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Microwavecavities

Physics 401, Fall 2013

Eugene V. Colla

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Agenda

Waves in waveguides

Standing waves and resonance

Setup

Experiment with microwave cavity

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Maxwells

Equationsuniform plane wave traveling

in z-direction H E

wave equation

general form of solution

propagation speed

E vs H

( )

0

i t kz

xE E e

Y

X

z

Ex

Hy

0D0B

BE

t

D

Ht

2 2

2 2 2

1x x

z v

E

t

E

( , )z

z zE z t f t g t v v

Z

xyH E

yxE ZH

1v

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Y

X

Z

( )

0sin i t kz

y xE E k x e

X

Y

Zi

Ey=Ey(x) at Zi

Z

Y

Xi

Ey=Ey(z) at xi

v

a

b

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Ey

Z

Z

X

Y

X

H-field

Z

X

Y

Ey=Ey(z)

Ey=Ey(x or z)

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2 2 2

2 2

0mnpm n pv

a b c

2

0v

-phase velocity

TE101mode: m=1, n=0, p=1

2 2

2 2 2101 0 1 1v

a c

a

bc

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coupling loop

coaxial wave guide

cavity

inner conductor

outer

conductor

Y

Z

X

M

R

CLL0line

R

C

L

Z0

Impedance of

wave guide

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Gunn diode

MW oscillator11/4/2013 9

Resonance Cavity

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A

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Use detector to find distance between minimums in the slotted

line (wave guide)

Slotted linedetector

TunerOpen

end

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Use detector to find distance between minimums in the slotted line

(wave guide). Distance between consequent minima correspond l/2

0 2 4 6 8 10 12 14 16 180

10

20

30

40

50

E(mV)

x (cm)

l/2

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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. IdentifyTE101and TE102.

cavity

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2 2

2 2 2

102 01 2va c

2 2

0

1021 2

2vf

a c

Df

f0

0 ~ 450f

Qf

D

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By moving the plunger we

changing the resonance

frequency of the cavity1stposition of the

plunger

2nd position of

the plunger

Frequency of the oscillator

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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 data3. 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

mod0.03706 2.9349f V

G

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Voltage tunable

oscillator ZX95-3250a-

S+ from

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FM Calibration for microwave oscillator

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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

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While in resonance: turn orientation of theinput loop from the vertical direction in 10

o

steps to 360o.

Read cavity detector.

DetectorB field

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0 50 100 150 200 250 300 350

0

2

4

6

8

10

12

I(mA)

grad)

Experimental result.

Fitted to

(cos(+)) +

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Presence of dielectric reduces length of cavity at a given resonance

frequency 0.

This effect grows with the electric field strength Ey.

(0) Without dielectric the cavity length at resonace is c0.

(1) Place dielectric into cavity and move in 0.5cm steps, li.

(2) At each place tune plunger to resonance and record ci.

(3) Plot ci=|c0-ci|versus li: this measures now Eyvs l!

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Z

X

Y

TE102

Courtesy of P. Debevec

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Z

X

Y

TE102

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4. Part IV: (a) Plot cD versus . (b) On the same graph, plot sin c versus . (c)

A small writeup correction:

This works for TE101 mode but more general it should be: where p is

mode index (TEmnp); p=1 for TE101and p=2 for TE102modes

sin

p l

c

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2 20 3 3 2 2

2

abc a c Q

b a c ac a c

Quality factor (TE101mode) of unloaded cavity can be calculated as:

a

bc

is the skin depth at frequency 02 /

resistivity of the cavity materialr004x10 7

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a

bc

2 / For red brass =6x10-8m4x10 72.25x10-6m a=7.22cm, b=3.42 cm, c=6.91cm (TE101)

2 2

0 3 3 2 22

abc a c Q

b a c ac a c

Q0~7700

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