This project report describes the design and measurement of a 2.4GHz branch-line coupler. Binh Pham Quang designed the coupler using ADS software, simulating both the schematic and electromagnetic models. Key steps included calculating transmission line impedances from design specifications, synthesizing physical dimensions, and tuning for optimal performance. The coupler was then fabricated on an RO4350B substrate and measured using a vector network analyzer. Results showed good agreement with simulations, achieving high reflection coefficient, coupling, and directivity near the target frequency.

1. Frankfurt University of Applied Sciences
Faculty 2: Computer Science & Engineering
Project Report
Design and Realization of 2.4GHz
Branch-line Coupler
Binh Pham Quang
Matriculation number: 1067767
Supervisor: Prof. Dr.-Ing. Gernot Zimmer
August 20, 2017

2. Contents
1 Introduction 2
2 Review 3
2.1 Microstrip line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Branch-line coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Design 5
3.1 Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Schematic Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.3 EM Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4 Fabrication and Measurements 9
4.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.3 Result analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5 Conclusion 13
6 Reference 14
1

3. Chapter 1
Introduction
A branch-line coupler, or quadrature hybrid, is a passive device, which is widely ap-
plied in power distributing and combining systems[1]. Other applications exploit their
ability of providing a high degree of port-to-port isolation even while the ports are
mismatched.
With the purpose of investigating characteristics of branch-line couplers, this project
aims to designing and fabricating a branch-line coupler fulfilling the following require-
ments:
• Center frequency: 2.4GHz
• Low coupling factor: -10dB
• High directivity
• Test substrate RO4350B
The coupler is designed on software Advanced System Design (ADS). The design is
fabricated and afterward measured. Finally, a comparison between the experimental
results and the simulation results is performed to qualify the product.
2

4. Chapter 2
Review
2.1 Microstrip line
The Microstrip line has been widely used for RF and microwave circuits due to the
ease of fabrications, good integration with SMD devices, small size and low cost.
The general structure of a microstrip line includes a conducting strip with a width W
and a thickness t is on the top of a dielectric substrate that has a relative dielectric
constant r and a thickness h and a ground plane underneath the dielectric.
Figure 2.1: Cross section of a microstrip line
Transmission characteristics of microstrips are described by two main parameters: the
effective dielectric constant eff and characteristic impedance. In the field configura-
tion of a microstrip line, there is more than one dielectric in which the Electromagnetic
(EM) field are located. Hence eff is introduced to evaluate properly the characteris-
tics of the microstrip line.
Figure 2.2: Field configuration a microstrip line
In this project, LineCalc is utilized to reduce the complication in characteristics equa-
tions of microstrips. LineCalc would be able to approximate the impedances of trans-
mission lines as well as synthesize the physical dimensions of a transmission line from
the given frequency, impedance and electrical length.
3

5. Figure 2.3: Interface of LineCalc
2.2 Branch-line coupler
Figure 2.4: Structure of a branch-line coupler
The geometry of a branch-line coupler is shown in figure 2.4. A signal applied to port
1 is split into ports 2 and 3 with one of the outputs exhibiting a relative 90 phase
shift. The characteristics of a coupler are defined as follows:
• Transmission factor (dB) = 10log P2
P1
= 20log(S21)
• Coupling factor (dB) = 10log P4
P1
= 20log(S41)
• Isolation (dB) = 10log P3
P1
= 20log(S31)
• Directivity (dB) = 10log P4
P3
= 20log S41
S31
4

6. Chapter 3
Design
Figure 3.1 introduces steps to design a branch-line coupler with ADS. First of all,
impedances of the transmission lines are calculated from the specifications of the cou-
pler. These impedance are synthesized into physical parameters using LineCalc. The-
ses physical parameters are tuned to achieve optimal results. The circuit afterwards
is realized and measured.
Figure 3.1: The design flow of the branch-line coupler
3.1 Calculation
The first step is to calculate the impedance of the arms. The impedance ZS of the
series arms and ZP of the parallel arms can be determined from the coupling factor
C and Z0, regarding the equation 3.1 and 3.2[2].
C(dB) = 10log
1
1 − (ZS
Z0
)
2 (3.1)
ZP
Z0
=
ZS/Z0
1 − (ZS/Z0)2
(3.2)
The length and width of the arms are consequently synthesized from their impedances
and electrical lengths by LineCalc. The properties of the substrate must be entered,
as a part of inputs. The following critical parameters of substrate RO4350B are in-
cluded:
5

7. • Relative Permittivity (Er) : 3.66
• Substrate Height (H) : 0.762 mm
• Conductor Thickness (T): 17 µm
• Conductivity (Cond) : 5.8.107
S/m
• Loss Tangent (TanD) : 0.0037
The electrical length of the series arms and parallel arms are a quarter of wavelength
according to the branch-line structure. The length of 50Ω arms should be long enough
so that SMA connectors could be soldered to.
With -10dB coupling, the corresponding width of the parallel arms is nearly 0.1mm,
which exceeds the limit of the milling machine. Therefore, the coupling is reduced to
-9.5dB. The respectively physical parameters that are computed from coupling -9.5dB
and Z0 50Ω is shown in table 3.1.
Table 3.1: Calculated physical parameters
Impedance (Ω) Width (mm) Length (mm)
ZS 47.1 1.81 18.44
ZP 140.6 0.125 19.96
Z0 50 1.65 8
3.2 Schematic Simulation
A schematic in ADS is created, using the model of microstrip line library. At the
intersections of the arms, T-junctions are implemented to account for the microstrip
discontinuity [3].
Figure 3.2: Schematic of the coupler with T-junctions
The physical lengths of the arms are tuned and the simulation of the schematic is run
over. The tuning step is carried out until the resonance of every S-parameter is at the
center frequency 2.4GHz. The simulation results are illustrated in figure 3.3.
6

8. (a) S-parameters (b) Directivity
Figure 3.3: S-paramters and directivity of the schematic simulation
3.3 EM Simulation
Figure 3.4: Layout of the coupler
EM simulations are performed on the layout generated from the schematic. Foremost,
substrate RO4350B must be created. Then the following EM simulation setups are
used:
• Frequency plan: 0 - 4.8GHz
• Mesh density: 100 cell/wavelength
• Edge mesh enabled
• Simplifying layout disabled
The physical length of the arms are tuned again. The S-parameter of EM simula-
tion should be similar to that of the schematic simulation. The tuned values of the
layout are summarized in table 3.2
7

9. Table 3.2: Tuned physical parameters
Width (mm) Length (mm)
ZS 1.8 18.6
ZP 0.15 19.7
Z0 1.65 8
The S-parameters and directivity by EM simulation are demonstrated in figure 3.4.
This simulation results are good so the design is thus proceeded to be fabricated.
(a) Reflection coefficient (b) Transmission factor
(c) Coupling factor (d) Directivity
Figure 3.5: Results of EM simulation versus results of schematic simulation
8

10. Chapter 4
Fabrication and Measurements
4.1 Fabrication
The design mentioned in the previous chapter is realized by a milling machine. Every
ports are labeled as figure 4.1. The coupler is connected to a Vector Network Analyzer
(VNA) through four soldered SMA connectors.
Figure 4.1: The realized circuit of the branch-line coupler
4.2 Measurement
The S-parameters of the coupler are measured by a VNA HP8772C. The VNA is firstly
calibrated in the frequency plan starting from 50MHz to 4800MHz. The calibration
method Open, Short, Load (OSL) is applied with calibration kit HP 3.5mm. The
setups for measuring S-Parameters follow the scheme in figure 4.2.
9

11. (a) Setup for 1-port measurement (b) Setup for 2-port measurement
Figure 4.2: Setup for 1-port and 2-port measurement
The data sets of the S-parameters are exported to S2P file and sketched into graphs
in ADS. The experimental data are placed in the same graphs with the simulation
results, as shown in figure 4.3.
(a) Reflection coefficient (b) Transmission factor
(c) Coupling factor (d) Directivity
Figure 4.3: Experimental results versus EM simulation results
The reflection coefficient is shifted 70MHz off the center frequency compared with the
simulation results whereas the directivity is 20MHz off. Nevertheless, both parameters
reach high value at their resonances: -51dB for S11 and 39dB for the directivity. S21
and S41 are distorted by noise but still remain the similar shapes with their simulation
results.
10

12. Branch-line couplers have a high degree of symmetry, as any port can be used as the
input port. The symmetry is proved in figure 4.6, where the shape of every component
in a kind of characteristics is similar and partially overlapped.
(a) All reflection coefficients (b) All transmission factors
(c) All coupling factors (d) All directivity
Figure 4.4: All experimental S-parameters and directivities
11

13. Chapter 5
Conclusion
In this project, a branch-line coupler operating at center frequency 2.4GHz is designed
and realized on substrate ROB4350B. The design progresses includes calculation, syn-
thesizing, simulation and tuning before the realization and measurements.
Due the tolerance in physical dimensions and the discontinuity caused by SMA con-
nectors, there are disagreements between simulation results and measured results.
Nevertheless, the coupler achieves good characteristics at the center frequency: the
maximum reflection coefficient of -51dB, coupling of -9dB and maximum directivity
of 38dB.
12

14. Chapter 6
Reference
[1] David M. Pozar, ”Microwave Engineering”, John Wiley & Sons, Inc., NJ, 2012
[2] A. Nassari, ”Power Dividers and Couplers”, Massachusetts Institute of Technology,
USPAS 2010
[3] Unknown editor, ”Microstrip Discontinuity I: Quasi-Static Analysis and Character-
ization”, [Online] Available: http://traktoria.org/files/radio/microstrip and stripline
design/microstrip discontinuities quasi-static analysis and characterization.pdf
[Accessed 20 March 2016]
[4] Unknown editor, ”Component Characterization”, ELEC 518: RF/Microwave Cir-
cuit Design and Measurement
13