Microwave Engg- Passive Devices

Microwave Network Components

Microwave Network Components

Active

Solid state devices

Vacuum Tube devices

Active DevicesSolid State Devices

– MW BJTs– Hetero junction BJTs(HBTs)– MW FETs– MW Tunnel diode– Transferred Electron

Devices (TEDs)– Gunn Effect Diodes– LSA diodes– InP diodes– CdTe diodes– Read Diode– IMPATTS– TRAPATTS– BARRITS

Tube based Devices

―Klystrons― Multi cavity Klystrons― Reflex Klystrons― Helix TWT― Coupled cavity TWT― High power and grid control TWT― Magnetron ― Cross Field Amplifier

Passive DevicesDielectric based

– Waveguide Tees– Magic Tees– Hybrid rings– Waveguide

corners, bends, twists

―Directional Couplers

―Hybrid couplers

Ferrite based―Circulators―Isolators―Attenuators―Gyrators

S-parameter model at a glance

Microwave device

Port 1 Port 2

Vi1

Vr1

Vt2

Vi2

Vr2

Vt1

Transmission and reflection coefficients

i

t

V

V

i

r

V

V

Input signalreflected signal

transmitted signal

S-parameters

0111

2

1

r

r

Vi

V

VS

02

212

2

rVi

t

V

VS

01

121

1

rVi

t

V

VS

02

222

1

rVi

r

V

VS

Vr2=0 means port 2 is matched

Vr1=0 means port 1 is matched

S-parameters

212111 iir VVV

221212 iir VVV Hence

In matrix form

2

1

221

121

2

1

i

i

r

r

V

V

V

V

2

1

2221

1211

2

1

i

i

r

r

V

V

SS

SS

V

VS-matrix

•S11and S22 are a measure of reflected signal at port 1 and port 2 respectively•S21 is a measure of gain or loss of a signal from port 1 to port 2.•S12 is a measure of gain or loss of a signal from port 2 to port 1.

Logarithmic formS11=20 log(r1) S22=20 log(r2)S12=20 log(t12)S21=20 log(t21)

S-parameters

S-parameters are complex (i.e. they have magnitude and angle) because both the magnitude and phase of the input signal are changed by the network.

(This is why they are sometimes referred to as complex scattering parameters).

What do S-parameters depend on?

if the network is changed, the S-parameters change.

if the frequency is changed, the S-parameters change.

if the load impedance is changed, the S-parameters change.

if the source impedance is changed, the S-parameters change.

S-matrix of a Multi-port network

network

Port 1

Port 2

Port

3

Port 4

Port 5

5

4

3

2

1

5554535251

4544434241

3534333231

2524232221

1514131211

5

4

3

2

1

i

i

i

i

i

r

r

r

r

r

V

V

V

V

V

SSSSS

SSSSS

SSSSS

SSSSS

SSSSS

V

VV

V

V

Properties of S-matrix

1. Symmetry Property or

2. Unitary property

3. Phase shift property

][][ S jiijS ],[][ SS T

11

2||*

1

k

iSijSij

k

iSij

4. Zero PropertyThe sum of (each term of any column (row) multiplied by the complex conjugate of the corresponding terms of any column(row) is zero. )

Power loss calculation

Waveguide Tees

Tee JunctionA waveguide or coaxial-line junction with three independent ports

Matrix of third order, containing nine elements, six of which should be independent.

E-plane Tee(1)

Series Tee

A waveguide tee in which the axis of its side arm is parallel to the E-field of the main guide.

E-plane Tee(2)

If the collinear arms are symmetric about the side arm, There are two different transmission characteristics

Two wayTransmission of E-plane teea) i/p-main armb) i/p-side arm

E-plane Tee(3)

If E-plane tee is perfectly matched at the junction, the diagonal components of the S-matrix, S11, S22 and S33 are zero because there will be no reflection.When the waves are fed into the side arm (port 3), the waves appearing at port1 and port2 of the collinear arm will be in the opposite phase and in the same magnitude. Therefore,

S13 = -S23 (both have opposite signs)

E-plane Tee(4)

For a matched junction, S11 = S22=S33=0From Symmetry propertyS12 = S21, S13 = S31and S23 = S32From Zero property,S11S12* + S21S22* + S31S32* = 0Hence,S13S23* = 0i.e S13 = 0 or S23 = 0 or both = 0

E-plane Tee(5)

From Unity property,S21S21* + S31S31* = 1 IS12S12* + S32S32* = 1 IIS13S13* + S23S23* = 1 III

Substituting zero property in unitary property IV

E-plane Tee(6)

Eqn III and IV are contradictoryIf S13 = 0 then S23 = 0 and thus eqn III is false.

Similarly, if S23 = 0, then S13 = 0 and hence eqn IV is also not true.This inconsistency proves the statement that the tee junction cannot be matched to the three arms.

Diagonal elements are not all zero

E-plane Tee(7)

When an E-plane is constructed of an empty waveguide, it is poorly matched at the tee junction.Hence

However since the collinear arm is usually symmetric about the side arm, Thus,

E-plane Tee(8)• If port 3 is perfectly matched S33=0• Therefore S-matrix becomes

• Using unity property and some mathematical manipulations, we can write S-matrix of E-plane tee as

H-Plane Tee(1)Shunt teeA waveguide tee in which the axis of its side arm is “shunting” the E-field or parallel to the H-field of the main guide.

H-Plane Tee(2)If two input waves are fed into port 1 and port 2 of the collinear arm, the output wave at port 3 will be in phase and additive.If the input is fed into port 3, the wave will split equally into port 1 and port 2 in phase and in the same magnitude.Therefore the S matrix of H-plane tee is similar to E-plane tee except S13 = S23

Magic Tees (Hybrid Tees)

Combination of E-plane tee and H-plane tee.

Magic Tee Characteristics 1. If two waves of equal magnitude and the same phase

are fed into port 1 and port 2, the output will be zero at port 3 and additive at port 4

2. If a wave is fed into port 4 (H arm), it will be divided equally between port 1 and port 2 of the collinear arms and will not appear at port 3 (E arm).

3. If a wave is fed into port 3 (E arm), it will produce an output of equal magnitude and opposite phase at port 1 and port 2. Output at port 4 is zero i.e S43 = S34 = 0.

Magic Tee Characteristics

4. If a wave is fed into one of the collinear arms at port 1 or port 2, it will not appear in the other collinear arm at port 2 or port 1 because the E arm causes a phase delay while the H arm causes the phase advance. i.e S12 = S21 = 0.

S matrix of magic tee is

Hybrid Rings (Rat-Race Circuits)

Four arms are connected at proper intervals by means of series or parallel junctions to sustain standing waves.

Hybrid ring With series junctions

Hybrid Rings characteristics

Characteristics similar to hybrid tee.When a wave is fed into port 1, it will not appear at port 3 because the difference of phase shifts for the waves travelling in the clockwise and anticlockwise directions is 180.Thus the waves are cancelled at port 3.

Similarly the waves fed into port 2 will not emerge at port 4 and so on.

Hybrid Rings

S matrix for an ideal hybrid ring

Phase cancellation occurs only at designated frequencyfor an ideal hybrid ring.

In actual hybrid rings there are small leakage couplings, and hence the zero elements in the matrix above are not quite equal to zero.

Waveguide Corners, Bends, and Twists

E plane Corner

H-plane corner


Bend

Continuous twist

These waveguide components are normally used to change the direction of the guide through an arbitrary angle.In order to minimize reflections from the discontinuities, it is desirable to have the mean length L between continuities equal to an odd number of quarter wavelengths. i.e


If the mean length L is an odd number of quarter wavelengths, the reflected waves from both ends of the waveguide section are completely cancelled. For the waveguide bend, the minimum radius of curvature for a small reflection is given by

Where a and b are the dimensions of the bend.


Power Dividers and CouplersIn low frequency design, it is common to sum signals by adding their currents or voltages.

In high frequency design direct summation is not used. Instead there is a class of circuits used to sum or split power.

Power SplitterPower Combiner

Power Dividers and CouplersTwo basic types of these circuits are: Power Divider and Power Combiner.

1

Three port networks are shown here, but both dividers and combiners can be multi-port networks. The most common value for in splitter is –3 dB (when P2 = P3 ). The power ratio in splitter can range up to –40 dB for one path.

Directional Coupler

This is a four port device that samples the power flowing into port 1 coupled in to port 3 (the coupled port) with the remainder of the power delivered to port 2 (the through port) and no power delivered to the isolated port.

Directional CouplerUsually the isolated port is terminated within the coupler casing. In such case, the coupler appears to be a three port device. In ideal case no power is delivered to port 4 (the isolated port).

Hybrid Couplers• Hybrid couplers are special cases of

directional couplers, where the coupling factor is 3 dB.

• There are two types of hybrids. 1) The quadrature hybrid has a 90 degree phase shift between port 2 and 3 when fed from port 1, with the following [S] matrix.

2) The magic-T hybrid or rat-race hybrid has a 180 degree phase shift between port 2 and 3 when fed from port 4, with the following [S] matrix:

010

100

001

010

2

1

j

j

j

j

S

0110

1001

1001

0110

2

1S

The Lossless T JunctionThe simplest type of power divider is the T junction. T junction can be implemented using virtually any type of transmission line. However, the T junction is very simple to implement, it must be treated with care because it does not offer any isolation between its ports.

Matching requirement for the T junction input:

132

111

ZZZ

The Lossless T JunctionIn order for the input port to be matched, the output lines must be matched (terminated in their characteristic impedance). The power dividing ratio can be selected by using different values of characteristic impedance for ports 2 and 3.

11321 PPPPP 1

2

1

1

2

12

2

2 2

1

2

1

Z

Z

Z

VP

Z

VP oo

3

1

1

2

13

2

3 2

1

2

1

Z

Z

Z

VP

Z

VP oo

The Lossless T Junction

Input matching requirement: 0||

||

312132

312132

132

132

1

11

ZZZZZZ

ZZZZZZ

ZZZ

ZZZ

ZZ

ZZ

L

L

32

32132132 )(

ZZ

ZZZZZZZZ

Therefore, the input to the T junction can be matched through the correct choice of impedances in port 2 and 3. What about matching of port 2 and 3?

The Lossless T JunctionNow lets consider matching of port 2.

322132

322132

231

231

2

22 ||

||

ZZZZZZ

ZZZZZZ

ZZZ

ZZZ

ZZ

ZZ

L

L

If port 2 is matched, then 2 = 0 and we will have:

31

31231231 0)(

ZZ

ZZZZZZZZ

Substitution of yields Z2 = 0.

Which shows that the lossless T junction cannot be matched at all three ports simultaneously.

32

321 ZZ

ZZZ

Ferrite Devices(1)A FERRITE is a device that is composed of material that causes it to

have useful magnetic properties and, at the same time, high

resistance to current flow.

The primary material used in the construction of ferrites is

normally a compound of iron oxide with impurities of other oxides

added.

The compound of iron oxide retains the properties of the

ferromagnetic atoms, and the impurities of the other oxides

increase the resistance to current flow.

Ferrite Devices(2)This combination of properties is not found in conventional

magnetic materials

Iron, for example, has good magnetic properties but a relatively

low resistance to current flow

Ferrites, on the other hand, have sufficient resistance to be

classified as semiconductors.

As in the construction of transistors, a wide range of magnetic and

electrical properties can be produced by the proper choice of

atoms in the right proportions

“F” Devices that are of interest

ISOLATOR

ATTENUATOR

CIRCULATOR

GYRATOR

Faraday Rotation

A Circularly polarized wave is made to pass through a ferrite

rod, which has been excited by an axial magnetic field B, the

axis of polarization gets tilted in clock wise direction and

the amount of tilt depends upon the strength of the

magnetic field and geometry of the ferrite rod

Circulator

A microwave circulator is a multiport device in which the power

is circulated from nth port to its (n+1)th port only in one

direction

A four port circulator is commonly used

The ferrite in circulator provides a 450 rotation in clock wise

direction

A four port circulator has s-matrix

IsolatorAn isolator is a two-port device that transmits microwave power in one direction only.

An ideal isolator transmits all the power entering port 1 to port 2, while absorbing all the power entering port 2

Its S-matrix is

Faraday rotation IsolatorA faraday rotation isolator is a circular wave guide section axially loaded with a ferrite rod of smaller diameter

Provides 1dB insertion loss in forward transmission and about 20 to 30dB isolation in reverse direction

GyratorGyrator is a non reciprocal two

port device with relative phase

shift of 1800 in forward direction

and 00 in reverse direction

the s-matrix for the gyrator is

Attenuator

An attenuator is an electronic device that reduces the power of a signal without appreciably distorting its waveform

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Microwave Engg- Passive Devices