Dhanalakshmi College of Engineering

Department of ECE

EC6701 – RF and Microwave Engineering

Unit 3

1. Draw the diagram of H-plane Tee junction. [N/D – 12]

2. Draw the structure of two hole directional coupler. [N/D – 11]

3. What is meant by directivity of directional coupler? [M/J – 08]

The directivity of directional coupler is defined as the ratio of forward power Pr to f the back power Pb andexpressed in dB.

4. What are the basic parameters to measure the performance of a directional coupler? [N/D – 08]

The basic parameters to measure the performance of a directional coupler are,

i. Coupling co-efficient

ii. Directivity

iii. Insertion loss

iv. Isolation

5. What are the basic types of directional coupler? [N/D – 09]

The basic types of directional coupler are,

i. Two hole directional coupler

ii. Four hole directional coupler

iii. Reverse coupling directional coupler

iv. Bethe hole directional coupler

6. How a Faraday rotation isolator can be constructed by using ferrite rod? [N/D – 08]

Isolators can be made by inserting ferrite rod along the axis of a rectangular waveguide.

7. State the significance of Rat-race junctions. [M/J - 13]

i. easy to realize in planar technologies such as microstrip and stripline

ii. a rat-race needs no matching structure to achieve correct operation.

iii. Rat-race couplers are used to sum two in-phase combined signals with essentially no loss

iv. It equally split an input signal with no resultant phase difference between its outputs.

8. What is gyrator? [N/D – 13]

A gyrator is a passive, linear, lossless, two-port ferrite device. An ideal gyrator is a linear two port devicewhich generate relative phase shift of 180 degree in forward direction zero degree phase shift in reverse direction.

9. State the applications of gyrator and isolator. [N/D – 14]

A gyrator is a nonreciprocal electrical network. It is capable of transforming signals or energy representedin terms of one electrical quantity, such as voltage or magnetic field, to another electrical quantity, such as currentor electric field.

An isolator is a two-port device that transmits microwave or radio frequency power in one direction only. Itis used to shield equipment on its input side, from the effects of conditions on its output side; for example, toprevent a microwave source being detuned by a mismatched load.

10. State transferred electron effect. [N/D – 12]

When GaAs is biased above a threshold value of the electric field, it exhibits a negative differential mobility.The electrons in the lower energy band will be transferred into the higher energy band. This behavior is calledtransferred electron effect.

11. State Gunn Effect. [M/J – 08] [M/J – 13]

When the electric field is varied from zero to threshold value, the carrier drift velocity is increased from zeroto maximum. When the electric field is beyond the threshold value of 3000V/cm, the drift velocity is decreased andthe diode exhibits negative resistance.

12. What are the major disadvantages of IMPATT diodes? [N/D – 08]

The major disadvantages of IMPATT diodes are,

i. Avalanche process makes the IMPATT diode noisy

ii. Poor noise figure of 30dB

iii. Low efficiency due to induced electron current

13. State the basic materials required for microwave integrated circuit. [N/D – 07]

The basic materials required for microwave integrated circuit are,

i. Substrate materials

ii. Conductor materials

iii. Dielectric materials

iv. Resistive materials

14. State the different types of lithography. [M/J – 08]

The different types of lithography are,

i. Electron-beam lithography

ii. Ion-beam lithography

iii. Optical lithography

iv. X-ray lithography

Microwave Engineering - E-Plane Tee

An E-Plane Tee junction is formed by attaching a simple waveguide to the broader dimension of a rectangular waveguide, which alreadyhas two ports. The arms of rectangular waveguides make two ports called collinear ports i.e., Port1 and Port2, while the new one, Port3is called as Side arm or E-arm. T his E-plane Tee is also called as Series Tee.

As the axis of the side arm is parallel to the electric field, this junction is called E-Plane Tee junction. This is also called as Voltage orSeries junction. The ports 1 and 2 are 180° out of phase with each other. The cross-sectional details of E-plane tee can be understood bythe following figure.

The following figure shows the connection made by the sidearm to the bi-directional waveguide to form the parallel port.

The properties of E-Plane Tee can be defined by its matrix.

It is a 3×3 matrix as there are 3 possible inputs and 3 possible outputs.

........ Equation 1

Scattering coefficients and are out of phase by 180° with an input at port 3.

........ Equation 2

The port is perfectly matched to the junction.

........ Equation 3

From the symmetric property,

Properties of E-Plane Tee[S]3x3

[S] =⎡⎣⎢

S11

S21

S31

S12

S22

S32

S13

S23

S33

⎤⎦⎥

S13 S23

= −S23 S13

= 0S33

7/17/2017 Microwave Engineering E Plane Tee

........ Equation 4

Considering equations 3 & 4, the matrix can be written as,

........ Equation 5

We can say that we have four unknowns, considering the symmetry property.

From the Unitary property

Multiplying we get,

(Noting R as row and C as column)

........ Equation 6

......... Equation 7

......... Equation 8

......... Equation 9

Equating the equations 6 & 7, we get

......... Equation 10

From Equation 8,

......... Equation 11

From Equation 9,

Or ......... Equation 12

Using the equations 10, 11, and 12 in the equation 6,

we get,

Or ......... Equation 13

Substituting the values from the above equations in matrix,

We get,

We know that =

=Sij Sji

= = =S12 S21 S23 S32 S13 S31

[S]

[S] =⎡⎣⎢

S11

S12

S13

S12

S22

−S13

S13

−S13

0

⎤⎦⎥

[S][S]∗ = [I]

=⎡⎣⎢

S11

S12

S13

S12

S22

−S13

S13

−S13

0

⎤⎦⎥⎡

⎣⎢⎢

S∗11

S∗12

S∗13

S∗12

S∗22

−S∗13

S∗13

−S∗13

0

⎤

⎦⎥⎥

⎡⎣⎢

1

0

0

0

1

0

0

0

1

⎤⎦⎥

: + + = 1R1C1 S11S∗11 S12S∗

12 S13S∗13

+ + = 1| |S112 | |S11

2 | |S112

: + + = 1R2C2 | |S122 | |S22

2 | |S132

: + = 1R3C3 | |S132 | |S13

2

: − = 1R3C1 S13S∗11 S13S∗

12

=S11 S22

2 or =| |S132

S1312√

( − )S13 S∗11 S∗

12

= =S11 S12 S22

+ + = 1| |S112 | |S11

2 12

2 =| |S112 1

2

=S1112

[S]

[S] =

⎡

⎣

⎢⎢⎢⎢

12

12

12

12

12

− 12√

12√

− 12√

0

⎤

⎦

⎥⎥⎥⎥

[b] [S][a]

⎡ 1 1 1 ⎤

7/17/2017 Microwave Engineering E Plane Tee

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This is the scattering matrix for E-Plane Tee, which explains its scattering properties.

=⎡⎣⎢

b1

b2

b3

⎤⎦⎥

⎡

⎣

⎢⎢⎢⎢

12

12

12

12

12

− 12√

12√

− 12√

0

⎤

⎦

⎥⎥⎥⎥⎡⎣⎢

a1

a2

a3

⎤⎦⎥

Microwave Engineering - E-H Plane Tee

An E-H Plane Tee junction is formed by attaching two simple waveguides one parallel and the other series, to a rectangular waveguidewhich already has two ports. This is also called as Magic Tee, or Hybrid or 3dB coupler.

The arms of rectangular waveguides make two ports called collinear ports i.e., Port 1 and Port 2, while the Port 3 is called as H-Arm orSum port or Parallel port. Port 4 is called as E-Arm or Difference port or Series port.

The cross-sectional details of Magic Tee can be understood by the following figure.

The following figure shows the connection made by the side arms to the bi-directional waveguide to form both parallel and serial ports.

If a signal of equal phase and magnitude is sent to port 1 and port 2, then the output at port 4 is zero and the output at port 3 willbe the additive of both the ports 1 and 2.

If a signal is sent to port 4, (E-arm) then the power is divided between port 1 and 2 equally but in opposite phase, while therewould be no output at port 3. Hence, = 0.

If a signal is fed at port 3, then the power is divided between port 1 and 2 equally, while there would be no output at port 4.Hence, = 0.

If a signal is fed at one of the collinear ports, then there appears no output at the other collinear port, as the E-arm produces aphase delay and the H-arm produces a phase advance. So, = = 0.

The properties of E-H Plane Tee can be defined by its matrix.

Characteristics of E-H Plane Tee

S34

S43

S12 S21

Properties of E-H Plane Tee[S]4×4

7/17/2017 Microwave Engineering EH Plane Tee

It is a 4×4 matrix as there are 4 possible inputs and 4 possible outputs.

........ Equation 1

As it has H-Plane Tee section

........ Equation 2

As it has E-Plane Tee section

........ Equation 3

The E-Arm port and H-Arm port are so isolated that the other won't deliver an output, if an input is applied at one of them. Hence, this canbe noted as

........ Equation 4

From the symmetry property, we have

........ Equation 5

If the ports 3 and 4 are perfectly matched to the junction, then

........ Equation 6

Substituting all the above equations in equation 1, to obtain the matrix,

........ Equation 7

From Unitary property,

......... Equation 8

......... Equation 9

......... Equation 10

......... Equation 11

From the equations 10 and 11, we get

........ Equation 12

........ Equation 13

Comparing the equations 8 and 9, we have

......... Equation 14

[S] =

⎡

⎣⎢⎢⎢

S11

S21

S31

S41

S12

S22

S32

S42

S13

S23

S33

S43

S14

S24

S34

S44

⎤

⎦⎥⎥⎥

=S23 S13

= −S24 S14

= = 0S34 S43

=Sij Sji

= , = , =S12 S21 S13 S31 S14 S41

= , = , =S23 S32 S24 S42 S34 S43

= = 0S33 S44

[S]

[S] =

⎡

⎣⎢⎢⎢

S11

S12

S13

S14

S12

S22

S13

−S14

S13

S13

0

0

S14

−S14

0

0

⎤

⎦⎥⎥⎥

[S][S = [I]]∗

⎡

⎣⎢⎢⎢

S11

S12

S13

S14

S12

S22

S13

−S14

S13

S13

0

0

S14

−S14

0

0

⎤

⎦⎥⎥⎥

⎡

⎣

⎢⎢⎢⎢

S∗11

S∗12

S13

S14

S∗12

S∗22

S13

−S14

S∗13

S∗13

0

0

S∗14

−S∗14

0

0

⎤

⎦

⎥⎥⎥⎥

=

⎡

⎣⎢⎢⎢

1

0

0

0

0

1

0

0

0

0

1

0

0

0

0

1

⎤

⎦⎥⎥⎥

: + + = 1 + = 1R1C1 | |S112 | |S12

2 | |S132 | |S14

2

: + + = 1 + = 1R2C2 | |S122 | |S22

2 | |S132 | |S14

2

: + = 1R3C3 | |S132 | |S13

2

: + = 1R4C4 | |S142 | |S14

2

=S1312√

=S1412√

=S11 S22

7/17/2017 Microwave Engineering EH Plane Tee

Using these values from the equations 12 and 13, we get

......... Equation 15

From equation 9, we get ......... Equation 16

Now we understand that ports 1 and 2 are perfectly matched to the junction. As this is a 4 port junction, whenever two ports are perfectlymatched, the other two ports are also perfectly matched to the junction.

The junction where all the four ports are perfectly matched is called as Magic Tee Junction.

By substituting the equations from 12 to 16, in the matrix of equation 7, we obtain the scattering matrix of Magic Tee as

We already know that, =

Rewriting the above, we get

Some of the most common applications of E-H Plane Tee are as follows −

E-H Plane junction is used to measure the impedance − A null detector is connected to E-Arm port while the Microwave source isconnected to H-Arm port. The collinear ports together with these ports make a bridge and the impedance measurement is done bybalancing the bridge.

E-H Plane Tee is used as a duplexer − A duplexer is a circuit which works as both the transmitter and the receiver, using a singleantenna for both purposes. Port 1 and 2 are used as receiver and transmitter where they are isolated and hence will not interfere.Antenna is connected to E-Arm port. A matched load is connected to H-Arm port, which provides no reflections. Now, there existstransmission or reception without any problem.

E-H Plane Tee is used as a mixer − E-Arm port is connected with antenna and the H-Arm port is connected with local oscillator.Port 2 has a matched load which has no reflections and port 1 has the mixer circuit, which gets half of the signal power and half ofthe oscillator power to produce IF frequency.

In addition to the above applications, an E-H Plane Tee junction is also used as Microwave bridge, Microwave discriminator, etc.

+ + + = 1| |S112 | |S12

2 12

12

+ = 0| |S112 | |S12

2

= = 0S11 S22

= 0S22

[S]

[S] =

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢

0

0

12√

12√

0

0

12√

− 12√

12

12

0

0

12√

− 12√

0

0

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥

[b] [S][a]

=

∣

∣

∣∣∣∣

b1

b2

b3

b4

∣

∣

∣∣∣∣

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢

0

0

12√

12√

0

0

12√

− 12√

12

12

0

0

12√

− 12√

0

0

⎤

⎦

⎥⎥⎥⎥⎥⎥⎥

∣

∣

∣∣∣∣

a1

a2

a3

a4

∣

∣

∣∣∣∣

Applications of E-H Plane Tee

7/17/2017 Microwave Engineering EH Plane Tee

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go

Microwave Engineering - Directional Couplers

A Directional coupler is a device that samples a small amount of Microwave power for measurement purposes. The power measurementsinclude incident power, reflected power, VSWR values, etc.

Directional Coupler is a 4-port waveguide junction consisting of a primary main waveguide and a secondary auxiliary waveguide. Thefollowing figure shows the image of a directional coupler.

Directional coupler is used to couple the Microwave power which may be unidirectional or bi-directional.

The properties of an ideal directional coupler are as follows.

All the terminations are matched to the ports.

When the power travels from Port 1 to Port 2, some portion of it gets coupled to Port 4 but not to Port 3.

As it is also a bi-directional coupler, when the power travels from Port 2 to Port 1, some portion of it gets coupled to Port 3 but notto Port 4.

If the power is incident through Port 3, a portion of it is coupled to Port 2, but not to Port 1.

If the power is incident through Port 4, a portion of it is coupled to Port 1, but not to Port 2.

Port 1 and 3 are decoupled as are Port 2 and Port 4.

Ideally, the output of Port 3 should be zero. However, practically, a small amount of power called back power is observed at Port 3. Thefollowing figure indicates the power flow in a directional coupler.

Properties of Directional Couplers

7/17/2017 Microwave Engineering Directional Couplers

Where

= Incident power at Port 1

= Received power at Port 2

= Forward coupled power at Port 4

= Back power at Port 3

Following are the parameters used to define the performance of a directional coupler.

The Coupling factor of a directional coupler is the ratio of incident power to the forward power, measured in dB.

The Directivity of a directional coupler is the ratio of forward power to the back power, measured in dB.

It defines the directive properties of a directional coupler. It is the ratio of incident power to the back power, measured in dB.

Isolation in dB = Coupling factor + Directivity

This is a directional coupler with same main and auxiliary waveguides, but with two small holes that are common between them. Theseholes are distance apart where λg is the guide wavelength. The following figure shows the image of a two-hole directional coupler.

Pi

Pr

Pf

Pb

Coupling Factor (C)

C = 10 lo dBg10Pi

Pf

Directivity (D)

D = 10 lo dBg10Pf

Pb

Isolation

I = 10 lo dBg10Pi

Pb

Two-Hole Directional Coupler

/4λg

7/17/2017 Microwave Engineering Directional Couplers

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A two-hole directional coupler is designed to meet the ideal requirement of directional coupler, which is to avoid back power. Some of thepower while travelling between Port 1 and Port 2, escapes through the holes 1 and 2.

The magnitude of the power depends upon the dimensions of the holes. This leakage power at both the holes are in phase at hole 2,adding up the power contributing to the forward power Pf. However, it is out of phase at hole 1, cancelling each other and preventing the

back power to occur.

Hence, the directivity of a directional coupler improves.

As a waveguide system cannot be built in a single piece always, sometimes it is necessary to join different waveguides. This joining mustbe carefully done to prevent problems such as − Reflection effects, creation of standing waves, and increasing the attenuation, etc.

The waveguide joints besides avoiding irregularities, should also take care of E and H field patterns by not affecting them. There are manytypes of waveguide joints such as bolted flange, flange joint, choke joint, etc.

Waveguide Joints

i)Voltage-controlled and

ii) current controlled modes as shown in Fig.

In the voltage-controlled mode the current density can be multivalued, whereas in the current-controlled

mode the voltage can be multivalued.

The major effect of the appearance of a differential negative-resistance region in the currentdensity-

field curve is to render the sample electrically unstable. As a result, the initially homogeneous sample

becomes electrically heterogeneous in an attempt to reach stability.

In the voltage-controlled negative-resistance mode high-field domains are formed, separating two low-

field regions. The interfaces separating lowand high-field domains lie along equipotentials;

thus they are in planes perpendicular to the current direction as shown in Fig. 7-2-2(a). In the current-

controlled negative-resistance mode splitting the sample results in high-current filaments running along

the field direction as shown in Fig. 7-2-2(b).

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

Expressed mathematically, the negative resistance of the sample at a particular region is

If an electric field Eo (or voltage Vo) is applied to the sample, for example, the current density is

generated. As the applied field (or voltage) is increased to E2 (or V2), the current density is decreased to

J2.

When the field (or voltage) is decreased to E1 (or V1), the current density is increased to J1 . These

phenomena of the voltage controlled negative resistance are shown in Fig. 7-2-3(a).

Similarly, for the current controlled mode, the negative-resistance profile is as shown in Fig. 7-2-3(b).

Two-Valley Model Theory

According to the energy band theory of then-type GaAs, a high-mobility lower valley is separated by an

energy of 0.36 eV from a low-mobility upper valley

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

When the applied electric field is lower than the electric field of the lower valley (£ < Ec), no electrons

will transfer to the upper valley as show in Fig. 7-2-S(a).

When the applied electric field is higher than that of the lower valley and lower than that of the upper

valley (Ec < E < Eu), electrons will begin to transfer to the upper valley as shown in Fig. 7-2-S(b).

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

And when the applied electric field is higher than that of the upper valley (Eu < E), all electrons will

transfer to the upper valley as shown in Fig. 7-2-S(c).

If electron densities in the lower and upper valleys are nc and nu , the conductivity of the n -type GaAs is

When a sufficiently high field E is applied to the specimen, electrons are accelerated and their effective

temperature rises above the lattice temperature. Furthermore, the lattice temperature also increases. Thus

electron density n and mobility f-L are both functions of electric field E. Differentiation of Eq. (7-2-2)

with respect toE yields

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

If the total electron density is given by n = nt + nu and it is assumed that f.Le and /Lu are proportional to

EP, where p is a constant, then

Substitution of Eqs. (7-2-4) to (7-2-6) into Eq. (7-2-3) results in

Then differentiation of Ohm's law J = aE with respect toE yields

Equation (7-2-8) can be rewritten

Clearly, for negative resistance, the current density J must decrease with increasing

field E or the ratio of dJ!dE must be negative. Such would be the case only if the

right-hand term of Eq. (7-2-9) is less than zero. In other words, the condition for

negative resistance is

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

Substitution of Eqs. (7-2-2) and (7-2-7) with/= nu/ne results in [2]

4.7 AVALANCE TRANSIT TIME DEVICES:

Avalanche transit-time diode oscillators rely on the effect of voltage breakdown across a reverse-

biased p-n junction to produce a supply of holes and electrons. Ever since the development of

modern semiconductor device theory scientists have speculated on whether it is possible to make

a two-terminal negative-resistance device.

The tunnel diode was the first such device to be realized in practice. Its operation depends on the

properties of a forward-biased p-n junction in which both the p and n regions are heavily doped.

The other two devices are the transferred electron devices and the avalanche transit-time devices.

In this chapter the latter type is discussed.

The transferred electron devices or the Gunn oscillators operate simply by the application of a de

voltage to a bulk semiconductor. There are no p-n junctions in this device. Its frequency is a

function of the load and of the natural frequency of the circuit. The avalanche diode oscillator

uses carrier impact ionization and drift in the high-field region of a semiconductor junction to

produce a negative resistance at microwave frequencies.

The device was originally proposed in a theoretical paper by Read in which he analyzed the

negative-resistance properties of an idealized n+p- i-p+ diode. Two distinct modes of avalanche

oscillator have been observed. One is the IMPATT mode, which stands for impact ionization

avalanche transit-time operation. In this mode the typical dc-to-RF conversion efficiency is 5 to

10%, and frequencies are as high as 100 GHz with silicon diodes.

The other mode is the TRAPATT mode, which represents trapped plasma avalanche triggered

transit operation. Its typical conversion efficiency is from 20 to 60%. Another type of active

microwave device is the BARITT (barrier injected transit-time) diode [2]. It has long drift

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology

Fatima Michael College of Engineering & Technology