Design of Equal

Split Wilkinson

Power Divider

Submitted by

Bhanwar Singh, ECE 4th Year, En. No. 08116009

J.Muralidhara Chary, ECE 4th Year, En. No. 08116019

Under the guidance of

Dr. M. V. Kartikeyan

DEPARTMENT OF ELECTRONICS AND COMPUTER ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY ROORKEE

ROORKEE – 247667

Acknowledgement

With deep sense of gratitude, we express our humble thanks unto our

esteemed supervisor, Dr. M.V. Kartikeyan (Professor, Department of Electronics

and Computer Engineering), for assigning us this project and hence helping us

to learn. His valuable guidance helped us to carry out this work under his

effective supervision.

We also express our heartiest gratitude to our friends for their invaluable advice

and

encouragement.

J.Muralidhara Chary

Bhanwar Singh Place:

IIT Roorkee

Table of Contents

1. Introduction

……………………….….……..……………………….….…..……..…………..………… 5

2. Problem Statement……………….…

...…………………………………………………………………5

3. Theory

...……….………..………………………………………………………….….…..……...…...… 6

4. Calculation and Simulation

…….….………..………..…………...………..…………………………..... 8

5.

Results……………………………………………………………………………………………………9

5. Conclusion

...…………………………………………………………………………….…..…………. 10

Abstract

Power dividers (also power splitters and, when used in reverse, power

combiners) are passive devices used in the field of radio technology. They

couple a defined amount of the electromagnetic power in a transmission line to

another port where it can be used in another circuit. Directional couplers and

power dividers have many applications, these include; providing a signal

sample for measurement or monitoring, feedback, combining feeds to and from

antennas, antenna beam forming, providing taps for cable distributed systems

such as cable TV, and separating transmitted and received signals on telephone

lines. The Wilkinson divider splitter / Wilkinson combiner is a form of power

splitter / power combiner that is often used in microwave applications. It uses

quarter wave transformers, which are easily fabricated as quarter wave lines on

printed circuit boards and as a result it offers the possibility of proving a very

cheap and simple splitter / divider / combiner while still providing high levels

of performance.

Introduction

With The Rapid Development in wireless/wireline communications, their functions are

further enhanced, and the applications are also broadened. For industrial systems,

however, circuits/devices with much more stringent requirements are suffering from

the system cost, compactness, stability, reliability, and other specifications , as

compared with those systems like consumer electronics. It is known that any wireless /

wireline (RF) system is generally composed of passive and active circuits . Among

various RF passive circuits, Wilkinson power divider is a basic and important

component in application to RF power amplifiers, mixers, phased-array antennas, and

many kinds of equipment.

Problem Statement

Design of Equal -Split Wilkinson power divider of Frequency 2.4 GHz.

Specifications are:

1. Source Impedance = 50 ohms.

2. Load Impedance = 50 ohms

3. Substrate permittivity = 3.38

4. Thickness of substrate = 1.524 mm

5. Thickness of conductor = 0.15 mm

Simulate the circuit of Equal -Split Wilkinson power divider and plot the graphs of

various

S parameters.

Theory The mostly used one is the three port network equal two way divider. It is

also called 3 dB power divider.

In this type of dividers, there are four different sections.

1-) Input port

2-) Quarter-wave transformers

3-) Isolation resistors

4-) Output ports

Input and output ports are identical and the value of the impedances of

them are Zo. Quarterwave transformer parts are called as quarter-wave

transformer because of the length of these parts. The length of these parts

are equal to the one fourth of the wavelength of the electromagnetic wave,

which is propagating in this three port network. This length is also related to

the operation frequency.

Wavelength * Frequency = Phase velocity (Usually the speed of light)

Why the quarter-wave transformers are used in the circuit? The reason for

this leads us to understand the matching conditions for this network.

Matching of the output ports is necessary for the better power transfer from

input to output, because if the output ports are matched, the reflected

power from the network when we input some amount of power is zero. This

means, there is no reflection from the outputs and all of the power is

transmitted to the output ports. Consider the case of inputing power at port

1 and terminate the ports 2 and 3 with the reference loads. Then the

reflected power for inputing power at port-1 is zero ( S11 = 0 ). All the

power is transferred at that frequency. The quarter-wave transformer part

leads to the matched ports. Isolation resistor is to isolate the output ports. If

there is a coupling effect between output ports or in other words, the power

comes from one output port has an effect on other output port, the perfect

division of the power cannot be possible. This isolation resistor avoids the

coupling

effects of the output ports. Output ports are the ports that divided power

comes to. These ports have the same impedance value with the input port's

impedance.

To analyze the Wilkinson power divider, even-odd mode analysis method is

used. In even-odd mode analysis the aim is finding the S-parameters of the

divider. S-parameters give all voltage and power information about the

network we consider. To find S-parameters, from the definition of them, we

should input power at a port and measure the contributions of that power to

the other ports. In even-odd mode analysis, the superposition of the two

modes is inputing power at port-2 and finding the effects at all ports. First

of all our circuit becomes symmetric, made symmetric with respect to the

axis at the middle. This symmetricity makes the analyze easy. An ideal half-

split power divider would divide incident power at port 1 equally between

ports 2 and 3. The S-matrix for the ideal Wilkinson divider is given below:

This ideal Wilkinson power divider would have perfect matching at all ports (S11

= 0, S22 = 0,

S33=0). Also, there would be perfect isolation between ports 2 and 3 (S23 = 0).

The insertion loss between ports 1 and 2 should be 1/√2 , and the insertion

loss between ports 1 and 3 should be 1/√2 (|S12| = |S13| = 1/√2 ). Even-odd

mode analysis can be used to derive the proper three-port circuit to use to

create the ideal Wilkinson power divider. The results are shown below, in Figure

1.

For this project, Z0 is 50 Ω and f = 2.4 GHz. This results in the following group

of ideal

values at λ/4, presented in Table 1:

Calculation and Simulation

These values were used as the first-cut microstrip design in ADS . These

values were then

converted to microstrip line values using LINECALC. These resulting

microstrip widths and

lengths were used in generating the layout for the circuit. After several

rounds of tweaking

the circuit, the following schematic was generated.

1.Calculation of Width and Length of Microstrip

Based on the specification given in the problem statement, width and length of

the microstrip

lines are calculated. According to it –

Zo = 50 Ohm, Frequency, fo = 2.4 GHz

Substrate Permittivity, ɛ r = 3.38

Thickness of Substrate, d = 1.524 mm

Thickness of Conductor = 0.15 mm

ADS provides a LineCalc utility to calculate the width, w and length, l in mils according

to your specifications. Using LineCalc:

For Zo=50 Ohm, at λ/4 W=3.37 mm, L= 19.19mm

For Z= √2Zo=70.71 Ohm at λ/4 W= 1.56mm, L=19.86 mm

2.Schematic Design

Figure 2 : Simulation Circuit

This schematic was then converted into a layout, and the final layout is

presented below, in

Figure 3.

Figure 3 : Layout

Results

The circuit’s three main S-parameters were plotted S11 ,S12,S23 and S31.

These indicate

matching, power division, and port isolation, respectively.

1.5 2.0 2.5 3.0 3.51.0 4.0

-20

-15

-10

-5

-25

0

freq, GHz

dB(S

(1,1

))dB

(S(2

,1))

Readout

m1

dB(S

(3,1

))

m1freq=dB(S(2,1))=-3.042

2.466GHz

Conclusion:

The schematic of equal split Wilkinson power divider was drawn and the layout

was generated.

The results of the project were in agreement to the theoretical available results

,so the various S parameters were plotted as shown above.