Qualitative Studies

with Microwaves

Physics 401, Spring 2017Eugene V. Colla

3/27/2017 Physics 401 2

This is two weeks Lab

The main goals of the Lab:

Refreshing the memory about the

electromagnetic waves propagation

Microwaves. Generating and detecting of

the microwaves

Microwaves optic experiments

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The microwave range includes ultra-high frequency (UHF) (0.3–3 GHz),

super high frequency (SHF) (3–30 GHz), and extremely high frequency

(EHF) (30–300 GHz) signals.

Microwave

Electromagnetic spectrum* *by courtesy Wikipedia

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*by courtesy Wikipedia

Microwave oven (2.45GHz)Satellite TV (4-18GHz)

Communication

(0.8-2.69GHz)

Radar

(up to 110GHz)

Motion detector (10.4GHz)

Weather radar (8-12Ghz)

Physics 401

GPS 1.17-1.575 GHz

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James Clerk Maxwell

(1831–1879)

D

0B D

H Jt

BE

t

If = 0 and J = 0 and taking in account that

(1) and (4) can be rewritten as

(1) (3)

(4)(2)

0y zx

E EED

x y z

DH

t

D E

B H

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Now assuming that plane wave propagate in z direction and what leads

to Ey=Ez=0 and Hx=Hz=0

Y

X

z

Ex

Hy

Now (3) and (4) could be simplified as

y yH E

z t

yxHE

z t

whereo r

o r

0 is the free space permeability, 0 is the free space permittivity

r is permeability of a specific medium , r is permittivity of a specific medium

(5)

(6)

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Combining (5) and (6) (see Lab write-up for more details) we finally can

get the equations of propagation of the plane wave:

Y

X

z

Ex

Hy

2 2

2 2 2

1x xE E

z v t

2 2

2 2 2

1y yH H

z v t

where1

v

(7) (8)

Solution for (7) and (8) can found as

0cos( )

x xE E t kx

0cos( - )

y yH H t kx

y xH E

or

x yE ZH

where Z

known as characteristic impedance of medium

k is wave vector and is defined as2

k

or k

v

0

0

377fs

Z ohms

For free space (r=1 and r=1)

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Y

X

z

Ex

Hy

1v

0cos( )

x xE E t kx

0cos( - )

y yH H t kx

y xH E

x yE ZHZ

2k

or k

v

0

0

377fs

Z ohms

For free space (r=1 and r=1)

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Vacuum tubes: klystron, magnetron, traveling wave tube

Solid state devices: FET, tunneling diodes, Gunn diodes

Tunable frequency

from 9 to 10GHz;

maximum output

power 20mW

426A

Microwave oven magnetron;

typical power 0.7-1.5kW

Heated cathode as

electron source

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Russell Harrison

Varian (April 24, 1898

– July 28, 1959)

Sigurd Fergus

Varian (May 4, 1901

– October 18, 1961)

Varian Brothers...Klystron Tube (1940)

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Generating of the microwaves. Klystron.

Single transit klystron Reflection klystron

Advantages: well defined

frequencies,

high power

output

High power klystron

used in Canberra Deep

Space Communications

Complex (courtesy of

Wikipedia)

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2K25 Klystron

GENERAL CHARACTERISTICS

Frequency Range ·······················8,500 to 9,660 Mc

Cathode Oxide-coated, indirectly heated

Heater Voltage····································6.3Volts

Heater Current···························0.44 Amperes

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Klystron

frequency

meter

attenuator

detector

horn horn

detectortermination

Microwave Transmitter Arm Microwave Receiver Arm

Digital Volt Meter

or Oscilloscope

Digital Volt Meter

or Oscilloscope

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Experimental setup. Main components.

Attenuator

KlystronFrequency meter detector

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0[exp 1]

eVI I

kT

Typical I-V dependence

for p-n diode

Taylor expansion for exp function will give:

...!3!2

1)exp(32

xx

xx

And finally

...2 bVaVI

RF

choke

Detector diode

Bypass

capacitor

RF inV out

If V=V0sint

𝑏 ∗𝑉2

0

𝟐𝟏 − 𝒄𝒐𝒔𝟐𝝎𝒕

2

0 ...2

DC

VI b

0(DC)

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fc ~ 200GHz

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The Nobel Prize in Physics 1907

Albert Abraham Michelson

(1852 - 1931)

Mirror A

Mirror B

Receiver

Transmitter

Beam splitter

2 BR L kL

LB

LR

Condition for constructive interference

LR, LB optical paths (OP) for

“red” and “blue” rays

OP = n*LG

n – refraction index;

LG – geometrical length

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Physics 403 Lab Michelson interferometer setup

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Thomas Young

(1773 – 1829)

r1

r2

For constructive

Interference

Dr=n or dsinq=n

d

qDr=r1-r2=dsinq

b

2

2 2 2

0

sincos ( sin( / 2)

ss

xkd

x q

The measured envelope of the diffraction

pattern can be defined as:

where sin( / 2)x kb q and

2k

is wave vector of the plane wave

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Transmitter

Physics 401 Lab setup and

example of the data

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2

2 2 2

0

sincos ( sin( / 2)

ss

xkd

x q

sin( / 2)x kb q

Model Two_slit (User)

Equation y=I0*(sin(K1*sin(pi*x/360+f))/(K1*sin(pi*x/360+f)))

^2 *(cos(K2*sin(pi*x/360+f)))^2+I00

Reduced Chi-Sqr 94.62111

Adj. R-Square 0.96659 Value Standard Error

I0 190.6014 3.042882

K1 4.384042 0.074754

K2 13.51332 0.052244

f -0.01525 7.19E-04

I00 9.572049 1.440409

-100 -50 0 50 1000

100

200

I (n

A)

qo

=3.141cm

Here in fitting expression:

𝑰𝟎 = 𝝍𝟎𝟐;

𝑲𝟏 = 𝒌𝒃;𝑲𝟐 = 𝒌𝒅

𝒚 = 𝑰𝟎 ∙𝐬𝐢𝐧(𝑲𝟏 𝐬𝐢𝐧

𝝅𝒙

𝟑𝟔𝟎+𝒇

𝑲𝟏 𝒔𝒊𝒏𝝅𝒙

𝟑𝟔𝟎+𝒇

2𝐜𝐨𝐬𝟐 𝑲𝟐𝐬𝐢𝐧𝝅𝒙

𝟑𝟔𝟎+ 𝒇 +I00

Fitting equation

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h

d1 d2

Mirror

Transmitter Receiver

2 2 2 2( 1 21 )2h d h d dS d D

Difference of the wave paths of

“red” and “blue” rays is:

For constructive interference

DS=n

Lab setup picture

Humphry Lloyd

1802-1881

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q1

q2

n1

n2

Claudius Ptolemaeus

after AD 83–c.168)

n1sinq1=n2sinq2

n1>n2

Equation for critical angle:

n1sinqc=n2sin90o

qc=sin-1(n2/n1)

Willebrord Snellius

1580-1626

Snell’s law

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Transmitter

Lucite prism

n1(lucite)

n2(air)

0 20 40 60 80 1000.0

0.5

1.0

1.5

Sig

nal

in

ten

sity

(

A)

Angle q0

Experimental setup and the example of the data

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Transmitter Receiver

Polarizer

Metallic gridq

Tra

ns

mit

ter

E=E0cosq

I∞E2

I=I0cos2q

Etienne-Louis Malus

1775 – 1812

Malus law

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I=I0cos2q

Transmitter Rotatable receiver

Polarizer

Experimental data

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Sir William Henry Bragg

1862-1942

William Lawrence Bragg

1890-1971

The Nobel Prize in Physics 1915"for their services in the analysis of

crystal structure by means of X-rays"

Interference of the EM waves

reflected from the crystalline layers

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(100) (110) (210)

Different orientations of the crystal

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n=2dsinq <2d

In our experiment ~3cm;

For cubic symmetry the

angles of Bragg peaks

can be calculated from:

2 2

2 2 2

sin

2d h k l

q

where h,k,l are the Miller Indices.

For crystal with d=5cm and =3cm

the 3 first Bragg peaks for (100)

orientation can be found at

angles: ~17.5o; 36.9o and 64.2oExperimental setup

crystal

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q

q

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*courtesy of Matthew Stupca

0 10 20 30 40 50 60 70 80 900

2

4

(100)

(110)(111)

(200)(210) (211) (220)(300)

I (

A)

(degree)

Matthew Stupca

Longxiang Zhang

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Bragg diffraction. X-rays.

*courtesy of Wikipedia

X-ray tube

0.0110nm

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Bragg diffraction. X-rays.

*courtesy of Matthew Stupca

Target Kβ₁ Kβ₂ Kα₁ Kα₂

Fe 0.17566 0.17442 0.193604 0.193998

Co 0.162079 0.160891 0.178897 0.179285

Ni 0.15001 0.14886 0.165791 0.166175

Cu 0.139222 0.138109 0.154056 0.154439

Zr 0.70173 0.68993 0.78593 0.79015

Mo 0.63229 0.62099 0.70930 0.71359

David R. Lide, ed. (1994). CRC Handbook

of Chemistry and Physics 75th edition.

CRC Press. pp. 10–227

X-ray K-series spectral line wavelengths (nm) for some common target materials

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Bragg diffraction. X-rays.

*courtesy of Matthew Stupca

Comments and suggestions

1. Klystron is very hot and the high voltage (~300V) is applied

to repeller.

2. You have to do 6 (!) experiment in one Lab session – take

care about time management. The most time consuming

experiment is the “Bragg diffraction”.

3. Do not put on the tables any extra stuff – this will cause

extra reflections of microwaves and could result in

smearing of the data.

4. This is two weeks experiment but the equipment for the

week 2 will be different. Please finish all week 1

measurements until the end of this week

Good luck !

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