Design and Analysis of
a Lossless T-Junction
Power Divider with
Quarter-Wave
Transformers
Murat Hancı 19290429
Emir Şeker 20290498
Contents
1.
2.
3.
4.
5.
Introduction
Calculations
Design and Simulation
Conclusion
References
01
Introduction
Our focus today is on the T-junction
power divider, a three-port network
where input power at one port is
divided among the other two. This
device plays a pivotal role in radio
frequency applications, allowing us to
distribute power efficiently.
A key aspect of this process is
impedance matching, which is essential
for ensuring maximum power transfer. A
mismatch in impedance can lead to
power loss, decreased efficiency, and in
some cases, damage to the
components.
In this presentation, We'll be sharing
our theoretical calculations, our
approach to circuit design, and the
results we obtained. We'll explore how
these findings underscore the
importance of impedance matching and
careful design in power splitting
applications.
02
Calculations
Lossless T-Junction divider network contains passive and isotropic
materials. Hence, the network is reciprocal. From theory, we know that a
network cannot be reciprocal, lossless and symmetric at the same time.
Therefore reflected s-parameters S(1,1), S(2,2), S(3,3) cannot be 0
simultaneously.
02
Calculations
It is desired to make S(1,1) = 0 to eliminate the reflection and
to increase the power transmission. For the 3:1 power split
operation, we calculate the impedance values as below:
P2 = ¾ * P1 = Vo²/Z2 (For the second port)
Z2 = 4*Zo/3 = 30*4/3 = 40 Ω
P3 = ¼ * P1 = Vo²/Z3 (For the third port)
Z3 = 4*Zo = 30*4 = 120 Ω
02
Calculations
To have a reading of 30 Ω impedance values from port 2 and port 3, we
will design two quarter-wave transformers. We know that for quarter-wave
transformers: Zt² = Zo*ZL
Hence, the characteristic impedances found by:
02
Calculations
Now, we can compute the s-parameter magnitudes by using the power and impedance relations. For reflection coefficients,
S11, S22, S33 = (ZL – Zo) / (ZL + Zo) In our case, ZL changes for each case since the reference points vary.
Also, Zo1 = 30 Ω, Zo2 = 40 Ω, Zo3 = 120 Ω .
S11 = (40 // 120 – 30) : (40 // 120 + 30) = 30-30 / 30+30 = S11 = 0 (desired)
S22 = (30 // 120 – 40) : (30 // 120 + 40) = S22 = -0.25
S33 = (30 // 40 – 120) : (30 // 40 + 120) = S33 = -0.75
For transmission coefficients, S12 = S21, S23 = S32 and S31 = S13 (From reciprocity)
For lossless t-junction power dividers: P1(+) = P2(-) + P3(-) . Hence,
02
Calculations
Also, we know that for a lossless network,
|S11|² + |S12|² + |S13|² = 1
|S21|² + |S22|² + |S23|² = 1
|S31|² + |S32|² + |S33|² = 1
Therefore, |S21|² + |S22|² + |S23|² = 1 = 0.866² + (-0.25)² + |S23|² = 1
> |S23| = |S32| = 0.433
Now, the necessary calculations are completed and we are ready to compare these calculations with our
simulations on AWR.
03
Design and Simulation
At first, we design an ideal network by using TLIN components as quarter-wave transformers
according to the calculated impedance values. We choose a specific frequency value: 5000MHz.
Also, the electrical length is selected as 90 degree since the network will consist of quarter-wave transformers.
03
Design and Simulation
03
Design and Simulation
Now, we can turn our ideal design into a real design by using MLIN components as quarter-wave transformers. For
this, we need to use TXLine and tune tool of AWR. TXLine will give us the required width and length values for the
microstrip lines(MLIN) according to the impedance, dielectric, frequency etc. information of verified ideal design. We
will get closer to the ideal design by tuning the width and length values slightly.
03
Design and Simulation
03
Design and Simulation
Design of the Real Circuit
In order to design a practically
feasible power divider we need
to adjust our model. In this
modified version, sections of
impedance matching quarterwave transmission lines have
been used at the output port in
order to remove the limitations
of the first model and generate
a practically feasible layout.
Their values have been
calculated as follows:
Due to the electromagnetic coupling and discontinuity caused by the materials, the
design before does not work for EM and Extract simulation on Axiem. That is way
another model is designed which consists of a more detailed construction.
Using the TXLine tool, the widths of all the transmission lines were calculated as per
their respective calculated impedances as follows:
IMPEDANCE VALUE
WIDTH
30Ω
6.293 mm
150Ω
0.134 mm
40Ω
2.39 mm
75Ω
1.33 mm
TXLINE Calculations
30Ω
150Ω
40Ω
75Ω
The Schematic for Our Power Divider Design
2D Layout for the Modified Model
04
Conclusion
We have successfully designed a lossless T-junction power divider with
a source impedance of 30 Ω. The quarter-wave transformers have been
successfully designed to match the chosen output impedances of 40 Ω and
120 Ω to the source impedance which worked fine for MWO simulations. For
EM simulation on Axiem, another modified design has been develop in order
to obtain closer results with the ideal design.
The results highlight the importance of impedance matching and careful
design in power splitting applications.
05
References
i. Microwave Engineering by David M. Pozar - 4th edition Wiley 2012.
ii. https://studylib.net/doc/18192080/lecture-24--t-junction-and-resistive-power-dividers
iii. Singh, Jayati, et al. “Design of a Power Divider with High Output Power Ratio.”
International Journal of Innovative Research & Development, vol. 4, no. 11, Oct. 2015.
iv. https://kb.awr.com
Thanks!
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