Directional Coupler Report (1)

DESIGN PROJECT

QUADRATURE 900 3DB COUPLER

2014

ECE 571 QUADRATURE 900 3DB COUPLER Field & Waves II

CONTENTS

1. ABSTRACT

2. INTRODUCTION:

3. DIRECTIONAL COUPLERS

4. HYBRID COUPLERS

5. MICROSTRIP TRANSMISSION LINE

6. MICROSTRIP DESIGN

7. TYPES OF COUPLERS

8. APPLICATION

9. CONCLUSION

REFERENCES

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LIST OF FIGURES

Figure 1 90 Degree hybrid design.........................................................................................................4Figure 2 DIRECTION COUPLER.......................................................................................................5Figure 3PART OF POWER DIVIDER AND DIRECTIONAL............................................................7Figure 4Block diagram of 90 Degree hybrid coupler feeding into LNAs.............................................9Figure 5 Geometry of a branch-line coupler.......................................................................................11Figure 6 Even modes of Configuration...............................................................................................13Figure 7 Odd modes of Configuration................................................................................................13Figure 8 Even & Odd modes..............................................................................................................14Figure 9 Micro Strip Dimensions........................................................................................................15Figure 10 Model of Coupler...............................................................................................................15Figure 11 Microstrip Cross-Section....................................................................................................17Figure 12 Embedded Microstrip Cross-Section..................................................................................17Figure 13 S21 and S31 magnitude using Electronic Calibration.........................................................18Figure 14 Phase difference using Electronic Calibration....................................................................19Figure 15 Amplitude difference using Electronic Calibration.............................................................19Figure 16 Bi-directional Coupler.......................................................................................................20Figure 17 Dual-directional coupler.....................................................................................................21Figure 18 Micro-strip Zo as a function W/h.......................................................................................26

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ABSTRACT

90o QUADRATURE HYBRID COUPLER

We intend to design a Quadrature Hybrid (90 degree) microwave coupler. The

component will include both lumped and distributed elements including resistors and

quarter-wave transmission lines. We could include both hand calculations (including

Smith Charts) and computer simulations to verify that our coupler works.

Applications of the hybrid include mono pulse comparators, mixers, power

combiners, dividers, modulators and phased array radar antenna systems. By the basis

of equation in microstrip, simulation by microwave office software terminated by 50

ohm is made using ideal transmission line. Also from microstrip technology, the design

was fabricated on the copper clad board.

Block Diagram:

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INTRODUCTION:

The Conventional Quadrature Coupler:

Quadrature hybrid is a 3dB directional coupler, and has a 90o phase difference between the outputs.

The [S] matrix of the 90o hybrid is:

The [S] matrix above shows that all ports are matched, and the input power is divided equally between the coupled and through outputs only.

The conventional 90ohybrid design is shown in figure below.

Figure 1 90 Degree hybrid design

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DIRECTIONAL COUPLER

A directional coupler is a passive device which couples part of the

transmission power by a known amount out through another port, often by

using two transmission lines set close enough together such that energy

passing through one is coupled to the other. As shown in Figure, the device

has four ports: input, transmitted, coupled, and isolated. The term "main

line" refers to the section between ports 1 and 2. On some directional

couplers, the main line is designed for high power operation (large

connectors), while the coupled port may use a small SMA connector.

Often the isolated port is terminated with an internal or external matched

load (typically 50 ohms). It should be pointed out that since the directional

coupler is a linear device, the notations on Figure are arbitrary. Any port

can be the input, which will result in the directly connected port being the

transmitted port, adjacent port being the coupled port, and the diagonal

port being the isolated port.

Figure 2 DIRECTION COUPLER

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Common properties desired for all directional couplers are wide

operational bandwidth, high directivity, and a good impedance match at all

ports when the other ports are terminated in matched loads. These

performance characteristics of hybrid or non-hybrid directional couplers

are self-explanatory.

POWER DIVIDER:

Power dividers also power splitters and, when used in

reverse, power combiners and directional couplers are passive devices used

in the field of radio technology. They couple a defined amount of the

electromagnetic power in a transmission line to a port enabling the signal

to be used in another circuit. An essential feature of directional couplers is

that they only couple power flowing in one direction. Power entering the

output port is coupled to the isolated port but not to the coupled port.

Directional couplers are most frequently constructed from two

coupled transmission lines set close enough together such that energy

passing through one is coupled to the other. This technique is favoured at

the microwave frequencies the devices are commonly employed with.

However, lumped component devices are also possible at lower

frequencies. Also at microwave frequencies, particularly the higher bands,

waveguide designs can be used. Many of these waveguide couplers

correspond to one of the conducting transmission line designs, but there

are also types that are unique to waveguide.

Directional couplers and power dividers have many applications,

these include; providing a signal sample for measurement or monitoring,

feedback, combining feeds to and from antennae, antenna beam forming,

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http://en.wikipedia.org/wiki/Lumped_element_model

http://en.wikipedia.org/wiki/Microwave

http://en.wikipedia.org/wiki/2-port_network

http://en.wikipedia.org/wiki/Transmission_line

http://en.wikipedia.org/wiki/Passive_component


providing taps for cable distributed systems such as cable TV, and

separating transmitted and received signals on telephone lines.

Figure 3PART OF POWER DIVIDER AND DIRECTIONAL

COUPLING FACTOR

The coupling factor is defined as:

Where P1 is the input power at port 1 and P3 is the output power

from the coupled port. The coupling factor represents the primary property

of a directional coupler. Coupling is not constant, but varies with

frequency.

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ISOLATION

Isolation of a directional coupler can be defined as the difference in

signal levels in dB between the input port and the isolated port when the

two output ports are terminated by matched loads, or:

Isolation can also be defined between the two output ports. In this

case, one of the output ports is used as the input; the other is considered the

output port while the other two ports (input and isolated) are terminated by

matched loads.

Consequently:

DIRECTIVITY

Directivity is directly related to Isolation. It is defined as:

Where: P3 is the output power from the coupled port and P4 is the power

output from the isolated port.

The directivity should be as high as possible. Waveguide directional

couplers will have the best directivity. Directivity is not directly

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measurable, and is calculated from the isolation and coupling

measurements as:

Directivity (dB) = Isolation (dB) - Coupling (dB)

HYBRID COUPLERS

The hybrid coupler, or 3 dB directional coupler, in which the two outputs are of

equal amplitude, takes many forms. Not too long ago the quadrature (90 degree) 3 dB

coupler with outputs 90 degrees out of phase was what came to mind when a hybrid

coupler was mentioned. Now any matched 4-port with isolated arms and equal power

division is called a hybrid or hybrid coupler. Today the characterizing feature is the

phase difference of the outputs. If 90 degrees, it is a 90 degree hybrid. If 180 degrees, it

is a 180 degree hybrid. Even the Wilkinson power divider which has 0 degrees phase

difference is actually a hybrid although the fourth arm is normally imbedded.

Applications of the hybrid include monopulse comparators, mixers, power

combiners, dividers, modulators, and phased array radar antenna systems.Hybrid

couplers are four-port devices that split 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. Three decibel attenuation means that 50%

of the input power is lost [2]. 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. A block diagram of this functionality.

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Figure 4Block diagram of 90 Degree hybrid coupler feeding into LNAs

90-degree hybrid couplers are often called branch-line couplers. As the name

implies power is equally divided between the output ports and are therefore electrically

and mechanically symmetrical. These branch-line couplers are built using transmission

lines and their size is proportional to the wavelength of the designated center frequency,

which can be meters long. This becomes a significant drawback in applications where a

small footprint is required. Hybrid couplers can also be built by using lumped

components, which are resistors,

inductors, and capacitors with an ideal (lossless) connection. The lumped component

design is promising because it provides low insertion loss, wider bandwidth, and a

smaller size circuit, making it a good fit for a monolithic microwave integrated circuit

(MMIC).

AMPLITUDE BALANCE

This terminology defines the power difference in dB between the two output

ports of a 3 dB hybrid. In an ideal hybrid circuit, the difference should be 0 dB.

However, in a practical device the amplitude balance is frequency dependent and

departs from the ideal 0 dB difference.

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PHASE BALANCE

The phase difference between the two output ports of a hybrid coupler should

be 0, 90, or 180 degrees depending on the type used. However, like amplitude balance,

the phase difference is sensitive to the input frequency and typically will vary a few

degrees.

The phase properties of a 90 degree hybrid coupler can be used to great

advantage in microwave circuits. For example in a balanced microwave amplifier the

two input stages are fed through a hybrid coupler. The FET device normally has a very

poor match and reflects much of the incident energy. However, since the devices are

essentially identical the reflection coefficients from each device are equal. The reflected

voltage from the FETs is in phase at the isolated port and is 180E different at the input

port. Therefore, all of the reflected power from the FETs goes to the load at the isolated

port and no power goes to the input port. This results in a good input match (low

VSWR).

A hybrid coupler is a passive device used in radio and telecommunications. It is

a type of directional coupler where the input power is equally divided between two

output ports. Hybrid couplers are the special case of a four-port directional coupler that

is designed for a 3-dB (equal) power split. Hybrids come in two types, 90 degree or

quadrature hybrids, and 180 degree hybrids.

ANALYSIS:

Quadrature 90 degrees hybrid couplers are 3dB couplers with a 90 degrees

phase difference between the two output ports. This is achieved using 4 quarter-wave

transmission lines connected and matched as shown below:

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Figure 5 Geometry of a branch-line coupler

When all ports are matched, power is entered through port 1 and divided evenly

(3dB loss) across ports 2 and 3. Ports 2 and 3 are also 90 degrees out of phase, with no

power being coupled or reflected to port 4. Hence, high isolation results from the

design. In addition, the coupler is also symmetrical...meaning that ports 2 and 3 can

serve as the input and isolation ports, respectively, while ports 1 and 4 can serve as the

outputs. In addition to all ports being matched, the coupler is reciprocal and lossless.

The S-parameters are defined by the matrix:

[S] = | 0 ej 0 |

| 0 0 ej |

| ej 0 0 |

| 0 ej 0 |

For 90 degrees, symmetrical: = = 90 degrees:

[S] = | 0 j 0 |

| 0 0 j |

| j 0 0 |

| 0 j 0 |

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In order to achieve equal power division: = = 1/2:

[S] = 1/2 * | 0 1 j 0 |

| 1 0 0 j |

| j 0 0 1 |

| 0 j 1 0 |

Even and Odd modes

Even and odd mode analysis is a technique used to extract the even and odd-

modeImpedances of a circuit. It is employed in horizontally or vertically symmetric

circuits. ThisTechnique is based on two principles: symmetry of the circuit and

superposition. An example of a Hybrid coupler is shown in Figure 10. The coupler is

properly terminated (matched) so that the reflected power at the input port is zero.

For even mode analysis the TL is cut in half and set as an open circuit. This is

shown in Figure 12 the voltage supply in port 1 and 2 of the quad hybrid has the same

polarity.

Figure 6Even modes of Configuration

For the odd mode analysis the TL is cut in half and grounded along the

symmetry line, as is shown in Figure 13. The voltage supply of ports 1 and 2 of the

quad hybrid has the opposite polarity. Since the hybrid coupler is a 4 port device, it is

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analyzed based on the 4x4 matrix representation of the S-parameters. See section 4 for

a more in depth analysis.

Figure 7 Odd modes of Configuration

There are two modes of current flow in an electromagnetic situation such as

this: the first is one flowing down one conductor with a contra-flow current back up the

other conductor caused by displacement current coupling between the two conductors.

This is termed the odd mode or differential mode current, and has associated odd mode

characteristic impedance, styled Z0o. Imagine it conceptually like this. Energy couples

from one line into the other, flowing away from the source to the matched load. No

energy returns from the far end matched loads, but some flows back out towards the

source, so there is a plus arrow going away down one conductor and a minus arrow

coming back out of the other conductor.

The other component of current flows by displacement current between each

center conductor carrying the same polarity, and the ground that is common between

them. Hence this is called the common or even mode current, and has an associated

even mode characteristic impedance, styled Z0e.

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Figure 8 Even & Odd modes

From the electrostatic field patterns, it is clear that there are 3 values of

capacitance involved for the odd mode, and each must figure in the Z0 formula

somewhere. The first is the direct capacitance to ground of each trace, the second is the

mutual capacitance between the traces, and the third represents the distortion of each

caused by the presence of the coupled element.

MICROSTRIP LINE

A microstrip transmission line is a "high grade" printed circuit construction,

consisting of a track of copper or other conductor on an insulating substrate. There is a

"backplane" on the other side of the insulating substrate, formed from a similar

conductor. Looked at one end, there is a "hot" conductor, which is the track on the top,

and a "return" conductor, which is the backplane on the bottom. A microstrip is

therefore a variant of a two-wire transmission line.

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Figure 9 Micro Strip Dimensions

If one solves the electromagnetic equations to find the field distributions in the

vicinity of a microstrip, one finds very nearly a completely TEM (transverse

electromagnetic) wave pattern. This means that there are only a few regions in which

there is a component of electric or magnetic field in the direction of (as opposed to

perpendicular to the direction of) wave propagation. This field pattern is commonly

referred to as a Quasi TEM pattern.

Figure 10 Model of Coupler

Since some of the electric energy that is stored in this conductor configuration is in the

air, andsome is in the dielectric, the effective dielectric constant for the waves on the

transmission linewill lie somewhere between that of the air and that of the dielectric.

Typically, the effectivedielectric constant will be 50-85% of the substrate dielectric

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constant, depending on the2geometry of the microstrip. This effective dielectric

constant determines the phase velocity ofelectromagnetic waves on the microstrip

transmission line.

Microstrip parameters

The basic configuration of the microstrip is shown in the picture above. One of

the mostchallenging problems associated with this configuration arises from the fact

that the small strip isnot immersed in a single dielectric. On one side there is the board

dielectric, and on the top isusually air. The technique that has been developed to handle

this challenge uses, as wasmentioned above, the concept of effective relative dielectric

constant, εeff. This value representssome intermediate value between the relative

dielectric constant of the board material, εr, andthat of air (assumed equal to 1) that can

be used to compute microstrip parameters as though thestrip were completely

surrounded by material of that effective relative dielectric constant. Oneobvious

advantage of the microstrip structure is the "open" line which makes it very easy

toconnect components. On the other hand, the configuration doesn't provide the

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"shielded" signalline advantage of the stripline. Another advantage is that microstrips

can be packed togetherwith fairly high density (multiple channels) with only minimal

"crosstalk" interference, andtherefore lends itself well to RF and microwave IC design.

Figure 11Microstrip Cross-Section

Figure 12 Embedded Microstrip Cross-Section

Aside from the difficulty of calculating the value of εeff, there is another

important effect. It isclear that εeff will depend on both W and h. Hence, the phase

velocity along the microstrip willdepend on these parameters. Assuming the relative

permeability of all materials in the linedesign is well approximated by μr = 1, the phase

velocity will be given by:Since the characteristic impedance (Zo) of the line will also

depend on these parameters, everytime we need to design a microstrip with a new

characteristic impedance, we will be faced withup = cεeff

The additional complication of having to deal with a change in phase velocity

(or delay time) andconsequently of the wavelength of waves on that microstrip. Note

that this is not a problem withcoaxial cable or stripline design.To get an idea of the

range of εeff, consider the cases of a very wide W and then a very narrow W.For a wide

microstrip, nearly all of the electric field lines will be concentrated between the

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metalplanes, similar to the case of a parallel plate capacitor that you studied in physics.

Thus:

On the other extreme, for narrow W the electric field lines will be about equally

divided between the air and the board dielectric so that:

This gives you a range:

Several different equations have been developed for use in calculating

characteristic impedance for microstrip design. Probably the most useful are the

following which are reported to be accurate to within about 1%:

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Figure 13 S21 and S31 magnitude using Electronic Calibration

Figure 14 Phase difference using Electronic Calibration

Figure 15 Amplitude difference using Electronic Calibration

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Microstrip Design Equation Set SelectionProcedure

Design Logic

The correction for finite thickness “t” of the microstrip is small and can be neglected in

the

design logic.

Assume W/h = 1 and calculate Zo1 using equations 1 and 2.

D1 = Zo1 – Zo (If Zo is smaller than Zo1, then W/h must be greater than 1.)

If D1 ≥ 0, compute using equations 3, 4, and 5 (micro3)

If D1 < 0, assume W/h = 1/(2π) and calculate Zo2 using equations 1 and 2.

D2 = Zo2 – Zo (If Zo is smaller than Zo2, then W/h must be greater than 1/2π.)

If D2 ≥ 0, compute using equations 1, 2, and 5 (micro2)

If D2 < 0, compute using equations 1, 2, and 6 (micro1)

Types of Couplers

Bethe-hole coupler

Bethe-hole is a waveguide directional coupler, using a single hole, and it works

over a narrow band. The Bethe-hole is a reverse coupler, as opposed to most waveguide

couplers that use multi-hole and are forward couplers.The origin of the name comes

from a paper published by H A Bethe, titled "Theory of Diffraction by Small Holes",

published in the Physical Review, back in 1942. If you google it you might find it, even

though it is probably subject to copyright protection. This is a tough read, unless you

like to ponder equations.

Multi-hole coupler

In waveguide, a two-hole coupler, two waveguides share a broad wall. The

holes are 1/4 wave apart. In the forward case the coupled signals add, in the reverse

they subtract (180 apart) and disappear. Coupling factor is controlled by hole size. The

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"holes" are often x-shaped, or perhaps other proprietary shapes. It is possible to provide

very flat coupling over an entire waveguide band.

Bi-directional property

Any directional coupler is bi-directional, that is, it performs equally well when

the signal is incident on port 2 versus port 1, but the coupled and isolated ports flip. All

direction couplers are bi-directional, unless you terminate one of the ports. Consider the

coupled-line coupler below. Port 4 is the coupled port when a signal is incident on port

1, and port 3 is the coupled port when a signal is incident on port 2.

Figure 16 Bi-directional Coupler

Dual-directional coupler

Here we have two couplers in series, in opposing directions, with the isolated

ports internally terminated. This component is the basis for the reflectometer. Using

internal, well-matched loads helps remove errors associated with poor terminations that

might be present in real systems. We'll analyze that statement one of these days. Oops,

we have violated our clockwise notation rule below!

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Figure 17 Dual-directional coupler

Micro-strip Design &Calculation:

In this part, the calculation for width (W) and Length(L) has been finding, the

value from the calculation has been use in the circuit

Specifications & Assuming Wh

<2 at f=2.5GHz

zo=50 Ω

Er=10

h=1.5mm

Wh

=8∗e A

e2∗A−2

Z=50

A=Zo

60 √ E r+12

+E r−1E r+1

(0.23+ 0.11Er

)

A=5060 √ 10+1

2+[10−1

10+1 ](0.23+ 0.1110 ) [∴E r=10 ]

A=0.833√ 112

+[ 911 ] (0.23+0.00916 )

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A=0.833× (5.5 )+0.818 (0.197 )

A=2.115

wh= 8e2.115

e2∗2.115−2

wh=0.993

∅=900

∅= βl

π2

=2 * π * f x

lc

√ Eeff

L=c

4∗f∗√Eeff

wh

>1

Eeff =Er+1

2+

E r−1

2 [(1+12hw

)−1/2]

¿ 10+12

+ 10−12 [(1+12

1.51.490

)−1 /2]

¿5.5+4.5(0.276)

Eeff =6.744

L=c

4 f √Eeff

=3 x108

4 x 2.5 x109 √6.744Where C=3 x108

=0.01155mts

=1.15cm

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Since wh

>0.6

λ=λo

√E r

¿¿

λ=λo

√10 [ 101+ (0.63 ) (10−1 ) (0.99 ) ]

1/2

λ=0.387 λo

λo=cf

¿ 3 x 108

2.5 x 109

λo=0.03

λ=0.03 x0.387

=0.01161

zo 1=zo

√2

¿ 50

√2

¿35.355

Assuming Wh

<2 at f=2.5 GHz

Er=10

h=1.5mm

Wh

=8 e A

e2 A−2

z=50

A=zo

60 √ E r+12

+E r−1E r+1

(0.23+ 0.11Er

)

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A=35.355

60 √ 10+12

+[ 10−110+1 ](0.23+ 0.11

10 ) [∴E r=10 ]

A=0.589√ 112

+[ 911 ] (0.23+0.00916 )

A=0.589× (1.658 )+0.818 (0.197 )

A=1.543

wh= 8 e1.543

e2∗1.543−2

wh=1.881

h=1.5mm (given)

W=1.881*1.5mm

=2.822mm∅=900

∅= βl

π2

= βl

π2=Wl

V p

π2

=2 πfl

c∗√ Eeff

L=C

4∗f∗√Eeff

wh

>1

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Eeff =Er+1

2+

E r−1

2 [(1+12hw

)−1/2]

¿ 10+12

+ 10−12

¿

¿5.5+4.5(0.371)

Eeff =7.169

L=c

4 f √Eeff

=3 x 108

4∗2.5∗109 √7.169C=3 x108

¿0.0112mts

=0.280cm

Since wh

>0.6

λ=λo

√E r

¿¿

λ=λo

√10¿¿

λ=0.37 λo

λo=cf

¿ 3 x 108

2.5 x 109

λo=0.03

λ=0.03 x0.37

=0.012

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Figure 18 Micro-strip Zo as a function W/h

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CONCLUSION

Bycalculating to get the correct parameters. The value of characteristic width

and wavelength had been found. The comparison is made between theoretical and

practical. The part is discussed abut the theory to analyze directional coupler

(Quadrature (90o) Hybrid) which are by calculation an simulation and the part is discuss

about the practical which is fabrication and testing.

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References:

Books

Microwave Engineering By Matthew Radmanesh Class notes of ECE 671

Microwave Engineering Second edition, John Wiley & sons,1998 Book by

David M Pozar

W ebsite

Website Title: - Microwave Encyclopedia, Article Title: Microstrip,

Website:http://www.microwaves101.com/encyclopedia/microstrip.cfm

Website Title: Directional Couplers - Microwave Encyclopedia -

Microwaves10,Article Title: Directional Couplers - Microwave Encyclopedia -

Microwaves10

,Website:<//www.microwaves101.com/encyclopedia/directionalcouplers.cfm>

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http://www.microwaves101.com/encyclopedia/microstrip.cfm

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