1 basics of microwave measurements steven anlage
TRANSCRIPT
1
Basics of Microwave Measurements
Steven Anlage
http://www.cnam.umd.edu/anlage/AnlageMicrowaveMeasurements.htm
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Electrical Signals at Low and High Frequencies
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Transmission LinesTransmission lines carry microwave signals from one point to another
They are important because the wavelength is much smaller than the length of typical T-linesused in the lab
You have to look at them as distributed circuits, rather than lumped circuits
The wave equations
V
4
Transmission Lines
Wave Speed Take the ratio of the voltage and current wavesat any given point in the transmission line:
= Z0
The characteristic impedance Z0 of the T-line
Reflections from a terminated transmission line
ZLZ0 0
0
ZZ
ZZ
a
b
V
V
L
L
right
left
Reflectioncoefficient
Some interesting special cases:
Open Circuit ZL = ∞, = 1 ei0
Short Circuit ZL = 0, = 1 ei
Perfect Load ZL = Z0, = 0 ei
These are used in error correction measurements to characterize non-ideal T-lines
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Transmission Lines and Their Characteristic Impedances
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The power absorbed in a termination is:
Transmission Lines, continued
Model of a realistic transmission line including loss
TravelingWavesolutions
with
ShuntConductance
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How Much Power Reaches the Load?
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Waveguides
Rectangular metallic waveguide
H
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Network Analysis
Assumes linearity!
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N-Port Description of an Arbitrary Enclosure
N – Port
System
N Ports
Voltages and Currents,
Incoming and Outgoing Waves
Z matrix
NN I
I
I
V
V
V
2
1
2
1
][
S matrix
NN V
V
V
S
V
V
V
2
1
2
1
][
1V
1VV1 , I1
VN , INNVNV
)()( 01
0 ZZZZS
)(),( SZ Complicated Functions of frequency
Detail Specific (Non-Universal)
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Linear vs. Nonlinear Behavior
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Network vs. Spectrum Analysis
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Resonator Measurements
Sample
MicrowaveResonator
CavityPerturbation
input output
Traditional Electrodynamics Measurements
Hrf
rf currents
inhomogeneities
~ microwavewavelength
These measurementsaverage the propertiesover the entire sample
frequency
transmission
f0
f
f0’
f’
f = f0’ – f0 (Stored Energy)(1/2Q) (Dissipated Energy)
Quality FactorQ = Estored/Edissip.
Q = f0 / f
T1 T2
B
sample
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Electric and Magnetic Perturbations
Sample
E
1 - i 2
/tRs + i Xs
Varying capacitance (1) and inductance (1) change the stored energy and resonant frequency f
f = f0’ – f0 (Stored Energy)(1/2Q) (Dissipated Energy)
Varying sample losses (/t, tan, 2) change the qualityfactor (Q) of the microscope
Magnetic Field Pert.
1 + i 2
tRs + i Xs
SampleE
Electric Field Pert.
B B
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The Variable-Spacing Parallel Plate Resonator
Principle of Operation: Measure the resonant frequency, f0, and the quality factor, Q, of the VSPPR versus the continuously variable thickness of the dielectric spacer (s), and to fit them to theoretical forms in order to extract the absolute values of and Rs.
Vary ss: contact –~ 100 m
in steps of 10 nm to 1 m
The measurements are performed at a fixed temperatureIn our experiments L, w ~ 1 cm
rfB
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The VSPPR Experiment
Films held and aligned by two setsof perpendicular sapphire pins
Dielectric spacer thickness (s)measured with capacitance meter
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VSPPR: Theory of Operation
V. V. Talanov, et al., Rev. Sci. Instrum. 71, 2136 (2000)
US Patent # 6,366,096
ss
ff
eff
PCSC
1
1
/21,0
,0
Superconducting samples
Quality Factor
r
PCL
cf
2,0
00
2ln423.0
1
sfL
)/coth( deff
fringeeffect
SC Trans.line resonator
Resonant Frequency
raddSC QQQQ
1111
sf
f
sf
R
QSC
eff
eff
SC
tan)2(
1**
0
*
Assumes: 2 identical and uniform films, local electrodynamics, Rs(f) ~ f2
2
*
,0*
f
fRR SCeffeff f* is a reference frequency
L/1
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High-Tc Superconducting Thin Films at 77 K
0 20 40 60 80 100
11.4
11.6
11.8
12.0
12.2
12.4
Dielectric Spacer Thickness (m)
Re
so
na
nt
Fre
qu
en
cy
(G
Hz
)
0
200
400
600
800
1000
1200750nm-YBCO/LAO
VSPPR, T=77 K
LN2 dielectric spacer
Q-fa
cto
r
fit: 257 ± 25 nm
Rs fit: 200 ± 20 @ f* = 10 GHz
L = 9.98 mm, w = 9.01 mm, film thickness d = 760 ± 30 nm, Tc = 92.4 K
Mutual Inductance Measurements
(1+2)/2 = 300 ± 15 nm