Microwave cavities. Physics 401, Spring 2017 Eugene V. Colla

Transcription

1 Microwave cavities Physics 401, Spring 2017 Eugene V. Colla

2 Agenda Waves in waveguides Standing waves and resonance Setup Experiment with microwave cavity Comments on Bragg diffraction experiment 4/3/2017 2

3 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 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

4 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

5 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

6 Y X Ey=Ey(z) Y X Z Z X Ey=Ey(x or z) E y H-field Z 4/3/2017 6

7 m n p v a b c 2 2 mnp v0 -phase velocity TE 101 mode: m=1, n=0, p=1 c b v0 a c a 4/3/2017 7

8 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

9 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 QL Q0, 2 Q - quality factor without external load 0 4/3/2017 9

10 Resonance Cavity 4/3/2017 Gunn diode MW oscillator 10

11 A 4/3/

12 Slotted line Tuner detector Open end Use detector to find distance between minimums in the slotted line (wave guide) 4/3/

13 50 40 E (mv) l/ x (cm) Use detector to find distance between minimums in the slotted line (wave guide). Distance between consequent minima correspond l/2 4/3/

14 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 /3/

15 v0 a c f 102 v a c 2 2 f Q 0 ~ 450 Df Df f 0 4/3/

16 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/

17 4/3/

18 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 V mod 18

19 Voltage tunable oscillator ZX a- S+ from 4/3/

20 FM Calibration for microwave oscillator 4/3/

21 4/3/

22 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/

23 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/

24 12 10 I (ma) Experimental result. Fitted to A (cos( + )) n + A grad) 4/3/

25 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/

26 TE 102 X Y Z Courtesy of P. Debevec 4/3/

27 Quality factor (TE 101 mode) of unloaded cavity can be calculated as: Q 2 2 abc a c b 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/

28 For red brass =6x10-8 m 4x / 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 c b Q 0 ~7700 a 4/3/

29 q =90 0 -q 4/3/

30 4? Matthew Stupca Longxiang Zhang I (A) 2 (100) (110) (111) (200)(210) (211) (220) (300) (degree) 4/3/

31 Second order reflection? Lloyd s mirror effect 4/3/