Quadrature Coupler

Quadrature Hybrid Coupler EECS 420 Semester Project

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

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Table of Contents

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

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

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

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

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

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

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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:

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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.

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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:

Γe = even mode reflection coefficient

Γo = odd mode reflection mode reflection coefficient

Te = even mode transmission coefficient =

T0 = odd mode transmission coefficient =

The calculation of Γe 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:

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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.

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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

terminated in matched loads.

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

matched loads.

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.

ADS Design & Simulation Results:

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

we utilized the knowledge of Advanced Design Software (ADS) which we had previously learnt.

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.

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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

and with microstrip lines instead of ideal transmission lines. This lead to the following ADS

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))

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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))

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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

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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

-5

-25

0

freq, GHz

dB

(S(1

,1))

dB

(S(1

,2))

dB

(S(1

,3))

dB

(S(1

,4))

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This simulation was more in agreement with the behavior of the quadrature

hybrid, so the momentum simulation was performed to yield the following result:

Figure 10: Momentum simulation results

As can be deduced from the plot of S11 above, the center frequency had moved to 4.8

GHz. Although this was acceptable, we used the “Line calc” tool again and further adjusted the

length and width of the microstrip lines in our design. Thereby leading to the following

schematic and momentum simulation result:

4.5 5.0 5.54.0 6.0

-20

-18

-16

-14

-12

-10

-22

-8

Frequency

Ma

g.

[dB

]

S11

4.5 5.0 5.54.0 6.0

20

40

0

60

Frequency

Ph

ase

[d

eg

]

S11

freq (4.000GHz to 6.000GHz)

S11

Tue Apr 27 2010 - Dataset: optimization_with_term_mom_a

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Figure 11: Adjusted width and length of MLINES

Figure 12: Momentum simulation reuslt (final)

4.5 5.0 5.54.0 6.0

-18

-16

-14

-12

-10

-8

-20

-6

Frequency

Mag

. [dB

]

S11

4.5 5.0 5.54.0 6.0

10

20

30

40

50

0

60

Frequency

Pha

se [d

eg]

S11

freq (4.000GHz to 6.000GHz)

S11

Tue Apr 27 2010 - Dataset: optimized_2_mom_a

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These changes to the length and width of the microstrip lines moved the center

frequency to 4.9 GHZ. We then created the layout of this design which was sent to the

EECS shop to be fabricated. To do this we followed the instructions given in the

ADS_Momentun document and had the following result:

Figure 13: Layout to be fabricated

Testing:

Once the layout was fabricated, the four ports were soldered onto it and testing was

carried out using a network analyzer. As previously leant in lab, the one port and two port

calibration of the network analyzer was carried out first. It is important to note here that the

theoretical design described earlier in the report and the final layout, have ports defined

differently. The testing procedure was started by connecting the board to the network analyzer

and plotting S13 and S14. The following plots were obtained:

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Figure 14: S13 from testing


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We can see from figure (9) that both S13 and S14 were expected to give a value of nearly

3dB at the center frequency of 5GHz. However, this was not the case, as testing revealed -20dB

and -25dB for S13 and S14 respectively. Although this was a deviation from expected behavior,

S13 and S14 still behaved symmetrically, which was expected from our design. The plot obtained

for S23 is shown below.


This plot reveals a similar discrepancy in the value of S23 at 5GHz which is nearly -21dB

as opposed to the expected value of -3dB. Similar result was obtained for S24 which gave a value

of -25dB. Thus, despite this deviation from expected behavior, S23 and S24 still behaved

symmetrically, which was expected from our design. The plot obtained for S24 was as follows:

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The trend discrepancy in the four s-parameters described above shows the symmetry

expected from port 1 and port 2 of the board, since value at center frequency of S14 was equal to

S24 and S13 was equal to S34.

The S12 and S34 parameters could not be plotted using the network analyzer due to

physical constraints (the board was too small to plug VNA probes into very close ports). The

value of S11 parameter at center frequency was expected to be nearly -22dB, however, value

obtained from the VNA was 9.8dB. The plot obtained for S11 was as follows:

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Conclusion:

This project surfaced a problem that engineers encounter on a daily basis: The discrepancy

between theory and physical application. During the first stage of this project, we used ADS to

simulate a 5GHz Quadrature Hybrid consisting of ideal transmission lines. When the network

was matched, we were able to obtain the theoretical S-Parameter behavior seen above in Figure

2. The center frequency of Quadrature was exactly 5 GHz with a 500 MHz band pass

frequency. This design met the design requirements of the project.

The next phase project involved simulating the Quadrature designed above with non-ideal,

physical micro-strip transmission lines. Once the circuit was implemented, ADS produced the S-

Parameter Reflections seen in Figure 4. These results were far from the theoretical expectations.

From here we decided to use the functionality of ADS to improve upon the design. Therefore,

we inserted the BL COUPLER in place of our circuit. This produced simulations that were very

agreeable, as we were able to achieve a Quadrature Hybrid with a center frequency of 4.9 GHz.

Although we were unable to obtain a Quadrature Hybrid with a center frequency of 5

GHz, this project was successful as we designed a coupler with a similar 4.9 GHz center

frequency. This could be improved upon in future projects by adjusting the lengths of the

transmission lines so that the desired center frequency is reached. But, one of the greatest

lessons to take away from this project is the difference between theory and physical application.

Quadrature Coupler

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