Qualitative Studies with Microwaves
Physics 401, Fall 2015 Eugene V. Colla The main goals of the Lab: Refreshing the memory about the electromagnetic waves propagation Microwaves. Generating and detecting of the microwaves Microwaves optic experiments
This is two weeks Lab
10/26/2015 Physics 401 2 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*by spectrum*courtesy Wikipedia
10/26/2015 Physics 401 3 Microwave oven (2.45GHz) Communication (0.8-2.69GHz) Satellite TV (4-18GHz)
Radar Motion detector (10.4GHz) (up to 110GHz) Weather radar (8-12Ghz)
*by courtesy Wikipedia
10/26/2015 Physics 401 4 B D (1) E (3) t
D (2) HJ (4) B 0 t James Clerk Maxwell (1831–1879) If = 0 and J = 0 and taking in account that DE BH (1) and (4) can be rewritten as
E Ex y Ez D D 0 H xyz t
10/26/2015 Physics 401 5 Now assuming that plane wave propagate in z direction and what leads
to Ey=Ez=0 and Hx=Hz=0 Now (3) and (4) could be simplified as X H Ex y Ex (5) zt z Hy HE yy zt(6) Y where or or
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
10/26/2015 Physics 401 6 Combining (5) and (6) (see Lab write-up for more details) we finally can get the equations of propagation of the plane wave: 22 22 EExx1 HH1 X (7) yy (8) zvt222 zvt222 1 Ex where v z H y Exx E0 cos( t kx )
HHtkxyy 0 cos(-) Y Solution for (7) and (8) can found as HE yx or EZHxy where Z known as characteristic impedance of medium 2 k or k k is wave vector and is defined as v Zohms0 377 For free space (r=1 and r=1) fs 0
10/26/2015 Physics 401 7 EEtkxxx0 cos() X HHtkxyy 0 cos(-)
Ex z Hy
1 v HE Y yx
2 Z EZH k or k xy v
0 Zohmsfs 377 0
For free space (r=1 and r=1)
10/26/2015 Physics 401 8 Vacuum tubes: klystron, magnetron, traveling wave tube
Solid state devices: FET, tunneling diodes, Gunn diodes
426A
Heated cathode as electron source
Tunable frequency from 9 to 10GHz; Microwave oven magnetron; maximum output typical power 0.7-1.5kW power 20mW
10/26/2015 Physics 401 9 Russell Harrison Sigurd Fergus Varian (April 24, 1898 Varian (May 4, 1901 – July 28, 1959) – October 18, 1961)
Varian Brothers...Klystron Tube (1940)
10/26/2015 Physics 401 10 Generating of the microwaves. Klystron.
Single transit klystron Reflection klystron
High power klystron Advantages: well defined used in Canberra Deep frequencies, Space Communications high power Complex (courtesy of output Wikipedia)
10/26/2015 Physics 401 11 Digital Volt Meter or Oscilloscope Digital Volt Meter or Oscilloscope
attenuator horn horn
frequency termination detector detector meter Klystron
Microwave Transmitter Arm Microwave Receiver Arm
10/26/2015 Physics 401 12 Experimental setup. Main components.
Attenuator
Frequency meter detector Klystron
10/26/2015 Physics 401 13 Detector diode
V out RF RF in choke Bypass capacitor
eV Typical I-V dependence for p-n diode II0[exp1] kT
Taylor expansion for exp function will give: x2 x3 2 exp(x) 1 x ... I aV bV ... 2! 3! 0(DC) 2 If V=V0sint 2 V0 푉 0 푏 ∗ ퟏ − 풄풐풔ퟐ흎풕 IbDC ... And finally ퟐ 2
10/26/2015 Physics 401 14 fc ~ 200GHz
10/26/2015 Physics 401 15 Mirror A
Mirror B LR Transmitter
Albert Abraham Michelson Beam splitter (1852 - 1931) LB The Nobel Prize in Physics 1907
LR, LB optical paths (OP) for Condition for constructive interference “red” and “blue” rays Receiver OP = n*L G 2 LR LB n n – refraction index;
LG – geometrical length
10/26/2015 Physics 401 16 Physics 403 Lab Michelson interferometer setup
10/26/2015 Physics 401 17 For constructive Interference r1 Dr=n or dsinq=n Thomas Young (1773 – 1829) r2
The measured envelope of the diffraction pattern can be defined as:
2 Dr=r1-r2=dsinq 22sin x 2 q qss 0 cos (kd sin( / 2) x
where xkb sin(/q 2) and d 2 k is wave vector of the plane wave b
10/26/2015 Physics 401 18 Transmitter
Physics 403 Lab setup and example of the data
10/26/2015 Physics 401 19 2 22sin x 2 xkb sin(/q 2) qss 0 cos(sin(/ kd 2) x
Model Two_slit (User) =3.141cm 200 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 100 K2 13.51332 0.052244
I (nA) f -0.01525 7.19E-04 I00 9.572049 1.440409
Fitting equation 0 -100 -50 0 50 100 o q Here in fitting expression: 흅풙 ퟐ 퐬퐢퐧(푲ퟏ 퐬퐢퐧 +풇 푰ퟎ = 흍ퟎ ; ퟑퟔퟎ 2 ퟐ 흅풙 풚 = 푰ퟎ ∙ 흅풙 퐜퐨퐬 푲ퟐ 퐬퐢퐧 + 풇 +I00 푲ퟏ 풔풊풏 +풇 ퟑퟔퟎ 푲ퟏ = 풌풃; ퟑퟔퟎ 푲ퟐ = 풌풅
10/26/2015 Physics 401 20 Mirror
h Transmitter Receiver
Humphry Lloyd 1802-1881 d1 d2 Difference of the wave paths of 2222 “red” and “blue” rays is: DS hdhd1 2 (d 12 d )
For constructive interference DS=n
Lab setup picture
10/26/2015 Physics 401 21 n1sinq1=n2sinq2
Snell’s law
Willebrord Snellius n1>n2 Claudius Ptolemaeus 1580-1626 q1 after AD 83–c.168)
n1
n Equation for critical angle: 2 q2 o n1sinqc=n2sin90
-1 qc=sin (n2/n1)
10/26/2015 Physics 401 22 Transmitter
n1(lucite)
n2(air) Lucite prism
1.5
)
A
(
1.0
0.5 Signal intensity Experimental setup and the example of the data
0.0 0 20 40 60 80 100
0 Angle q 10/26/2015 Physics 401 23 Polarizer
Transmitter Receiver
Etienne-Louis Malus
1775 – 1812 Transmitter Malus law Metallic grid q E=E0cosq I∞E2 2 I=I0cos q
10/26/2015 Physics 401 24 Transmitter Rotatable receiver
Polarizer
2 I=I0cos q Experimental data 10/26/2015 Physics 401 25 Interference of the EM waves reflected from the crystalline layers
Sir William Henry Bragg William Lawrence Bragg 1890-1971 1862-1942 The Nobel Prize in Physics 1915 "for their services in the analysis of crystal structure by means of X-rays"
10/26/2015 Physics 401 26 (100) (110) (210)
Different orientations of the crystal
10/26/2015 Physics 401 27 In our experiment ~3cm; For cubic symmetry the angles of Bragg peaks can be calculated from: n=2dsinq <2d
2 qsin2 222 crystal 2dhkl
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
Experimental setup angles: ~17.5o; 36.9o and 64.2o
10/26/2015 Physics 401 28 q q
10/26/2015 Physics 401 29 4 Matthew Stupca Longxiang Zhang
)
A
(
I 2 (100)
(110)(111) (220) (200)(210) (211) (300)
0 0 10 20 30 40 50 60 70 80 90 (degree)
*courtesy of Matthew Stupca
10/26/2015 Physics 401 30 Bragg diffraction. X-rays.
0.0110nm
X-ray tube
*courtesy of Wikipedia
10/26/2015 Physics 401 31 Bragg diffraction. X-rays.
X-ray K-series spectral line wavelengths (nm) for some common target materials
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
*courtesy of Matthew Stupca
10/26/2015 Physics 401 32 Bragg diffraction. X-rays.
*courtesy of Matthew Stupca
10/26/2015 Physics 401 33 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 !
10/26/2015 Physics 401 34