MuWave Comm Lecture Slides3 5

7/31/2019 MuWave Comm Lecture Slides3 5

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Scattering Matrix Characterization

of Microwave Components


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i

i

Where :V is voltage of incident wave;

V is voltage of reflected wave;

i 1, 2, 3....n

+

=

Scattering Matrix of an N Port Network


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Properties Scattering Matrix of an N Port Network

Shift in Reference Planes


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Symmetry Property

' '

11 121 1 111 12 1N

21 22 2 N2 2 2

N1 N 2 NNN N N

For a reciprocalnetwork :S S .V V VS S .........S

S S .........SV V V&

........................... ... ...

S S .......SV V V

+ +

+ +

+ +

= =

'

1N 1

' ' '

21 22 2 N 2

' ' 'NN1 N 2 NN

' ' '

11 12 1N

' ' '

21 22 2 N

........S V

S S .........S V

...........................

VS S .......S

thisis only possibleif :

S S .........S

S S .........S

.....................

[ ]

[ ]

T

11 12 1N

T21 22 2 N '

' ' 'N1 N 2 NNN1 N 2 NN

S S .........S

S S .........Sor S S

...........................

S S .......SS S .......S

This condition itself means that S is a symmetric matrix.

= =


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Unitary Property:

The product of transpose and complex conjugate of a scattering matrix is a unity matrix.


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Scattering Matrix Characterization of Microwave Components

Microwave Junction/Network Components


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E-Plane Tee :


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H-Plane Tee :

Similar to that of E plane tee except that


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Magic Tee :


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Hybrid Ring:


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Directional Coupler:

Two Hole Directional Coupler:


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Circulator:


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Circulator made up of two magic tees

Isolator:

21

0 0S =

S 0

For an Ideal Isolator:


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Corners , Bends & Twists:


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, above,


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Microwave Active Devices


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Tunnel Diode

Negative Resistance Region

Doping of both P & N regions are very high resulting in a thin barrier potential. It is so

suggested from quantum mechanical theory or Schrdinger's equations that a barrier

potential of less than 3 A0 can result in a transition across the junction despite the fact that the

electrons /holes are not energized enough to break the potential barrier. This phenomenon of

current across the junction is called tunneling and the diode is thus called tunnel diode.


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Equivalent Circuit


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MESFET (Metal Semiconductor Field Effect Transistor)

A potential difference is applied so that the majority carriers move from source to the drain

and a reverse potential to the majority carriers is applied at the gate so as to make a depletion

region and create pinch off.


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Integrating the above equation twice and

application of boundary conditions yield

the pinch-off voltage as

Here:


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Drain Current


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Gunn Diode (TED)Negative Conductance

Eg=1.4eV Forbidden Band

Valence Band

Gunn diode also show negative

resistance after a threshold voltage,

this property makes it a goodmicrowave source.

Conductivity


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Conductivity

Where

p is the field exponent and must be negative and large


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Modes of Operation

Frequency of oscillations is given by:

With respect to different drift velocities following modes exist:

When transit time is so chosen that the domain is collected but E< Eth then new domain

cant be formed until the field rises again above threshold consequently oscillation period is

grater than the transit time. This mode is also called inhibited mode( efficiency 20%)

( efficiency 10%)


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( efficiency 13%)

When the field drops below the sustained field Es during the negative half cycle then the

domain collapses and wont reach anode then as the positive cycle comes the field swings

back above threshold nucleating another domain, and the process repeats thereby creating

oscillations at resonant frequency rather than that of transit time.

In this mode due to high frequency of operation domains do not have enough time to get

formed therefore a limited space charge gets accumulated uniformly. The internal electric

field becomes uniform and proportional to the applied voltage and current becomes

proportional to drift velocity at the field level. ( efficiency 20%)


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Avalanche Resonant

Frequency

Transit Time Angle


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Three types of IMPATT Diodes


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Maximum Voltage & Current

Power Frequency Limitation

Efficiency


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In Amplitude Modulation the carrier is generated from a local oscillator and the carrier is

the modulated by the modulating signal in a non linear element such as mixer. In a

Parametric Amplifier the non-linear device is replaced by a varying capacitor/inductor such

as varactor diode and the oscillator is replaced by a pumping generator such as reflexklystron. The output circuit does not require an external excitation and is thus called idler

circuit.

( fs / f0 for down converter )


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PIN Diode


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PIN Diode

Forward bias equivalent circuitReverse bias equivalent circuit

Applications of PIN diode


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Applications of PIN diode

Attenuator:

Switch:

Phase Shifter:

Amplitude Modulator:

The pin diode has a VI characteristics which make it a good RF switch. When

reverse biased a small series junction capacitance leads to high diode impedance

while forward bias removes the junction capacitance to make a low impedance

state

Since the intrinsic forward resistance Ri is inversely proportional to the bias current,

the modulating signal is used to change/vary this resistance thereby producing a

Continuous Amplitude-Modulated RF wave.

C l Di d


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Crystal Diodes:

The crystal diodes have the distinction of being the first ever semiconductor device produced.

Primarily developed by the Indian scientist Sir Jagadish Chandra Bose the crystal diode forms a

metal semiconductor junction which was later coined as Schottky barrier junction (named

after Schottky). Here a thin metal wire loosely touches a semiconducting crystal( usuallygalena) to make an excellent microwave demodulator or envelope detector. The largest

differences between a Schottky barrier and a pn junction are its typically lower junction

voltage, and decreased (almost nonexistent) depletion width in the metal
http://en.wikipedia.org/w/index.php?title=File:Schottky_diode_symbol.svg&page=1http://en.wikipedia.org/w/index.php?title=File:Schottky_diode_symbol.svg&page=1


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Microwave Filters

Analysis & Design


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Periodic Structures:

Transmission lines and waveguides when loaded or connected with reactive elements at

spatial periodic gaps are known as periodic structures. Periodic structures support slow

wave propagation and are also called slow wave structures. Moreover, their frequency

domain characteristics match with those of filters and make them ideal candidates for filterimplementations. The also find application in TWTs, MASERs, Antennas, Phase Shifters etc.


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Low Pass Consideration


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High Pass Consideration


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High Pass Consideration



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P.T.O


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Ladder Circuits for Filter Design


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Lumped Distributed


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Using Richards Transforms

Now series stubs will be impractical to be implemented over usual transmission line like

microstrip. Therefore Kurodas identities are used to convert these series stubs to shunt. This is

done by first introducing redundant unit elements in to the circuit.


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MuWave Comm Lecture Slides3 5

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