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10/30/2017 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
10/30/2017 Physics 401 310/30/2017
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
10/30/2017 4
*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
10/30/2017 Physics 401 510/30/2017
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)
10/30/2017 Physics 401 910/30/2017
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)
10/30/2017 1210/30/2017
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
10/30/2017 Physics 401 1310/30/2017
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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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
10/30/2017 Physics 401 1910/30/2017
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
10/30/2017 Physics 401 2110/30/2017
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
10/30/2017 Physics 401 2310/30/2017
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
10/30/2017 Physics 401 2510/30/2017
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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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
10/30/2017 Physics 401 31
*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
10/30/2017 Physics 401 33
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
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 !
10/30/2017 Physics 401 35
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