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• Quadrature Hybrid Coupler EECS 420 Semester Project

Angela Oguna, Manas Bhatnagar, Levi Lyons, Hussain Al Hai 5/11/2010

• 2

Introduction: ................................................................................................................................................. 3

Objectives: .................................................................................................................................................... 3

Theoretical Design: ....................................................................................................................................... 3

ADS Design & Simulation Results: ................................................................................................................. 7

Testing: ........................................................................................................................................................ 14

Conclusion: .................................................................................................................................................. 19

• 3

Introduction:

In this project, we were asked to use the techniques learned in EECS 420 to design a 90

degree quadrature hybrid. Quadrature hybrids are passive components which are very important

for realizing balanced amplifiers, or to make reflective attenuator devices. Before the quadrature

hybrid can be simulated or fabricated, a theoretical design is needed to provide the fundamental

understanding of the quadrature hybrid. After developing a fundamental understanding, we used

the Advanced Design Software (ADS) to design the equivalent transmission line coupler. Then

we were ready to fabricate the quadrature hybrid and test it with the Vector Network Analyzer

(VNA).

Objectives:

a. To examine the knowledge that the students obtained from this lab.

b. To understand one of the most popular problem that engineer encounter in their daily basis.

c. To let the students know how to compare their theoretical work with the computer work.

d. To understand how to design a 90 degree quadrature hybrid and test every single mode that it has.

Theoretical Design:

A directional coupler is a passive four-port device that couples a specific proportion of

the power traveling in one transmission line out through another connection or port. A

quadrature hybrid is a special 3 dB coupler with a 900 phase difference in the outputs of the

through and coupled arms. The figure below illustrates the configuration of a quadrature hybrid:

• 4

Figure 1: Configuration of Quadrature Hybrid

When all the ports are matched, power entering port 1 is evenly divided between ports 2

and 3, with a 900 phase shift between these outputs. No power is coupled to port 4 which is the

isolated port. Due to the high degree of symmetry, any port can be used as the input port. The

output ports will always be on the opposite side of the input port, while the remaining port on the

same side as the input port is the isolated port.

However, if there is an impedance mismatch at port 2 with the input at port 1, the signal

power reflected back from port will be divided proportionally between ports 1 and 4. In this case,

port 3 will be the new isolated ports and no power will be fed to it. This shows that all

impedances must be matched in order for the quadrature hybrid to work as expected. Table 1

below shows the phasing arrangement of a quadrature hybrid.

1 2 3 4

1 Input 00 -90

0 Isolated

2 00 Input Isolated -90

0

3 -900 Isolated Input 0

0

4 Isolated -900 0

0 Input

Table 1: Phasing arrangement of quadrature hybrid

The quadrature hybrid has a degree of symmetry, as any port can be used as the input

port. The output ports will always be on the opposite side of the junction from the input port, and

the isolated port will be the remaining port on the same side as the input port. This symmetry is

reflected in the scattering matrix, as each row can be obtained as a transposition of the first row.

• 5

The schematic circuit of the quadrature hybrid is illustrated in the figure below:

Figure 2: Circuit of the quadrature hybrid in normalized form

The amplitudes of the incident waves for ports 1 and 4 can be expressed as:

--- [1]

--- [2]

--- [3]

--- [4]

Where:

e = even mode reflection coefficient

o = odd mode reflection mode reflection coefficient

Te = even mode transmission coefficient =

T0 = odd mode transmission coefficient =

The calculation of e and Te can be done by multiplying the ABCD matrices of each cascade

component in the circuit to give:

The even reflection and transmission coefficients can be obtained by the following formula:

• 6

For the odd transmission and reflection coefficient, we get:

Therefore equations 1-4 can be re-written as:

--- [5] --- [7] --- [6] --- [8]

The first row of the S parameter matrix can then be written as:

As explained before, the other rows of the S-parameter matrix can be obtained by

transposing the first row due to the high degree of symmetry. The scattering parameters (S-

Parameters can then be represented in the matrix below for the input, output and isolated ports:

The following parameters need to be defined to design a quadrature hybrid:

i. Frequency range Frequency band over which the given specifications are valid.

ii. Amplitude balance The peak to peak difference between the maximum and minimum

coupling values at any frequency within the specified bandwidth.

• 7

iii. Phase tolerance Maximum allowable deviation from perfect quadrature(900) measured

in degrees between output ports at any frequency within the specified bandwidth.

iv. Isolation Amplitude difference in dB between a signal appearing at an input port and

the amplitude of that signal as measured at the isolated port when both output ports are

v. VSWR maximum VSWR occurring at any port when all other ports are terminated in

vi. Insertion loss The difference in dB between the powers applied to the input and the sum

of the power appearing at the output when all ports are terminated in matched loads.

To begin designing a quadrature hybrid with the desired bandwidth and center frequency

We used ideal transmission line elements to design an equivalent circuit of the quadrature

hybrid.

Figure 3: Using ideal transmission lines

Then we simulated this design and plotted the S-parameters in dB over a range of

frequency, to obtain the following plot.

• 8

Figure 4: S-parameter behavior for ideal transmission line case

This graph was in accordance to the theoretically expected behavior of the Quadrature

hybrid. As can be seen from the graph, the center frequency was obtained to be 5GHz and the

bandwidth was 500MHz. However, this was only a theoretical model, which could not be

fabricated due to its ideal transmission line components and terminations. To build a model

which could be fabricated meant that the Quadrature hybrid must be designed upon a substrate

schematic below:

4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.44.5 5.5

-50

-40

-30

-20

-10

-60

0

freq, GHz

dB

(S(1

,1))

dB

(S(1

,2))

dB

(S(1

,3))

dB

(S(1

,4))

• 9

Figure 5: Using Microstrip lines

We can see that a microstrip line substrate has been defined as MSUB and the

transmission lines have been replaced by microstrip lines. The Term terminations were

included in the above schematic so that S-parameters could be simulated as follows:

Figure 6: S-parameter behavior for Microstrip line case

4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.44.5 5.5

-8

-7

-6

-5

-9

-4

freq, GHz

dB

(S(1

,1))

dB

(S(1

,2))

dB

(S(1

,3))

dB

(S(1

,4))

• 10

The results of this simulation were far from those simulated with the ideal

transmission lines and did not match the response of a Quadrature hybrid. To correct this

deviance from our desired design, a BL COUPLER from the Passive Circuits DG

Microstrip Circuits directory was used.

The BLCOUPLER element in ADS is a branch line coupler, which has four ports

and is internally composed of microstrip lines, whose parameters such as length and

width can be altered. We used the Line Calc tool to adjust the width and length of the

microstrip lines, in order to make the BLCOUPLER behave like a Quadrature hybrid.

The following schematic shows our design:

Figure 7: The Branch Line Coupler

• 11

Figure 8: Using the BL_COUPLER

This schematic was then simulated to give us the following response:

Figure 9: S-parameter behavior for BL_COUPLER case

4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.84.0 6.0

-20

-15

-10