1 basics of microwave measurements steven anlage

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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

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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

6

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