Microwave Breakdown in Air Collaboration

1

Confidential & Proprietary

Testing and Prevention

Microwave Breakdown in Air

2Confidential & Proprietary

Microwave Breakdown in Air Collaboration

T. Olsson, M. Hunton

D. Andersson, M. Lisak, U. Jordan

V. Semenov, D. Dorozhkina

J. Puech, L. Lapierre

Master thesis studentsA. Wrener, M. Åhlander

2


Outline

• Introduction on Power Handling• Testing

– Set-Up– Measurement Error

• Method and Prediction– Extrapolation– Breakdown in rectangular vs other wave forms– Suggestion for validating fly-units

• Prevention – Active methods?– By design– The sharp edge prediction and breakdown prevention


Power Handling

• In the filter, the peak electric field will depend on:– Peak input power– Load mismatch– Filter bandwidth (in-use / actual)– Number of resonators– Filter topology (cross-couplings)– Resonator design

• The breakdown electric field will depend on– Density of molecules i.e. temperature and pressure use; p*=p 298/T– Geometry and duration of high field

3


ESA/ESTEC Facility

• High-Power Measurement Facility

This facility involves research and test resources from 1 to 30 GHz. The RF power capabilities are frequency dependent with a maximum of 60 kW peak power at C-band. Two dedicated thermal-vacuum chambers are available. The four general activities are:

• Multipactor margin characterization (pulsed)

• High-power characterization (CW) • Corona characterization • PIM characterization


Set Up

DUT

LOAD

PVMPVM

PAPUMP

Repeated time to breakdown

Scanning pressure ~0.1 torr/s

Multi carrier/Pulsed

4


Trigger and Detection

• Trigger on return power – Slow channel; Rohde & Schwarz NRT/NRZ PEP mode

• Persistent plasma detected by low RL at instance of sampling (GPIB)

– Fast channel; Crystal Detector HP 423A + Tectronix TDS 220– Level above trigger � Acquisition Stop and read/reset

• Alternative Trigger Modes– Drop in Transmission– Acoustic– PIM– Light – Electronic, capacitive probes


Pressure

• Pressure Gauge MKS Baratron– Absolute Capacitance Manometer– Hermetic Evacuated Reference cell– Accuracy ±0.25 % of reading for 622A– Accuracy ±0.12 % of reading available

• Read Out HP 34401A– Accuracy ±0.0035 % of reading– plus ±0.0005 % of range

• Pressure Control– SW PI(D) regulator– Park ±1 torr

5


Temperature

• J/K elements on the filter body– Accuracy ~1C without stringent calibration

• Metallic rod resonators and tuning screws have often good thermal coupling to the body

• Temperature gradients may still be an issue!– Thermal Conductivity; Copper 401, Aluminum 237, Brass 120, Steel

45-60, Stainless Steel 14 [W/m K] – Rod 1 dm*1 cm2 transports 0.4�0.014 W/K

• Beware of poorly connected junctions, contacts and coupling elements. Local heat may emanate from high current regions.

• In persistent plasma, surface layers may be hot locally.


Air Flow

• Air flow in the breakdown prone region is expected to change the threshold– Convective heat transport– Convective electron loss

• Fluctuations ;– Sound pressure prms=100 Pa (level 134 dB)

corresponds to 0.1 % of normal pressure

6


Air Flow (cont)

• Flow through orifice at small pressure differences

• 10 Pa difference at 20000 Pa leads to 0.14 l/s through a square cm hole or air velocity 1.4 m/s

• This flow would keep up with a pump speed of about 2000 Pa/s if we assume a filter volume of 1 liter, i.e.

about 10% of gas per second.

5.3

1

1

24.1

1

1

21 115.0

−

⋅⋅⋅≈

p

p

p

p

T

pAQ µ

122

1pp ≥

SI units

1≈µ≤1


Humid Air

100µs 1 pulse/s

50% breakdown

UV Priming

J. Appl. Phys. 41, 7 1970 Bandel and MacDonald

Eb rms

Saturated Air @ 20C

23.4 mBar~17.2 Torr

7


Power

• Load – RL > 25 dB � ±0.5 dB (arbitrary phase)

• Power Gauge – Rohde & Schwarz NRT– NRT-Z44 Directional Power Sensor

• Accuracy for average and average burst (un-modulated)0.17 dB + zero set (RL>20 dB)

• Generator – Agilent ESG plus Powerwave “Harley” G3L-1929-120 MCPA

• Rectangular pulse ±0.03dB + drift 0.1dB – (startup sequence -3 dB ±(σ=2 dB) then 0 dB ± 0.3 dB

~10s) – Marconi plus four phased Ophir

• Rectangular pulse ±0.25dB + drift 0.2dB


Summary of errors

1 Total

0.50.5 dB {in filter}

Power reflection

0.2 0.2 dBPower detection

0.10.1 dB{ESG/Harley pulsed}

Power generation

0.1+3 K @ 310{achievable}

Temperature

0.11.5 torr@150Pressure

∆dB of threshold

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Method and prediction

2

4

33.5

7 104.6100

)/(104

Λ−⋅−

⋅=

p

DpE

p

effnetν

Indicated validity; Eeff / p <140 [V/(cm Torr)]

rms 22.7 kV/cm; peak 32 kV/cm @760Torr

20 40 60 80

Eeff/p

108

107

106

105

[V/cm Torr]2

2

22

1c

rmseff

EE

ν

ω+

=pc

9105 ⋅≈ν

Collisions;

From Taylor et. al.


Extrapolation using diffusion length

0.2 6kW

0.02 4.7kW

0.00015 2.4kW

Λ[cm] Pthr30

20

10

20 60 100 140 180 220

4 dB for full span in Λ

8

3

4

2

4

2

2

2

2

2

2

104.6760

)760(

104.6)(

)760(1

)(1

760

⋅+Λ

⋅+Λ

+

+

⋅=

D

p

pD

ppPP

c

cthrin

ν

ω

ν

ωThreshold vs. pressure

[ ]5.0W

[Torr]

Pressure

inP

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Method of Waiting for Breakdown

• Choose pressure and power above threshold• Wait for breakdown • Repeat

Number of survivals exceeding T

80

0 200 [seconds]

0

0,01

0,02

0,03

0,04

0,05

0,06

100 110 120 130 140 150

Exponential rate vs pressure

[Torr]

[S-1]


Proneness

• Definition; Fraction of time allowing sufficient subsequent growth

Time

super critical single pulse breakdown

τPτPR

∆T

n(t)

( ) BDpaBD

BD

PRp

p

PRp

TP

Pc

cGc

GTf ≡

−+−

+=

+

∆=

11

ββ τνττ

τ

ττ

Breakdown criterion GBD=20Critical power for single pulse breakdown c=1 thus c>1 β=8/3

•For validation;Use a signal thatadd much proneness per dB at threshold

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Proneness of Rectangular Pulse

• 10 % Dutycycle 1 ms +9ms

0.99 1

c

1

-10

-11

-12

))(log(10 cfT⋅

• Proneness 10% except for ~0.997*pressure ≈ 1 torr~0.05 dB

Add fluctuations

• In the pulse 0.05 dB

• 0.1 dB long term drift

• Gas pressure 1 torr~0.05 dB

0 100 200 300 400 500 600 700 800 900 1000

54 dBm

1ms

2 dB


Proneness of arbitrary wave form

• For real formats the exponent G(t) can be calculated numerically

∫=t

net dtttG0

')'()( ν

0•For each sample pointWhat happens in near future?

•Associate probability 1 with potential breakdown 0 with no breakdown!

Breakdown?

Breakdown?

t

End of local history

11


Proneness of UMTS Test Models 5

CW

BDPPmax

Calculated for homogeneous field at 760 torr

Clipping 8 dB Clipping 10 dB0.0005

0.0004

0.0003

0.0002

0.0001

0

CW

BDPPmax

1 2 3 1 2 3


UMTS Test Model Signals

0 500 1000 1500 2000 2500-50

-40

-30

-20

-10

0

10

20

30

40

0 500 1000 1500 2000 2500-60

-50

-40

-30

-20

-10

0

10

20

30

40

Pow

er-5

5 dB

[dB

m]

-30

-

0

10

0 50 100 %

• WCDMA TM5_1_10 47 dBm PAR=10 dB• WCDMA TM5_1_8 49 dBm PAR=8.5 dB

10 ms

10 ms

TM5_1_10 ESG vs Harley Trigger signals from crystal detector

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Probability of Breakdown

0 50 100 150 200 2500

-1

-2

-3

-4

-5 No Event

180 torr threshold hypothesis

49 dBm

54 dBm

47 dBm

Log

Γ [s

-1]

TM5_1_8

TM5_1_10

Pulsed

Pulsed lost trigg

~(pth-p)

Numerical fit

Pressure [torr]

200100


Axisradius

Hot Volume and Measured Rates

Factor 10

)()(760

HotVolumecfp

J T

i

⋅><

⋅=Γν

γ

0.02

0

100 150 200 250

0.002

0.001

0

• Hot Volume is the part of the resonator that has νi-νa>0

Axis

radius

Factor 10 in Hot Volume

220 260 300

[s-1] Meas.Calc. 2 e-/cc s

Calc. 2 e-/cc s

[s-1]

13


Hot Volume

• Estimation of Hot Volume

0

500

1000

1500

2000

2500

3000

220 240 260 280 300

Pressure

Ho

t V

olu

me

{m

m^

3}

0dB

1dB

2dB

3dB

4dB

5dB

est_Hot_Vol

Volume(νi-νa>0) The super criticality is here previously obtained relative to an experimental threshold curve and interpolated in a grid of hot volumes obtained from numerical calculations

Note the slow change of HV ~p-1

at a fixed super criticality


Threshold Estimation

• Compare UMTS waveforms and rectangular pulse train

UMTS TM5_1_8 TM5_1_10

Thresholds: 218 torr 202 torr4.1)63.1log(10545.849 ≈−−+

Stored Energy vs Pressure

0123456789

100 120 140 160 180 200 220 240 260 280

Pressure [torr]

mic

roJo

ule

calculated

7.0)7.1log(10541047 ≈−−+

This ”threshold” energy vs pressure is obtained by solving numerically a 2-D differential equation for the relevant resonator

1.4 dB

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Are thresholds consistent with calculation

• UMTS TM5_1_10 47.0 dBm at 760 torr

Applied to experiment ~180 torr Λ≈0.02

• Basic assumption

CW

BDBD PP ⋅= 7.1

CW

BDT PfP ⋅=⋅= − 4.2)105)7.1

4.2(( 4

max

7109.4 ⋅≈= aloss νν

7

2105.2 ⋅≈

Λ+=

Daloss νν

3.8 dB

2.3 dB Cth_U=1.7

C=2.4

2

1

2

max

1

2

max

1

2

1

2

1

2

1

HotVolume

HotVolume

p

p

f

f

i

i

T

T ⋅><

><⋅⋅=

Γ

Γ

γν

νγ

≈1 ?


Probability and threshold estimates

ΓR

pres

ΓU

pres

pth_R

εth

pressure

pth_R

÷c

pcR

ΓR(c)

pcR)(

)(

_

_

cf

cf

RT

UT•

pcU

εth

pcU

•c/cth_U

pth_U

Step 1

Step 2

Step 4

Step 3

Result!

202

and

216 torr165 and 205 torr

105 and 126 torr

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Waveform Test Object

• Discoloring after hours of persistent plasma burning

• Thermal compensation for long wait time : – 44 dBm�30°C – 47 dBm�36°C – 49 dBm�44°C

• Thus, 220 torr 44°C corresponds to ~210 torr 30°C in density, maybe an explanation for the few events indeed observed at 220 torr for TM5_1_8


Suggestion for test of ”fly”-units

• No breakdown is allowed, but what is the margin?• Pt Design target breakdown power roughly obtained by N objects• Ps Specified maximum power for “fly” unit • Survival measurement at intermediate power P, Ps<P<Pt a required time T~Γr

-1

• If N=0 because repeated experiment impossible, test-margin and time must be determined based on geometry?

Log Γ

Ps Pt Power

Log Γr

Spread of N objects

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Prevention (Active)

Flame detectors installed on antenna sites


Prevention by design

• Filter 12 kW_peak/15 MHz or 24 kW/32 MHz Features•Rod~cavity resonator

•Large gap

• 3mm outer radius

• Internal tuning screw

• Weak cross coupling

• Direct tap by sheet metal

)tan(

1

000 L

cZ

Ctop

ωω

=

Electron-density form-functionZ

R

17


140

0

)

960925 f

Storage caused by T and Q sections

• 10-pole EGSM transmit filter

900 920 940 960 980 1000-120

-100

-80

-60

-40

-20

0S21

dB

2πf Ws(f)/Pin(f)

T 9- 11(port)Q 0- 3

1 2

34

567

9

10

8

20

100

925 960

Internal topologiesT 8- 10 94@925 Q 1- 4 85@960T 5- 7 123@925 Q 7- 10 78@960

For power handling; Design as wide band as possible


Sharp Edge Object

• Combiner resonator full AM 3000 Hz total reflection

• No breakdown 4 channels•17 channels no breakdown in 1 to 4 tries

• Power scanned at normal pressure• 5 events per point for 84 channels

• Edge prone to thermal runaway• 6 dB lower threshold observed• Precursor flashes observed

•Cure; Smoothing edge and polyurethane AC-41/polyester AC43

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Sharp edge 90 degree corner

• First approximation effective field at 1 cm

• Second approximation effective field at 1 cm

3283104

100

1

72

0

22

0 ≈

⋅⋅⋅⋅⋅=

αγβ

p

D

apEeff V/cm

p=760 torra0=1cm distance to screenα=16/3κ=2/3γ=1/9β0=9.936..

β=17.86..

( ) 01.01

4090104

100

0

1

02

1

1

72

0

22

≈

−=

≈

⋅⋅⋅⋅⋅=

−ax

p

D

apEeff

γ

γ

α

β

βγ

γβ V/cm

Range not large at 760 torrbut x is independent of a0 in second approximation

cm


Sharp edge object

Qeff=2700 Wst = QeffPin/ω= 0.476 µJ for 1 W

Field mMVE /17.0≈ @10µJ

”Potential”Estimate 1.3 kV@ 1 cm 10 µJ

Threshold8.6 kV @ 438 µJ

920 WIn total reflection- 5.4dB 265 W !

But the edge is ona circular tube!

19


Sharp edged cylindrical object

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1100

120

140

160

180

200

220

240

260

280

d (cm)

variationalappendixlower bound

a0 [cm]

Pb

[W]

Extrapolation to the edge for 90 degree corner


Sharp Edges and Coatings

HASL Balver Zinn• Smoothing edges with dielectric– Green lacquer on circuit boards– Dolph’s Synthite AC-41 Polyurethane Varnish– Dolph’s Synthite AC-43 Polyester Varnish

20


Prevention

• Pressurization/Flushing• Cooling• Bandwidth• Filter Topology• Geometry

– Internal Tuning Screws– Rounded Smooth Corners – Minimal Tuning– Equalization of field (Balancing)– Coating of Sharp Structures


References

A.D. MacDonald, Microwave Breakdown in Gases, Wiley 1966W.C.Taylor, W.E. Scharfman and T. Morita, Voltage Breakdown of Microwave AntennasAdvances in Microwaves vol. 7 Edit. L.Young, Academic Press, New York 1971

Rates from Woo and DeGroot, Phys. Of Fluids 27(2), 475 (1984)Kinetic theory calculation of rates; Gurevich, Borisov and Milikh; Physics of Microwave Discharges ISBN 90 5699 008 X

Background radiation; Alvarez et. al. Lawrence Livermore National Laboratory UCRL-101807 (1990)

Herlin and Brown Phys.Rev 74, 1650 (1948)

Matthaei, Young, Jones, Microwave filters, impedance-matching networks and coupling structures, McGraw-Hill, 1964

Temporal dependence; Jordan et al; J. Phys. D: Appl. Phys. 36 (2003) 861-867

Waiting time phenomena; Dorozhkina et. al.Physics of Plasmas 13 013506 (2006)

Effective diffusion length; Jordan et al IEEE Transactions on Plasma Science april 2006 vol 34 No.2 421-430Sharp Edges; Jordan et al IEEE Transactions on Plasma Science accepted 2007

Microwave Breakdown in Air Collaboration

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