Experiment No .16

Aim :

To design 4 port hybrid ring coupler in Microstrip and CPW line

Design Specification :

Dielectric Constant of Substrate, for microstrip ε r=3.2, for CPW line ε r=10.2

Substrate Height, h=1.58 mm

Design Frequency, fd= 5 GHz

Characteristic Impedance, Zo=50 Ω

Theory and Design Steps:

The 180o hybrid junction is a four- port network with a 180o phase shift between the two output ports. It can also be operated so that the outputs are in phase . With reference to the 180o 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, it will be equally split in to two components with a 180o 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 180ohybrid thus has the following form:

[S ]=− j√2 [ 011 0

100−11 00 1

0−11 0]The S- matrix is unitary and symmetric.

The 180ohybrid 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

B1=12Γe+

12Γo

B2=12T e+

12T o

B3=12Γe−

12Γ o

B4=12T e−

12T o

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

[ A BC D ]e=[ 1 j√2j √2−1]

[ A BC D ]o=[−1 j√2

j√21 ]Then

Γe=− j√2

T e=− j√2

Γ o=j

√2

T o=− j√2

Using above results

B1=0

B2=− j√2

B3=− j√2

B4=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 phase difference of 180o 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

B1=12T e−

12T o

B2=12Γe−

12Γ o

B3=12T e+

12T o

B4=12Γ e+

12Γ o

The ABCD matrices for the even- and odd-mode circuits of above figure are

[ A BC D ]e=[−1 j√2

j√2 1 ][ A BC D ]

o=[ 1 j √2j√2−1]

The necessary reflection and transmission coefficients are

Γe=j

√2

T e=− j√2

Γ o=− j√2

T o=− j√2

Using above results, gives

B1=0

B2=j

√2

B3=− j√2

B4=0

Which shows that the input port is matched , port 1 is isolated, and the input power is evenly divided into ports 2 and 3 with a 180o 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 √2Z0 = 1.414 x 50 = 70.71 Ω

Compution of width and length of the microstrip using QUCS are

Section βl

(degree)

Zo

(ohm)

W

(width of conductor plate)

‘mm’

L

(Length of Microstrip)

‘mm’

1 90o 50 3.845 9.243

2 90o 70.71 2.116 9.474

3 270o 70.71 2.116 28.422

Compution of width and length of the CPW line using QUCS are

Section βl

(degree

)

Zo

(ohm)

W

(width of

conductor plate)

‘mm’

S

(Spacing between

conductor plate and

ground)

‘mm’

L

(Length of

CPW line)

‘mm’

1 90o 50 54.079 5 10.005

2 90o 70.71 11.366 5 8.907

3 270o 70.71 11.366 5 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)

PUFFQUCS

For Microstrip line For CPW line

Reflection Coefficient (for port1) (dB) >100 77.2 26.2 Insertion Loss (for Port 2) (dB) 3.01 3.03 3.05 Insertion Loss (for Port 3) (dB) 3.01 3.03 3.04 Insertion Loss (for Port 4) (dB) >100 71.6 48.5