Microwave Engineering Microwave Networks What Are Microwaves 589

8/3/2019 Microwave Engineering Microwave Networks What Are Microwaves 589

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Microwave Engineering

Microwave Networks

± What are Microwaves? ± S-parameters

± Power Dividers

± Couplers

± Filters

± Amplifiers



Microwave engineering: Engineering and design of

communication/navigation systems in the microwavefrequency range.

Microwave Engineering

Applications: Microwave oven, Radar, Satellite communi-

cation, direct broadcast satellite (DBS) television, personal

communication systems (PCSs) etc.



What are Microwaves? (Pozar Sec. 1.1)

P = 30 cm: f = 3 x 108/ 30 x 10-2 = 1 GHz

P = 1 cm: f = 3 x 108/ 1x 10-2 = 30 GHz

Microwaves: 30 cm ± 1 cm

Millimeter waves: 10 mm ± 1 mm

(centimeter waves)

P = 10 mm: f = 3 x 108/ 10 x 10-3 = 30 GHz

P = 1 mm: f = 3 x 108/ 1x 10-3 = 300 GHz

m

sm Hz

/103 wavelength

clightof velocityf frequency 8

PPv!!

Note: 1 Giga = 109



What are Microwaves?

1 cm

f =10 kHz, P = c/f = 3 x 108/ 10 x 103 = 3000 m

Phase delay = (2T or 360r) x Physical length/Wavelength

f =10 GHz, P = 3 x 108/ 10 x 109 = 3 cm

Electrical length =1 cm/3000 m = 3.3 x 10-6 P, Phase delay = 0.0012r

RF

Microwave

Electrical length = 0.33 P, Phase delay = 118.8r !!!

1P | 360 r

Electrically long - The phase of a voltage or current changes

significantly over the physical extent of the device

Electrical length = Physical length/Wavelength (expressed in P)



How to account for the phase delay?

A

B

A B

A B

Low Frequency

Microwave

A B

A B

Propagation

delay negligible

Transmission

line section!

l

P rinted Circuit Trace

Zo: characteristic impedance

K (=E+j F): Propagation constant

Zo, K

Propagation delay

considered



Scattering Parameters (S-Parameters)

Consider a circuit or device inserted into a

T-Line as shown in the Figure. We canrefer to this circuit or device as a two-port

network.

The behavior of the network can be

completely characterized by its scattering

parameters (S-parameters), or its

scattering matrix, [S].

Scattering matrices are frequently used to

characterize multiport networks, especially

at high frequencies. They are used to

represent microwave devices, such as

amplifiers and circulators, and are easilyrelated to concepts of gain, loss and

reflection.

? A11 12

21 22

S S S

S S

« »! ¬ ¼

- ½

Scattering matrix




The scattering parameters represent ratios of

voltage waves entering and leaving the ports(If the same characteristic impedance, Zo, at

all ports in the network are the same).

1 11 1 12 2.V S V S V

!

2 21 1 22 2.V S V S V

!

11 121 1

21 222 2

,S S V V

S S V V

!

« » « »« »¬ ¼ ¬ ¼¬ ¼

- ½- ½ - ½

In matrix form this is written

? A ? A? A .V S V

!

2

1

11

1 0V

V S

V

!

!1

1

12

2 0V

V S V

!

!

1

2

22

2

0V

V S

V

!

!2

2

21

1 0V

V S

V

!

!




Properties:

The two-port network is reciprocal if the

transmission characteristics are the same in

both directions (i.e. S21 = S12).

It is a property of passive circuits (circuits with

no active devices or ferrites) that they formreciprocal networks.

A network is reciprocal if it is equal to its

transpose. Stated mathematically, for a

reciprocal network

? A ? A ,t S S !

11 12 11 21

21 22 12 22

.

t

S S S S

S S S S !

« » « »¬ ¼ ¬ ¼- ½ - ½

12 21S S !Condition for Reciprocity:

1) Reciprocity




Properties:

A lossless network does not contain any resistive

elements and there is no attenuation of the signal.

No real power is delivered to the network.

Consequently, for any passive lossless network,

what goes in must come out!

In terms of scattering parameters, a network is

lossless if

2) Lossless Networks

? A ? A ? A*

,t

S S U !

1 0[ ] .

0 1U !

« »¬ ¼- ½

where [U ] is the unitary matrix

For a 2-port network, the product of the transpose matrix and the complex conjugate

matrix yields

? A ? A

2 2 * *

11 21 11 12 21 22*

2 2* *

12 11 22 21 12 22

1 0

0 1

t

S S S S S S

S S

S S S S S S

!

« »« »¬ ¼ ! ¬ ¼¬ ¼ - ½

- ½

2 2

11 211S S !

If the network is reciprocal and lossless* *

11 12 21 22 0S S S S !




Return Loss and Insertion Loss

Two port networks are commonly described by their

return loss and insertion loss. The return loss, RL,

at the ith port of a network is defined as

20log 20log .i

i i

i

V RL

V

! ! +

The insertion loss, IL, defines how much of a signal

is lost as it goes from a jth port to an ith port. In

other words, it is a measure of the attenuation

resulting from insertion of a network between a

source and a load.

20log .i

ij

j

V IL

V

!









Microwave Integrated Circuits

Microwave Integrated Circuits (MIC):

Traces: transmission lines,

P assive components: resistors, capacitors, and inductors

Active devices: diodes and transistors.

Substrate Teflon fiber, alumina, quartz etc.

Metal Copper, Gold etc.

Process Conventional printed circuit

(Photolithography and etching)

Components Soldering and wire bonding



Lossless T-junction Power Divider

T-junction (Lossless divider)

PD 1.1

021

111

Z Z Z jBY

in!!

Input Matching Condition

0! B

021

111

Z Z Z !

o

o

in Z

V P

2

2

1!

1

2

12

1

Z

V P

o!2

2

2

2

1

Z

V P

o!

Input Power Output Power

in P P

3

11

!

in P P

3

2

2!

;! 50o

Z

;!! 15031 o

Z Z

;!! 752

32 o

Z Z

;!! 50||21 Z Z Z

in

Power Divider

EXAMPLE 7.1

2:1

Input Port is matched

Input Impedance

Ingoring the junction

reactance

;!! 30||21 Z Z Z

oin ;!! 5.37||12

Z Z Z oin

0!

!+

oin

oin

Z Z

Z Z

Output Ports are not matched

Input Port Output Port 1 Output Port 2

Reflection

Coefficient333.0

22

22

2!

!+

Z Z

Z Z

in

in666.011

111 !

!+

Z Z

Z Z

in

in

Power Divider

A T-junction power divider consists of one input port and two output ports.

Design Example



? A

¼¼¼¼

½

»

¬¬¬¬

-

«

!

00

0000

00

E F

E F FE

FE

S

? A

¼¼¼¼

½

»

¬¬¬¬

-

«

!

0

0

00

342414

342313

242312

141312

S S S

S S S

S S S S S S

S

? A

¼¼¼¼

½

»

¬¬¬¬

-

«

!

00

0000

00

E F

E F FE

FE

j

j j

j

S

Symmetric Coupler Antisymmetric Coupler

122 ! FE

A reciprocal, lossless, matched four-port network

behaves as a directional coupler

Couplers COUPLERS

A coupler will transmit half or more of its

power from its input (port 1) to its through

port (port 2).

A portion of the power will be drawn off to

the coupled port (port 3), and ideally none

will go to the isolated port (port 4).

If the isolated port is internally terminated

in a matched load, the coupler is most

often referred to as a directional coupler .

For a lossless network:

Coupling coefficient: 3120 log .C S !

21

20 log . IL S ! Insertion Loss:

4120log , I S ! Isolation:

31

41

20 log ,S

DS

!¨ ¸© ¹ª º

Directivity:

(dB) D I C !



COUPLERS

Design Example

Example 10.10: Suppose an antisymmetrical coupler has the following characteristics:

C = 10.0 dB

D = 15.0 dB

IL = 2.00 dB

VSWR = 1.30

Coupling coefficient: 3120 log .C S !

21

20 log . IL S ! Insertion Loss:

10/ 20

3110 0.316.S

! !

2 / 20

2110 0.794.S

! !

111 0.130.1

VSWRS VSWR

! !

25 , I D C d B! !25/ 20

4110 0.056.S

! !

VSWR = 1.30

? A

0.130 0.794 0.316 0.056

0.794 0.130 0.056 0.316

0.316 0.056 0.130 0.794

0.056 0.316 0.794 0.130

S

!

« »¬ ¼¬ ¼¬ ¼¬ ¼- ½

Given



COUPLERS

? A

0 1 1 0

1 0 0 1.

1 0 0 12

0 1 1 0

jS

!

« »¬ ¼¬ ¼¬ ¼¬ ¼- ½

? A

0 1 0

0 0 11

1 0 02

0 1 0

,

j

jS

j

j

!

« »¬ ¼¬ ¼¬ ¼¬ ¼- ½

The quadrature hybrid (or branch-line hybrid) isa 3 dB coupler. The quadrature term comes

from the 90 deg phase difference between the

outputs at ports 2 and 3.

The coupling and insertion loss are both equal

to 3 dB.

Ring hybrid (or rat-race) coupler Quadrature hybrid Coupler

A microwave signal fed at port 1 will split evenlyin both directions, giving identical signals out of

ports 2 and 3. But the split signals are 180 deg

out of phase at port 4, the isolated port, so they

cancel and no power exits port 4.

The insertion loss and coupling are both equal to

3 dB. Not only can the ring hybrid split power to

two ports, but it can add and subtract a pair of signals.



Filters

Filters are two-port networks used to attenuate undesirable frequencies.

Microwave filters are commonly used in transceiver circuits.

The four basic filter types are low-pass, high-pass, bandpass and bandstop.

Low-pass High-pass

BandstopBandpass



A low-pass filter is characterized by the insertion loss

versus frequency plot in Figure. Notice that there maybe ripple in the passband (the frequency range

desired to pass through the filter), and a roll off in

transmission above the cutoff or corner frequency, fc.

Simple filters (like series inductors or shunt capacitors)

feature 20 dB/decade roll off. Sharper roll off is

available using active filters or multisection filters.

Active filters employ operational amplifiers that are

limited by performance to the lower RF frequencies.

Multisection filters use passive components (inductors

and capacitors), to achieve filtering.

The two primary types are the Butterworth and the

Chebyshev. A Butterworth filter has no ripple in thepassband, while the Chebyshev filter features sharper

roll off.

FiltersLow-pass Filters



Low-pass Filters

High-pass Filters Band-pass Filters

Lumped Element Filters

Some simple lumped element filter circuits are shown below.



Low-pass Filter Example


2

,l

L

o

v P

R! .

2

o

l s

o

Rv v

R j L[!

20log 1 .2

o

j L IL

R

[

! ¨ ¸© ¹

ª ºThe 3 dB cutoff frequency, also termed the corner frequency, occurs where

insertion loss reaches 3 dB.

1,2

o

L

R

[

!20 log 12

3o

j L

R

[

¨ ¸

!© ¹

ª º

3

201 10 22

o

j L

R

[

! ! .o

c

R f

LT!

2

2 2

2.

4

s

l s

A

o o o

v

v v P

R R R! ! !

10log L

A

ILP

P !

¨ ¸© ¹ª º

Power delivered to the load

Insertion Loss

Maximum available Power :



Low-pass Filter Example

Example 10.12: Let us design a low-pass filter for a 50.0 ; system using a

series inductor. The 3 dB cutoff frequency is specified as 1.00 GHz.


.o

c

R f

LT!

The 3 dB cutoff frequency is given by

9

5015.9 .

1 10 1

o R H

L n H f s x sT T

;! ! !

;¨ ¸© ¹ª º

Therefore, the required inductance value is



Filters

The insertion loss for a bandpass filter is shown in

Figure. Here the passband ripple is desired small.The sharpness of the filter response is given by the

shape factor, SF, related to the filter bandwidth at 3dB

and 60dB by

60

3

.d B

d B

BW SF

BW

!

A filter¶s insertion loss relates the power delivered to

the load without the filter in place (PL) to the power

delivered with the filter in place (PLf):

10log .

L

Lf

P

IL P !

¨ ¸

© ¹ª º

Band-pass Filters



Amplifier Design

Microwave amplifiers are a common and crucial component of wireless transceivers.

They are constructed around a microwave transistor from the field effect transistor (FET) or bipolar junction transistor (BJT) families.

A general microwave amplifier can be represented by the 2-port S-matrix network

between a pair of impedance-matching networks as shown in the Figure below. The

matching networks are necessary to minimize reflections seen by the source and to

maximize power to the output.



Example 11.3: Output Matching Network

S tep 1: P lot the reflection coefficient

S tep 3:Intersection points on 1+jb Circle

S tep 4:Open-Circuited S tub Length

S tep 2: Find the Admittance y L

S hunt S tub P roblem:

Admittance Calculation

r!+ 61876.0 L

L+

1

2

3

4

3¶

4¶

2 3 4



Example 11.3: Input Matching Network

S tep 1: P lot the reflection coefficient

S tep 3:Intersection points on 1+jb Circle

S tep 4:Open-Circuited S tub Length

S tep 2: Find the Admittance y s

1

2

3

4S hunt S tub P roblem:

Admittance Calculation

P120.01 !d

5.311 j y !

P206.01 !N

r!+ 123872.0 s

S +

XIgnore

Treat as a load

234

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Microwave Engineering Microwave Networks What Are Microwaves 589