Experiment No .
16
Aim :
To design 4 port hybrid ring coupler in Microstrip and CPW line
Design Specification :
Dielectric Constant of Substrate, for microstrip
r =3.2
, for CPW line
r =10.2
Substrate Height, h=1.58 mm
Design Frequency, fd= 5 GHz
Characteristic Impedance, Zo=50
Theory and Design Steps:
o
o
The 180 hybrid junction is a four- port network with a 180 phase shift between the two
output ports. It can also be operated so that the outputs are in phase . With reference to the
180
hybrid symbol shown in figure, a signal applied to port 1 will be equally split into two
in-phase components at port 2 and 3, and port 4 will be isolated. If the input is applied to port 4,
o
it will be equally split in to two components with a 180 phase difference at ports 2 and3, and
port 1 will be isolated. When operated as a combiner , with input signals applied at port 2 and3,
the sum of the inputs will be formed at port1, while the difference will be formed at port 4.
Hence, port 1 and 4 are referred to as the sum and difference ports, respectively . The scattering
matrix for the ideal 3 dB 180
[ ]
0 11 0
j 1 0 01
[ S ]=
2 1 0 01
011 0
hybrid thus has the following form:
The S- matrix is unitary and symmetric.
o
The 180 hybrid can be fabricated in several forms. The ring hybrid, or rat-race , can easily be
constructed in planar (microstrip or stripline) form. Analysis of ring coupler can be done using
even and odd mode analysis.
Even and odd mode alnalysis
First consider a unit amplitude incident at port 1 (the sum port) of the ring hybrid. At the junction
this wave will divide into two components, which both arrive in phase at ports 2 and 3, and
180o out of phase at port 4. Using even-odd mode analysis we can decompose this case into a
superposition of the simpler circuits and excitation shown in figure
(a) Even mode decompodition of ring hybrid coupler
(b) Odd mode decomposition of ring hybrid coupler
The amplitude of the scattered waves from the ring hybrid will be
1
1
B 1= e + o
2
2
1
1
B 2= T e + T o
2
2
1
1
B 3= e o
2
2
1
1
B 4= T e T o
2
2
We can evaluate the required reflection and transmision coefficients defined in above figure
using the ABCD matrix for the even- and odd-mode teo-port circuits in above figure. The results
are
2
[CA DB ] =[ j1j21
]
e
[CA DB ] =[1j j212]
o
Then
e=
j
2
T e=
j
2
o=
j
2
T o=
j
2
Using above results
B 1=0
B 2=
j
2
B 3=
j
2
B 4=0
Which shows that iinput port is matched , port 4 is isolated, and the input poer is evenly divided
and in phase between ports 2 and 3. These results form the first row and column of the scattering
matrix
Next consider a unit amplitube wave incident at port 4 (the difference port) of the ring hybrid .
the two wave components on the ring will arrive in phase at port 2 and port 3, with a ralative
o
phase difference of 180 out of phase at port 1. This case can be decomposed into a
superposition of the two simpler circuits and excitation as shown in figure below.
(a) Even mode decomposition of ring hybrid when port 4 is excited with unit amplitude wave
(b) Odd mode decomposition of ring hybrid when port 4 is excited with unit amplitude wave
The amplitudes of the scattered waves will be
1
1
B 1= T e T o
2
2
1
1
B 2= e o
2
2
1
1
B 3= T e + T o
2
2
1
1
B 4= e + o
2
2
The ABCD matrices for the even- and odd-mode circuits of above figure are
[CA DB ] =[1j j212]
e
2
[CA DB ] =[ j1j21
]
o
The necessary reflection and transmission coefficients are
e=
j
2
T e=
j
2
o =
j
2
T o=
j
2
Using above results, gives
B 1=0
B 2=
j
2
B 3=
j
2
B 4=0
Which shows that the input port is matched , port 1 is isolated, and the input power is evenly
o
divided into ports 2 and 3 with a 180 phase difference. These form the fourth row and
column of the scattering matrix . The remaining elements in this matrix can be found from
symmetry considerations.
The bandwidth of the ring hybrid is limited by the frequency dependence of the ring lengths, but
is generally on the order of 20% - 30% . Increased bandwidth can be obtained by using
additional sections, or a symmetric ring circuit .
Design Step
Calculation of the ring impedance i.e
2 Z 0 = 1.414 x 50 = 70.71
Compution of width and length of the microstrip using QUCS are
l
Zo
(degree)
(ohm)
90o
90o
270
Section
(width of conductor plate)
(Length of Microstrip)
mm
mm
50
3.845
9.243
70.71
2.116
9.474
70.71
2.116
28.422
Compution of width and length of the CPW line using QUCS are
Section
Zo
(degree
(ohm)
(width of
(Spacing between
(Length of
conductor plate)
conductor plate and
CPW line)
mm
ground)
mm
50
54.079
mm
5
10.005
90
90o
70.71
11.366
8.907
270o
70.71
11.366
26.721
Design and Response :
(a)Design using PUFF , for microstrip line
(b)Design using QUCS ,for microstrip line
S11 :
S21 :
S31:
S41 :
Comparing graphs of S11, S21, S31, S41 :
(c) Design using QUCS, for CPW line
S11 :
S21 :
S31 :
S41:
Comparing graphs of S11, S21, S31, S41 :
Result and Discussion:
The response of Branch line equal power coupler using microstrip line and CPW lline has been
studied successfully. Comparison of responses has been carried out in QUCS and Puff, on the
basis of insertion loss and reflection coefficient, at design frequency (fd=5 GHz)
PUFF
Reflection Coefficient (for port1) (dB)
Insertion Loss (for Port 2)
(dB)
Insertion Loss (for Port 3)
(dB)
Insertion Loss (for Port 4)
(dB)
>100
3.01
3.01
>100
QUCS
For Microstrip line For CPW line
77.2
3.03
3.03
71.6
26.2
3.05
3.04
48.5
