Electronics B.NO:30 Nourhan Reda Mohamed section: 4 B.NO:38

Electronics and
communications department

Faculty of Engineering

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Cairo University

 

 

 

A 900 quadrature hybrid design

This report is a part of the classwork of the course ELC305a

 

 

 

 

Submitted
to:  Dr.Eslam
Eshrah

 

Submitted
by:

 Ahmed Hassan El-Anwar                                     section:
1        B.NO:11

Salma
Khaled Hanafy                                           
section: 2        B.NO:30

Nourhan
Reda Mohamed                                   
section: 4         B.NO:38

Nourhan
Kassem Houssein                                 
section: 4        B.NO:39

Hagar
Hossam El-Dein Hussein                          
section: 4        B.NO:42

 

 

 

 

Table of Contents
Table of
figures
3
 
Introduction
4
 
Implementation
using lumped elements
6
Lumped schematic
6
Checking
requirements
7
 
Implementation
using microstrip lines
11
Microstrip lines schematic
11
Checking
requirements
12
Layout
16
 
Conclusion
17
 
References
18

 

 

 

 

 

 

 

 

 

 

 

 

Table of
Figures

Figure (2.1) : The quad hybrid TL circuit…………………………………………………………………………………………………..5

Figure (3.1) : The 900 hybrid design
using lumped elements…………………………………………………………………….6

Figure (3.2) : S parameters
………………………………………………………………………………………………………………………7

Figure (3.3) : internal matching of the
circuit…………………………………………………………………………………….…….7

Figure (3.4) : Orthogonal phase shift…………………………………………………………………………………………….…………8

Figure (3.5) : Isolated port…………………………………………………………………………………………………………………….…8

Figure (3.6) : mismatch at other frequencies…………………………………………………………………………………………..9

Figure (3.7) : bandwidth at -20db…………………………………………………………………………………………………………….9

Figure (3.8) : bandwidth at -30db…………………………………………………………………………………………………………..10

Figure (4.1) : The 900 hybrid design using
mictrostrip lines……………………………………………………………………11

Figure (4.2) :  S
parameters……………………………………………………………………………………………………………………12

Figure (4.3) : internal matching……………………………………………………………………………………………………………..12

Figure (4.4) : Orthogonal phase shift……………………………………………………………………………………………………..13

Figure (4.5) : Mismatch at other frequencies…………………………………………………………………………………………13

Figure (4.6) : isolation between ports…………………………………………………………………………………………………….14

Figure (4.7) : bandwidth at -20 dB………………………………………………………………………………………………………….15

Figure (4.8) : bandwidth at -30 dB……………………………………………………………………………………………………….…15

Figure (4.9) : microstrip
layout…………………………………………………………………………………………………………….…16

 

 

 

 

 

 

 

 

 

 

1.   Introduction

Splitting and recombining
of electromagnetic signals is a fundamental signal processing functionality in
electronics and wave theory. Power dividers are passive circuits which accept an input signal and divide its power among multiple
output signals with specific phase and amplitude characteristics to meet the
users’ specifications and fulfill their demands. The output signals
theoretically may possess the following characteristics: Equal or different power
division ratio between the output ports, input and output matching, high
isolation between the output ports and a phase relation between the output
signals. Some of the examples of the power dividers are Wilkinson, quadrature
hybrid and rat race.

In this design we were
asked to meet certain specifications such as input and output matching, equal
power division ratio, isolation between the output ports and an orthogonal
phase relation between the output signals. Thus we found that the 900
quadrature hybrid (that is shown in figure 1.1) is most suitable divider for
our design. At first, we are going to implement this circuit using lumped
components, observe its functionality and make sure it meets our standard. Then
we are going to implement the same circuit using micro strip transmission lines
and compare its performance with the previous one.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.Problem statement

One
of the various examples of power splitters is the 900 quadrature
hybrid circuit. It is a four-port device that splits the incident power signal
into two output ports. The signals at the outputs are attenuated by three
decibels (3dB) and have a 90-degree phase difference with respect to each
other. In addition, reflections due to mismatches are sent to the isolation
port preventing any power from reflecting back to the input port. In addition
to splitting a signal they can also be used to combine power signals with a
high degree of isolation between the ports.

Ideally the S parameters matrix for the hybrid
coupler is equivalent to:

 

              
  

 

 

Figure
(2.1): The quad hybrid TL circuit

Zeroes on the main diagonal indicate that
the device is internally matched as well as symmetric. S21 and S31
indicate that there is a phase shift by 90 degrees between output ports 2 and
3. S41 indicates full isolation between ports 4 and 1.and finally
the magnitude of S21 squared is equal to the magnitude of S31
squared equal half which means the power is divided equally between ports 2 and
3 consequently, it is evident that this design meets the required
specifications. We will implement this design in 3 different ways in the
following sections. Firstly, using lumped elements and secondly, using
microstrip lines. The operating frequency is 3 GHZ.

{displaystyle mathbf {S} ={frac {1}{sqrt
{2}}}{egin{bmatrix}0&-i&-1&0-i&0&0&-1-1&0&0&-i&-1&-i&0end{bmatrix}}}    

3.Implementation using
lumped elements

In this part we are using lumped elements implementation that
are equivalent to the ?/4 transmission lines
sections, the lumped elements design has a
narrower bandwidth than the transmission line hybrid coupler.

Figure (3.1) shows the circuit used for this
design. Given that we are operating this circuit at frequency equals to 3 GHZ
and all capacitors are equal with values  2.562 pF and each two opposite inductors are
equal with values L1= L2 = 1.876 nH  and
L3= L4 =2.653 nH. These Values are calculated using the “Lumped Quadrature
Coupler Designer” calculator 2.

In order
to observe the performance of the circuit, we will notice the simulation
results in the following graphs to make sure it meets the design specifications
mentioned before:

 

 

                     Figure (3.1): The 900
hybrid design using lumped elements

 

 

 

·       First we make sure that the S parameters that came from the simulation
matches the S matrix of the hybrid coupler.                   

·       Then, we check that the circuit is
internally matched by making sure the values of S11=S22=S33=S44=
-65.638 dB as shown in figure (3.3).

Figure (3.2): S
parameters

 

 

    Figure (3.3): internal matching of the
circuit

 

·       
The circuit has orthogonal phase relation
between the output signals as shown in figure (3.4).

·       

Figure (3.4):
Orthogonal phase shift

Since the
designed circuit is a two port power division network the third port is an isolated
port as shown in figure (3.5). Notice that S14 equals -65.622 dB.

 

 

 

 

 

 

 

 

 

 

 

Figure
(3.5): Isolated port

 

 

 

 

 

 

 

 

 

·       
The power delivered to the 2 ports is
maximum at fo and decreases at other frequencies as shown in figure
(3.6) as the S13, S24, S31 and S42 parameters
decrease.

 

                       Figure (3.6):
mismatch at other frequencies

                       Figure (3.7):
bandwidth at -20db

·       
Now if we want to
calculate the bandwidth, by choosing -20 dB to be the threshold the B.W will be
242 MHZ as shown in figure (3.7), if we choose -30 dB to be the threshold the
B.W becomes 77 MHZ as shown in figure (3.8).

                                Figure (3.8):
bandwidth at -30db

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.Implementation using microstrip lines

In this part we are using the microstrip
technology, which is one of the most popular types of planar TLs. ADS tool was
used to determine the width and length for each transmission line in this
design.

Figure (4.1) shows the circuit
and substrates used for this design. Given that we are operating this circuit
at frequency equals to 3 GHZ and the substrate is of relative permittivity 4.5,
the thickness of the substrate is 1.524 mm and the thickness of the
transmission line is 0.016 mm. loss tangent is equal to 0.001.

In order
to observe the performance of the circuit, we will notice the simulation
results to make sure it meets the design specifications mentioned before.

·         
First we make sure that
the S parameters that came from the simulation match the S matrix calculated
(notice figure 4.2).

 

 

 

Figure (4.1):
The 900 hybrid design using mictrostrip lines

 

 

 

·       Figure (4.3) proves that the circuit is internally matched as S11=S22=S33=S44=
-52.291 dB.

 

 

                                                                                
Figure (4.2): S parameters

                                     Figure
(4.3): internal matching
 

 

 

·       One of the most important qualities of our circuit is the
orthogonal phase shift between the output ports that is proven in figure (4.4).

·       Figure (4.5) shows that the power division between the output
ports is logical as at frequencies other than f0 the S13,
S24, S31 and S42 parameters decrease which
indicates that the power delivered is max at f0 and decreases
elsewhere.

Figure (4.4):
Orthogonal phase shift
 

 

                                             
Figure (4.5): Mismatch at other frequencies

                                

 

 

 

 

 

 

 

 

 

·       Isolation between the output ports is very important in this
design and to make sure this design meets it we must make sure that at f0
port 4 is isolated (S14 and S41 =0/-55.928 dB  at the operation frequency f0 as
shown in figure (4.6)).

 

 

 

 

Figure (4.6): isolation between ports

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

·       
Now we need to calculate
the bandwidth, by choosing any value to be the threshold -20 dB or -30 dB we
can measure it to be 312 MHZ in case of -20 dB and 99MHZ in case of -30 dB
(notice figures (4.7) and (4.8) respectively)

Figure (4.7):
bandwidth at -20 dB

 

 Figure (4.8):
bandwidth at -30 dB

 

Figure (4.9): microstrip
layout

After generating the layout of the
microstip schematic, (notice figure (4.9)) the lines with smaller
characteristic impedance have the wider widths.

 

 

 

 

 

 

 

 

 

 

 

5.Conclusion

·      
Power
dividers & combiners are used in a wide variety of applications in
electronics and wave theory.

·      
Power
dividers are passive circuits used to divide power among several loads either
equally or non-equally with or without output phase shift.

·      
Hybrid
couplers are 4-port devices which have input output matching, orthogonal phase
shift between output signals, equal power division ratio and isolation between
output ports.

·      
Microstrip
lines, which are one of the most popular types of planar TLs, are a very
powerful tool in designing power dividers which can meet their designers’
requirements in the RF range.

·       
We
shouldn’t be deceived by the results that show that lumped elements have a
better performance at our operating frequency. This is a simulation after all
using ideal lumped elements. However, in practice, the results of the lumped
elements won’t be so. Not even close, because at this operating frequency the
capacitor should be modeled as a cap with a resistance in shunt and the
inductor as an inductor with a resistance in series leading to undesired and
unexpected results.

·       
It is worthy to note that
the frequency response of the microstrip lines is periodic i.e. the graphs
which are drawn at f0 will be the same at 3f0 ,5f0
and so on.

·      
To get the required
specifications, the user has to use matched loads connected to the ports,
that’s it, loads which have impedances equal to 50 ohms in our case.

·      
It is worthy to note that
S(2,1) and S(3,1) decrease at frequencies different from  f0 and their maxima are at f0 that’s
due to reflections which would happen at frequencies different from f0 which
will make the relative power delivered to each port of 2 and 3 is less than
half.

 

 

 

 

 

 

 

 

 6. References

1     Marki microwave, “Microwave
Power Dividers and Couplers Tutorial Overview and Definition of Terms”

2     G. Breed, “Classic Designs
for Lumped Element and Transmission         Line 90-Degree Couplers,” High Frequency
Electronics, Sep. 2007

 

3   “Lumped Quadrature Coupler
Designer.” Internet : http://leleivre.com/rf_lumped90hybrid.html

 

 

         

 

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