ca6
8
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 1 a b d x y z Rectangular cavity: a metal enclosed box of volume V cav = a·b·d Magnetic field B 1 lines Electric field E 1 lines TE 102 - mode Electromagnetic fields can exist in a variety of different configurations called modes. If the electric field E 1 is perpendicular to the z- direction, these modes are denominated TE- modes. TE mnp : m,n,p are the number of half-cycles along the x,y,z, direction respectively.
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Transcript of ca6
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 1
a
b
d
x
y
z
Rectangular cavity: a metal enclosed box of volume Vcav = a·b·d
Magnetic field B1 lines
Electric field E1 lines
TE102 - mode
Electromagnetic fields can exist in a variety of different configurations called modes.
If the electric field E1 is perpendicular to the z-direction, these modes are denominated TE-modes.
TEmnp: m,n,p are the number of half-cycles along the x,y,z, direction respectively.
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 2
a
d
Magnetic field lines B1, TE102 mode
xmk a
π⋅= ynkbπ⋅= z
pkdπ⋅=
For the empty cavity, the resonance frequency for a generalTEmnp mode is:
2 2 2x y z0 22
c k cf k k kππ⋅
= = ⋅ + +
2 2 2
2 2 20 2c m n pf
a b d= ⋅ + +
2 20
1 4 12 2cf
a d= ⋅ +TEmnp TE102
a = 24 mm
Typical resonance frequencies of theBruker-rectangular cavities are 9.4 GHz.
This can be achieved by:
a = 24 mm
d = 42.7 mm
Calculation by: ´rechteckresonator.mws´
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 3
Modepicture: Reflected microwave-power versus frequency
50 MHz
In the tune-mode of ESR-spectrometers, the microwavefrequency is swept overa range of appr. 100 MHz around thenominal centrefrequency.
The reflected power isdepicted versus thefrequency on an oscilloscope display.
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 4
-25 -20 -15 -10 -5 0 5 10 15 20 25-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
Q = 9400 MHz/2.1883 MHz = 4296
Datafile: 'resonator.dat'
Formel1= lor(x,p0,p1,p2)+p3+p4*x
P0= -8.47285 R0= -8P1= 2.1883 R1= 3P2= -0.826127 R2= 1P3= 0.660709 R3= 2P4= -0.00303764 R4= 0.1
Fehlerquadratsumme= 0.00588067
width: ∆ν = 2.1883 MHz
data: 10.02.2003
Rechteck-Resonatorrectangular cavity
rechteck_resonator.opj
Ref
lect
ed P
ower
(rel
.uni
ts)
Frequency Offset (MHz)
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 5
The quality factor Qcc is the critically coupled cavity.
By the definition of critical coupling: Qcc = 1/2·Qu
Qu is the quality factor of the uncoupled cavity
The quality factor Qu can be calculated, if the dimensions a,b,d and the resisitvity ρ of the metal is known.
a = 24 mm, d = 42.5 mm, b = 10 mm
ρ = 1.5·10-8 Ωm (Cu at T = 295K) u 9663Q =
The measured value of Qcc = 4296 compares to an expected value of Qu/2 = 4831
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 6
3372 3373 3374 3375 3376 3377 3378
-1000
-500
0
500
1000
ses_power_02.opj
45 dB
40 dB
35 dB
30 dB
25 dBE
SR
-SIG
NA
L (1
st d
er.)
MAGNETIC FIELD (Gauß)
ESR-Signal: Sodium-Electro-Sodalite (SES), T = 295 K
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 7
3370 3372 3374 3376 3378 3380-1500
-1000
-500
0
500
1000
1500
20 db
15 db
10 db
0 db5 db
ses_power_01.opj
ES
R-S
IGN
AL
(1st d
er.)
MAGNETIC FIELD (Gauß)
ESR-Signal: Sodium-Electro-Sodalite (SES), T = 295 K
08/11/2005 GKMR WS2005/06 Denninger rectangular cavity 8
0 10 20 30 40 5015
20
25
30
35
40
45
att = 5 dB
att = 10 dB
att = 15 dB
att = 20 dB
att = 25 dB
att = 30 dB
att = 35 dB
att = 40 dB
att = 0 dB
att = 45 dB
slope: ESR-signal = const .power0.5174
ses_power_o3.opj
Sodium electro sodalite (SES)ESR-signal, T = 295 K
ES
R-s
igna
l int
ensi
ty (d
B)
Microwave power (dB)
