Qualitative Studies with Microwaves Physics 401, Fall 2017 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 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 Physics 401 3
Microwave oven (2.45GHz) Communication (0.8-2.69GHz) Satellite TV (4-18GHz) Radar (up to 110GHz) Weather radar (8-12Ghz) GPS 1.17-1.575 GHz Motion detector (10.4GHz) *by courtesy Wikipedia Physics 401 4
D E B t (1) (3) B 0 (2) D H J t D (1) and (4) can be rewritten as If = 0 and J = 0 and taking in account that B H (4) E James Clerk Maxwell (1831 1879) E x E E x y z y z D 0 H D t Physics 401 5
Y Now assuming that plane wave propagate in z direction and what leads to E y =E z =0 and H x =H z =0 Now (3) and (4) could be simplified as X E x H y z where o r E x H y z t H z y E t o r y (5) (6) 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 Physics 401 6
Y Combining (5) and (6) (see Lab write-up for more details) we finally can get the equations of propagation of the plane wave: X H y E x E 1 E z v t 2 2 x x 2 2 2 z H H 2 2 y 1 y 2 2 2 (7) (8) z v t where E cos( ) x Ex0 t kx H cos( - ) y H y0 t kx Solution for (7) and (8) can found as Hy where Z known as characteristic impedance of medium 2 k is wave vector and is defined as k or k v For free space ( r =1 and r =1) Z fs 0 0 v 1 E ZH Ex or x y 377ohms Physics 401 7
X E cos( ) x Ex0 t kx H cos( - ) y H y0 t kx E x H y z Y v 1 H y E x Z E x ZH y k 2 or k v Z fs 0 0 377ohms For free space ( r =1 and r =1) 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; maximum output power 20mW Microwave oven magnetron; typical power 0.7-1.5kW Physics 401 9
Russell Harrison Varian (April 24, 1898 July 28, 1959) Sigurd Fergus Varian (May 4, 1901 October 18, 1961) Varian Brothers...Klystron Tube (1940) Physics 401 10
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) Physics 401 11
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 12
Digital Volt Meter or Oscilloscope Digital Volt Meter or Oscilloscope attenuator horn horn Klystron frequency meter detector detector termination Microwave Transmitter Arm Microwave Receiver Arm Physics 401 13
Experimental setup. Main components. Attenuator Klystron Frequency meter detector Physics 401 14
Detector diode RF in RF choke Bypass capacitor V out I I 0 ev [exp 1] kt Typical I-V dependence for p-n diode Taylor expansion for exp function will give: exp( x) 1 And finally x If V=V 0 sint 2 x 2! 3 x 3!... b V2 0 2 I av 0(DC) 1 cos2ωt bv 2... I DC 2 V0 b... 2 Physics 401 15
f c ~ 200GHz Physics 401 16
Mirror A L R Mirror B Transmitter Beam splitter L R, L B optical paths (OP) for red and blue rays OP = n*l G n refraction index; L G geometrical length L B Receiver Albert Abraham Michelson (1852-1931) The Nobel Prize in Physics 1907 Condition for constructive interference 2 L B R L k Physics 401 17
Physics 403 Lab Michelson interferometer setup Physics 401 18
r 1 r2 For constructive Interference Dr=n or dsinq=n Thomas Young (1773 1829) Dr=r 1 -r 2 =dsinq b d q 2 2 2sin x 2 0 ss cos ( kd sin( q / 2) x k The measured envelope of the diffraction pattern can be defined as: where x kbsin( q / 2) 2 and is wave vector of the plane wave Physics 401 19
Transmitter Physics 401 Lab setup and example of the data Physics 401 20
2 2 2sin x 2 0 ss cos ( kd sin( q / 2) x x kbsin( q / 2) 200 =3.141cm 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 I (na) 100 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 0 y = I0-100 -50 0 50 100 q o Fitting equation sin(k1 sin πx 360 +f 2 K1 sin πx cos 2 K2 sin πx + f +I00 360 +f 360 Here in fitting expression: I 0 = ψ 0 2 ; K1 = kb; K2 = kd Physics 401 21
Mirror Transmitter h Receiver d1 Difference of the wave paths of red and blue rays is: d2 Humphry Lloyd 1802-1881 2 2 2 2 DS h d1 h d 2 ( d1 d2) For constructive interference DS=n Lab setup picture Physics 401 22
n 1 sinq 1 =n 2 sinq 2 Snell s law Willebrord Snellius 1580-1626 q 1 n 1 >n 2 Claudius Ptolemaeus after AD 83 c.168) n 1 n 2 q 2 Equation for critical angle: n 1 sinq c =n 2 sin90 o q c =sin -1 (n 2 /n 1 ) Physics 401 23
Transmitter n1(lucite) n2(air) Lucite prism 1.5 Experimental setup and the example of the data Signal intensity (A) 1.0 0.5 0.0 0 20 40 60 80 100 Angle q 0 Physics 401 24
Transmitter Polarizer Transmitter Receiver Metallic grid q Etienne-Louis Malus 1775 1812 Malus law E=E 0 cosq I E 2 I=I 0 cos 2 q Physics 401 25
Transmitter Rotatable receiver Polarizer I=I 0 cos 2 q Experimental data Physics 401 26
Interference of the EM waves reflected from the crystalline layers 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" Physics 401 27
(100) (110) (210) Different orientations of the crystal Physics 401 28
n=2dsinq <2d In our experiment ~3cm; For cubic symmetry the angles of Bragg peaks can be calculated from: crystal 2 2 sin q 2d h k l 2 2 2 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: ~17.5 o ; 36.9 o and 64.2 o Physics 401 29
q q Physics 401 30
4 Matthew Stupca Longxiang Zhang I (A) 2 (100) (110) (111) (200)(210) (211) (220) (300) 0 0 10 20 30 40 50 60 70 80 90 (degree) *courtesy of Matthew Stupca Physics 401 31
Bragg diffraction. X-rays. 0.0110nm X-ray tube *courtesy of Wikipedia Physics 401 32
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 Physics 401 33
Bragg diffraction. X-rays. *courtesy of Matthew Stupca Physics 401 34
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! Physics 401 35