characteristics impedance of output lines

In order to overcomes these factors, we:

1. Model the junction effect as a lumped

capacitor connected to ground

2. Use QWT for matching

Poor isolation between the two output port is the

main disadvantage of T-junction divider.



Use of QWT

Power Division

constraint becomes:

Matching constraint

becomes:

Disadvantage:

Use of QWT makes power splitter narrowband unfortunately.



Wilkinson Power Divider

• A Wilkinson power divider (WPD) is a two way power divider which offers wideband and equal phase, equal amplitudecharacteristics at each of its output port.

• Easy to construct. It consists of two quarter-wave transmission line sections. These lines can be made of coaxial, printed microstrip lines, or an equivalent T or pi lumped networks.



WPD

• Power Division: It can be designed to produce arbitrary power division.

• However, practically coupled output power of 3-dB is widely used in Wilkinson power divider.

• Reciprocal

• It is lossless when the output ports are matched

• Good isolation is achieved between the output ports



WPD Geometry

Isolation Resistor

A 3-dB Wilkinson

power divider



Analysis of WPD

For 1:1 Wilkinson power

divider, we will find the values of Z0,Q and the

isolation resistor R.



Even-Odd Mode Analysis

This mathematical process is called an “Even-odd mode

analysis”.

For Simplicity:



Analysis of WPD



Symmetric Excitation - Even Mode

Because V2 = V3, due to symmetric excitation,

notice that current I =0



Even mode Analysis

To simplify analysis, we can bisect this circuit as shown:

1

2

Find zine ,V1

e & V2e ?



Even mode analysis

3

4



Odd Mode Analysis

Anti-symmetric

excitation



Odd mode Analysis

To simplify analysis, we can bisect this circuit as shown:

Find zino & V2

o ?

1



Odd Mode Analysis

2

With this information, we will be able to deduce most of the

S-parameters!!

In practice, we are only interested in three S-parameters of

WPD. Even – odd mode analysis tells us values of these S-parameters.



By Superposition

By superposition of these two modes, we have an effective excitation of Vg2 = 4V from which we can find S-parameters



S-Parameters of WPD

Input reflection coefficient= 0

Transmission through port 2

Transmission through port 3

Isolation between port 2 & 3



Microstrip Realization

Coupling at port 2 and 3 = - 3.4dB

Isolation between port 2 and 3 = - 20 dB



A 1 x 8 Power Divider

InputOutputs

8 way Wilkinson power divider

RF & Microwave EngineeringBETE-Spring 2009

Department of Electrical EngineeringAir University

Couplers

900 Hybrid Coupler

1800 Ring Coupler



Quadrature (90o)Hybrid

• Four port reciprocal device with high degree of symmetry

• A special type of directional coupler in which the two outputs have equal amplitude but 90o phase difference

• Even-odd mode analysis gives us the S-parameters of this coupler

• Often made in microstrip of strip line form as a 3-dB coupler



900 Hybrid Coupler



S-Matrix

In particular when port 1 is excited, and all other ports are

terminated in matched loads, then even - odd mode analysis tells us that:



S-Matrix



Microstrip Quadrature Coupler

Observe that microstrip trace

width corresponds to different Z0!!



1800 Ring Coupler

• It is four port network

• As the name implies, the outputs from such a device can be 1800 out of phase

• Common applications are found in antenna feeding networks

• Can be used as in-phase and out-of phase power divider

• Various coupling ratios can be realized, mostly 3-dB is used



Port Definitions

• Signal at port 1: port 2, 3 in phase: port 4 is isolated

• Signal at port 4 : ports 2 , 3 have 180o phase shift: port 1 is isolated

Under these circumstances if:

• Signal at port 2 and 3 is applied, Sum will be at port 1 and difference will be at port 4.



Operation of Ring Coupler

• In-phase power splitter

• Out-of-phase power splitter

• Power Combiner

There are three common ways to operate this device:



In-phase Power Splitter



Out-of-phase Power Splitter



Power Combiner



3-dB Microstrip Ring Coupler



Design of Ring Hybrid

This highest achievable impedance value in microstrip lines is a function of the physical parameters of substrate

(like dielectric constant, thickness & type of material used).



Design of Ring Hybrid



Study

• Article 7.1,7.2,7.3,7.5 and 7.8

Documents

Lec.12 Wilkinson Divider and Ring Coupler