Download Wilkinson power divider is a lossless, 100% efficient, three port

NANYANG TECHNOLOGICAL UNIVERSITY
School of Electrical & Electronic Engineering
DESIGN AND INNOVATION PROJECT
DESIGN OF NARROWBAND AND BROADBAND
WILKINSON POWER DIVIDER
Group Number:
07
Supervisor Name:
Dr. Jeffrey Fu
Dr. Lee Ching Kwang
Student Name:
Huang Guangpu
Qing Songlin
Date:
31 May, 2006
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2
Table of Contents
Abstract ....................................................................................................................... 4
1 Introduction ................................................................ 5
2 Design Method ........................................................... 6
3 Calculations ................................................................ 8
4 Evaluation by Simulations ........................................ 10
4.1 Sigle-section Wilkinson power divider................ 10
4.2 Multi-section power divider ................................ 13
5 Discussion and Recommendations............................ 16
6 Conclusion ................................................................ 18
7 Reference List ........................................................... 19
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Abstract
Wilkinson power divider is a lossless, 100% efficient, three port network with matched
outputs. It splits an input signal into two equal phase output signals. Two sorts of
Wilkinson power dividers were investigated in our project: narrowband Wilkinson in
phase 3dB power divider (11.5-12.5 GHz), and broadband Wilkinson in phase 3dB power
divider (6-18 GHz). The broadband Wilkinson power dividers were designed on the basis
of the single-section circuit with more than two sections employed. It was found that the
Wilkinson power dividers cannot perform well with theoretical values. However, this
problem could be solved by fine tuning.
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1
Introduction
Power divider/splitter is a passive microwave component used for power division or
power combining. One major type, known as Wilkinson power divider, is a lossless three
port network with one input port and two output ports, where the output ports are
simultaneously isolated and matched [4]. It could be applied to balance amplifiers, highpower transmitters, and antenna array feed networks [1].
There are two types of Wilkinson power divider, namely equal power divider and
unequal power divider. In our investigation equal power divider, which splits an input
signal into two equal phase output signals, was designed and applied accordingly.
Moreover, single-section and multi-section Wilkinson power dividers were constructed to
operate in narrowband (11.5-12.5GHz) and broadband (6-18 GHz) regions respectively
[2].
In this report, method of schematic design, graphic design, layout design, and Gerber
design for fabrications will firstly be introduced, followed by evaluation through
simulations. Then related discussions and further recommendations will be presented and
conclusion will be drawn.
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2
Design Method
Power divider usually employs quarterwave transmission line sections at the design
center frequency, and Wilkinson power consists of two quarterwave line segmetns at the
center frequency f0 with characteristic impedance √2Z0, and a 2Z0 lumped resistor
connected between the output ports [2]. Such is the design of Wilkinson power divider
that it provides low loss, equal-split (ideally 3 dB) matching at all ports and high isolation
between output ports (figure 1) [4].
Figure 1 Wilkinson equal power divider
As shown in the figure above, there are four different sections [2].
1. Input port
2. Quarter-wave transformer
3. Isolation resistors
4. Output ports
Input and output ports are identical with impedance value Z0 [2] .
Quarter-wave transformer parts are characterized by the length of these parts, which are
equal to 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  g [5].
Nominal Wavelength  0 * Centre frequency f = Phase velocity V0
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Operation wavelength g =
no min al _ wavelength 0
r
The quarter-wave transformers are used in the circuit since they lead to the matched ports.
Matching of the output ports is necessary for 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 [3].
Isolation resistor is to isolate the output ports. If there is a coupling effect between output
ports, in other words, the power comes from one output port has an effect on the other
output port, the perfect division of the power would be impossible. This isolation resistor
avoids the coupling effects of the output ports [2].
Output ports are the terminals that divided power comes out. These ports have the same
impedance value Z0 as the input port [2].
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3
Calculations
As provided, the micro strip circuit was constructed on a substrate with Er = ErNorm =
2.5 and h=0.75mm.
There are two ways to determine the width of the quarter-wave transformer. First method
is the graph method, where from the figure below (figure 2), width-height ratio could be
figured out to be 2.8, therefore w = 2.8*0.75 = 2.1mm.
Figure 2 Microstrip characteristic impedance as a function of w/h and r
And the width could be also determined by calculation method using the following
equations.
For w/h < 1
 eff 
(  1) (  1)
h
w

(1  12 ) 0.5  0.04(1  ) 2
2
2
w
h
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For w/h > 1
 eff 
(  1) (  1)
h

(1  12 ) 0.5
2
2
w
Applying the above equations to verify the value obtained through graph method:
w=2.08mm, which is very close to 2.1. Therefore, w=2.1mm.
As mentioned in the design method section, input and output impedances are of the same
impedance of the isolation resistor Z0 = 50Ω, where the quarter wave length transformer
maintain the impedance of 2Zo  70.7 .
Nominal Wavelength  0 * Centre frequency f = Phase velocity V0
Or  0 
v0
3 *10^8

 25mm
f 0 12 *10^10
Operation wavelength g =
no min al _ wavelength 0
r

25
2.5
 15.81mm
Then the length of quarter-wave transformer is 3.95mm.
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4
Evaluation by Simulations
4.1
Sigle-section Wilkinson power divider
Based on the calculations shown above, the first phase design of narrow-band Wilkinson
power divider was constructed on a substrate with Er=2.5 and H=0.75 mm(figure 3). The
first design made use of the existing Wilkinson power divider model in Micro-Wave
Office database by applying the calculated values.
Figure 3 Schematic representation of narrowband
Wilkinson power divider (first phase design)
However, the first phase design was not ready for fabrication; more detailed circuit
should be designed. By adding bends and junctions and carefully adjusting the values, a
second-phased design of narrowband Wilkinson power divider was constructed (figure 4).
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Figure 4 Schematic representation of single-section
Wilkinson power divider (first design)
From narrow-band power divider second phase design, the following optimied result
could be obtained (Graph5).
Figure 5 Schematic illustration of performance of
Narrow-band Wilkinson power divider design
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In the figure above, S21, S31 are the voltage ratios from the output ports to input port.
Theoretically, power ratio of equal three-port Wilkinson power divider is 0.5 since the
input
signal
S21, S31 
is
equally
divided
into
two
parts.
Therefore,
voltage
ratios
P2
1

 0.707 and S21, S31 = 20log0.707 = -3dB [4].
P1
2
From the figure above, it could be observed that an upward parabolic curve with a peak
value of -3.1559dB at the central frequency, approximately the ideal value -3dB; the
voltage gain at Frequency 11.5 GHz and 12.5 GHz are -3.2543dB and -3.2333 dB
respectively, which are within the range of +/-0.1 dB with respect to the centre frequency
gain. Applying larger scale on y-axis, voltage gain, we are able to get a flat top with -3
dB gain value in the narrow band region, 11.5~12.5 GHz. The result is of satisfaction
considering the acceptable errors and defects in the design. Moreover, curves of S21, S31
overlap together, indicating a good equal division of the input signal [6].
The layout of the narrow-band Wilkinson power divider second phase design is shown
below (figure 6). The green rectangle is the resisitor.
Figure 6 Layout of narrow-band Wilkinson power divider (left:2D right: 3D)
The dimension of the narrow-band Wilkinson power divider is 20.26 mm*14.13mm, so
the whole micro stripe circuit can be confined within a 1 inch* 1 inch substrate. The size
of the resistor is 1.3mm* 2.0mm.
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The design shown above could effectively split input power into two equal phase output
signals in narrowband region 11.5~12.5 GHz. However, its performance is poor for
broad-band frequency signals. In fact, broadband matching could be achieved through
multi-stage imposition of single stage equal power dividers.
4.2
Multi-section power divider
Multi-section power divider is approached upon the basis of narrow-band Wilkinson 3 dB
power divider (figure 7). With more isolation from the resistor in each stage, better
performance is expected from the design [3].
Figure 7 Schematic representation of broadband
Wilkinson power divider
Multi-section power divider was also designed on the basis of the same substrate with
Er=2.5 and H=0.75 mm.
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From broad-band power divider design, the following optimized result could be obtained
(figure 8).
Figure 8 Schematic illustration of performance of
Broad-band Wilkinson power divider design
As mentioned previously, S21, S31 are the voltage ratios from the output ports to input port
and S21, S31 = 20log0.707 = -3dB.
From the figure above, we can observe an oscillating curve with a central peak of
-3.109dB. And the values of other peaks except the last one are also close to -3.109dB.
The value at the centre frequency 12GHz is -3.16dB, approximately the ideal value -3dB;
the voltage gain at Frequency 6GHz and 18GHz are -3.359dB and -4.839dB respectively.
Applying larger scale on y-axis, voltage gain, we are able to get a flat top with -3 dB gain
value in the region from 6GHz to 17GHz. However, the ratio declines sharply after
17GHz due to elementary limitation of the micro-stripe circuit.
The layout of the broad-band Wilkinson power divider is shown below (figure9).
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Figure 9 Layout of broad-band Wilkinson power divider (left:2D right:3D)
Figure 11 Layout of broad-band Wilkinson power divider-3D
The dimension of the broad-band Wilkinson power divider is 25 mm*14 mm, so the
whole micro stripe circuit can be confined within a 1 inch* 1 inch substrate. The size of
the resistor is 1.3mm* 2.0mm.
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5
Discussion and Recommendations
1
Parameter ajustment:
It was found that both the narrowband and broadband Wilkinson power dividers cannot
perform well with the theoretical values after adding the junctions and bends. For
simplicity, only narrowband Wilkinson power divider is taken out for illustration.
Although our first phase design (figure 3) which made use of the model in MWO
database could effectively divide the input signal into two equal output signals, the
second design which includes bends and junctions could not perform well. Therefore, it is
necessary to tune the values.
For single-section Wilkinson power divider, the values to be adjusted are shown below
(figure 10).
Figure 10 Notation of parameters in single-section
Wilkinson power divider
As observed, the center of curves for S21, S31 shifted to the left of 12GHz after adding the
bends and junctions. To increase the center frequency, lengths of the transformers should
be decreased. Moreover, in order to keep curves of S21 and S31 overlapping, symmetric
lengths were adjusted to a same value (eg. L2 and L3, L4 and L5).
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It was found that values of L1, L10 and L11 did not affect the output much. And so was
R1, where the reason might be that no current flows through the resistor in equal
Wilkinson power divider. Other lengths (from L2 to L9) were carefully adjusted to get
the optimized result (figure 3). Generally, except L4 and L5 were increased a bit, other
lengths were all decreased (chart 1).
Name
Value(mm)
Name
Value(mm)
L1
5.9
L7
0.4
L2
3.5
L8
0.4
L3
3.5
L9
2.05
L4
4.3
L10
5.9
L5
4.3
L11
5.9
L6
2.05
R1
100 Ω
Chart 1 Parameters of narrowband Wilkinson power divider
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Error analysis: Refer to figure 5 and 8; For narrow band power divider design, the
value at the centre frequency 12GHz is -3.1599dB, approximately the ideal value -3dB,
(3.1599-3)/3=5.33%  5% ; the voltage gain at Frequency 11.5 GHz and 12.5 GHz are 3.2543dB
and
-3.2333
dB
respectively,
(3.2543-3)/3=8.48%  10%
(3.2333-
3)/3=7.78%  10 %. Therefore, the graph is within the desired range, and it would be
approximately ideal. For broadband power divider design, at the centre frequency 12GHz
is -3.16dB; the voltage gain at Frequency 6GHz and 18GHz are -3.359dB and -4.839dB
respectively.
(3.16-3)/3=5.33%
 10%
(3.359-3)/3=11.97%
 15%
(4.839-
3)/3=61.3%  65%
Design defect: By choosing different micro-stripe elements, e.g. MBEND90X Mitered
90deg (EM Based) and MCURVE function differently as they work most effectively in
different frequency range. In actual design, MCURVE adds to the transformer
wavelength extra length, which affects the frequency response of the divider, while
MBEDN90X does not contribute any extra length due to geometrical property.
Recommendation: The performance of 3-dB Wilkinson Power Divider could be
effectively improved by fine-tuning and layout adjustment. Tuning process takes place
among the symmetrical micro-stripe length in the schematic circuit e.g. L6 and L9
(Figure10) should maintain the same value in order to keep output voltage ratio in phase.
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6
Conclusion
Wilkinson equal power divider is a passive microwave component which could
effectively divide input power into two identical output parts without any power loss,
power gain ratio -3 Db. It basically contains four parts: one input port, quarter-wave
transformers, isolation resistor and two output ports. In this report, 3 dB Wilkinson Power
Divider design, single-stage and multi-stage, were approached based on related theories
and calculation. It was found that the isolated resistor absorbs no power, and the quarterwave transformers length affects the output ports power gain and phase difference. Single
section Wilkinson power divider splits input power with frequency range 11.5-12.5 GHz,
and the narrowband design could be extended to broadband design applying three single
stages together. Possible errors and defects of both single-stage and multi-stage
Wilkinson power dividers were investigated to optimize the result in the design.
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Reference List
[1]
Brady Dana, “The design, fabrication and measurement of microstrip filter and
coupler circuits,” High Frequency Electronics., Jul 2002.
[2]
I. KASA, Microwave Integrated Circuits, Elsevier, 1991.
[3]
Mitsuyoshi Kishihara et al., “A Design of Multi-Stage, Multi-Way Microstrip
Power Dividers with Broadband Properties” IEEE MTT-S Digest, 2004.
[4]
Howe, “Stripline Circuit Design”, Artech House, 1974.
[5]
Helszajn, “Microwave Planar Passive Circuits and Filters”, Wilery, 1994.
[6]
Internet Source:
http://www.microwaves101.com/encyclopedia/Wilkinson_splitters.cfm
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