Microwave cavities Physics 401, Spring 2017 Eugene V. Colla
Agenda Waves in waveguides Standing waves and resonance Setup Experiment with microwave cavity Comments on Bragg diffraction experiment 4/3/2017 2
Maxwell s Equations D B 0 0 B E t H D t Y uniform plane wave traveling in z-direction H E X H y E x z wave equation E 2 2 x x 2 2 2 z general form of solution propagation speed E vs H 1 v t E z z Ez( z, t) f t g t v v v 1 Z Ex E e 0 i( t kz) H y E x Ex ZH y 4/3/2017 3
Y Y Ey=Ey(x) at Z i X Y Ey=Ey(z) at x i v Z i X i b X Z a y Z E E k x e sin i( t kz) 0 x 4/3/2017 4
E E k x e y y sin i( t kz) 0 x + E E k x e sin i( t kz) 0 x = L L=n*l/2 4/3/2017 5
Y X Ey=Ey(z) Y X Z Z X Ey=Ey(x or z) E y H-field Z 4/3/2017 6
m n p v a b c 2 2 mnp 0 2 2 2 2 v0 -phase velocity TE 101 mode: m=1, n=0, p=1 c b 2 2 2 2 2 1 1 101 v0 a c a 4/3/2017 7
cavity coaxial wave guide outer conductor coupling loop Y X Z inner conductor M line L 0 L R C Z0 Impedance of wave guide R C L 4/3/2017 8
coaxial wave guide outer conductor inner conductor cavity coupling loop Y X Z Q L L R Z 0 L Q0 QL R 1 Z0 1 Z0 : coupling coefficient, Z 0 Impedance of wave guide Maximum power transfer: Z R 1 0 1 QL Q0, 2 Q - quality factor without external load 0 4/3/2017 9
Resonance Cavity 4/3/2017 Gunn diode MW oscillator 10
A 4/3/2017 11
Slotted line Tuner detector Open end Use detector to find distance between minimums in the slotted line (wave guide) 4/3/2017 12
50 40 E (mv) 30 20 10 l/2 0 0 2 4 6 8 10 12 14 16 18 x (cm) Use detector to find distance between minimums in the slotted line (wave guide). Distance between consequent minima correspond l/2 4/3/2017 13
cavity Movable plunger (c direction) Use plunger to change the dimension of the cavity in z-direction and search for maxima in power stored using the cavity detector. Identify TE 101 and TE 102. 4/3/2017 14
2 2 2 2 2 1 2 102 v0 a c f 102 v 0 2 1 2 a c 2 2 f Q 0 ~ 450 Df Df f 0 4/3/2017 15
1 st position of the plunger By moving the plunger we changing the resonance frequency of the cavity 2 nd position of the plunger Frequency of the oscillator 4/3/2017 16
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1. Oscilloscope should run in X-Y mode 2. To plot the I(f) dependence you have to download both Ch1 and Ch2 data 3. Use triangular waveform as a voltage applied to modulation input of the oscillator 4. Use a proper time scale setting on the scope which could estimated from scanning frequency 5. Apply the calibration equation to calculate the frequency of the oscillator from the modulation voltage G 4/3/2017 f 0.03706 V 2.9349 mod 18
Voltage tunable oscillator ZX95-3250a- S+ from 4/3/2017 19
FM Calibration for microwave oscillator 4/3/2017 20
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By changing of the coupling between oscillator and cavity we can control the quality factor of the cavity resonance but in the same time we changing the power delivered to the cavity 4/3/2017 22
Detector B field While in resonance: turn orientation of the input loop from the vertical direction in 10 o steps to 360 o. Read cavity detector. 4/3/2017 23
12 10 I (ma) 8 6 4 Experimental result. Fitted to A (cos( + )) n + A 0 2 0 0 50 100 150 200 250 300 350 grad) 4/3/2017 24
Presence of dielectric reduces length of cavity at a given resonance frequency ω 0. This effect grows with the electric field strength E y. (0) Without dielectric the cavity length at resonace is c 0. (1) Place dielectric into cavity and move in 0.5cm steps, l i. (2) At each place tune plunger to resonance and record c i. (3) Plot c i = c 0 -c i versus l i : this measures now E y vs l! 4/3/2017 25
TE 102 X Y Z Courtesy of P. Debevec 4/3/2017 26
Quality factor (TE 101 mode) of unloaded cavity can be calculated as: Q 2 2 abc a c 0 3 3 2 2 2b a c ac a c is the skin depth at frequency 0 2 / c b resistivity of the cavity material r 0 0 4x10 7 a 4/3/2017 27
For red brass =6x10-8 m 4x10 7 2 / 2.25x10-6 m a=7.22cm, b=3.42 cm, c=6.91cm (TE 101 ) Q 2 2 abc a c 2b a c ac a c 0 3 3 2 2 c b Q 0 ~7700 a 4/3/2017 28
q =90 0 -q 4/3/2017 29
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) 4/3/2017 30
Second order reflection? Lloyd s mirror effect 4/3/2017 31