Iwashita - Laminated conductor structure for rf in normal conducting case

AccLab BmSci ICRKyotoUniversity

The 4th International WS on Thin Films and New Ideas for pushing the limits of RF Sc, 2010 Oct.4, Legnaro National Laboratories (Padua) ITALY

Laminated Conductor Structure for RF in Normal Conducting Case

Y. Iwashita, Kyoto U.



Normal vs SuperNc Sc

resistance

depth

E Limit Break down Cold Emission?

H Limit Heat (melt?) Hc



191PROCE1DINGS OF THE I.R.E.

match at the input terminals. The noise figure for thisconnection varies slightly with source impedance andhas been found to be a minimum when the source im-pedance is roughly equal to the input impedance of thestage.

It must be emphasized that this functional depend-ence of the noise figure on operating point and sourceimpedance has been measured for only one transistor.Further measurements may show that these results arenot typical.

FINAL COMMENTSIn this paper we have attempted to present what is

known about the circuit performance of n-p-n transis-tors. Since these devices are still undergoing exploratorydevelopment and since only a limited number havebeen produced, it is obviously impossible to give sta-tistical data on reproducibility or on such reliabilityfactors as the effect of ambient temperature.

It is much too soon to know what properties may beachieved after further development, but the results ob-tained to date seem encouraging and worth reporting.

ACKNOWLEDGMENTThe authors are happy to acknowledge their indebted-

ness to W. Shockley, who was first to conceive the n-p-ntransistor and has provided much of the inspiration andguidance which has made its physical realization pos-sible. His comments have been of great help in thepreparation of this paper.We are also much indebted to J. A. Morton for his

encouragement and helpful guidance, and to M. Sparksfor providing most of the transistors which have beenstudied. We wish to thank L. 0. Schott, L. C. Geiger,and K. D. Smith for taking some of the data presented,and G. Raisbeck and L. G. Schimpf for proofreading andcorrecting the manuscript.

Reduction of Skin-Effect Losses by the Use

of Laminated Conductors *

A. M. CLOGSTONt, SENIOR MEMBER, IRE

(Copyright 1951, American Telephone & Telegraph Company)

Summary-It has recently been discovered that it is possible toreduce skin effect losses in transmission Iines by properly laminatingthe conductors and adjusting the velocity of transmission of thewaves. The theory for such laminated transmission lines is pre-sented in the case of planar systems for both infinitesimally thinlaminae and laminae of finite thickness. A transmission line com-pletely filled with lamimated material is discussed. An analysis isgiven of the modes of transmission in a laminated line, and of theproblem of terminating such a line.

I. INTRODUCTIONT HAS LONG been recognized that an electro-magnetic wave propagating in the vicinity of anelectrical conductor can penetrate only a limited

distance into the interior of the material. This phenom-enon is known as "skin effect" and is usually measuredby a so-called "skin depth" 6. If y is measured from thesurface of a conductor into its depth, the amplitudeof the electromagnetic wave and the accompanyingcurrent density decreases as e-vJa, provided the con-ductor is several times 6 in thickness, so that for y=8the amplitude has fallen to 1/e=0.367 times its valueat the surface. The skin depth 8 is given by

/2a-/{/-} ~~~~~(1)

* This is one of a class of papers published through arrangementswith certain other journals. It is appearing also in the July, 1951,issue of the Bell System Technical Journal.

t Bell Telephone Laboratories, Inc., Murray Hill, N. J.

where a is the conductivity of the material, ju is its per-meability, and X is 2wx times the frequency f under con-sideration. Throughout this paper rationalized mksunits are used.From one point of view, skin effect serves a most use-

ful purpose; for instance, in shielding electrical equip-ment or reducing cross talk between communicationcircuits. On the other hand, the effect severely limitsthe high-frequency performance of many types ofelectrical apparatus, including in particular the variouskinds of transmission lines.

Surprisingly enough, it has been discovered that itis possible, within limits, to increase the distance towhich an electromagnetic wave penetrates into a con-ducting material. This is done essentially by fabricat-ing the conductor of many insulated laminae or fila-ments of conducting material arranged parallel to thedirection of current flow. If the transverse dimensionsof the laminae or filaments are small compared to theskin depth 8 at the frequency under consideration, andif the velocity of the electromagnetic wave along theconductor is close to a certain critical value, the wavewill penetrate into the composite conductor a distancegreat enough to include a thickness of conducting ma-terial many skin depths deep. Physically speaking, thelateral change of the wave through the conductingregions is very nearly cancelled by the change throughthe insulating regions.

1951 767

A. M. Clogston, Reduction of Skin-Effect Losses by the Use of Laminated Conductors, Proc. of the IRE, 39-7, July 1951, pp.767-782

But no product...



RF Power Loss

€

j(x) =1+ iδ

Hz (0)eiωte

−(1+ i)xδ

Current Distribution:

€

J = j (x) dx0

∞

∫ = Hz (0)eiωtTotal Current in

conductor:

€

Pbulk = j 2 σ dx0

∞

∫ =Hz (0)

2

σδ=

ωµ2σ

Hz (0)2

Power loss：

Higher conductance σ→ Thinner skin depth δ→ Higher current density j(x) → Less loss reductionIndependent current distribution control

possible?4



Current Distribution in Conductor

€

j(x) =1+ iδ

Hz (0)eiωte

−(1+ i)xδ

-0.5

0.0

0.5

1.0

0 1 2 3 4 5

Abs(j/jmax) Re(j/jmax) Im(j/jmax)

x/δ

Rel

ativ

e va

lues

5

δ : Skin Depth



EM Field in a Thin Foil Conductor

6

X

Y vacuum

αδ

Hz=H0eiωt Hz=ξH0eiωt vacuum

€

j(x) = Hz (0) j f e−(1+ i)x /δ + jbe

−(1+ i)(αδ −x ) /δ( )

€

j f =(1+ i)e(1+ i)α e(1+ i)α −ξ( )

δ e2(1+ i)α −1( ), jb =

(1+ i)e(1+ i)α ξe(1+ i)α −1( )δ e2(1+ i)α −1( )

.

Superposition of left and right traveling waves.

–



Current Distribution

Currents cancel each other in-between(simplified schematics ... have to consider phase)

HL HRjj

Conductor

jj

Conductor

HL HR

HL=HR HL>HR



Current Distribution in a Thin Foil

Same B: Zero net Current Half strength at right

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

ξ=1, α=8ξ=1, α=4ξ=1, α=2ξ=1, α=1.5ξ=1, α=1ξ=1, α=0.5

Im( j )

Re( j )

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

ξ=1, α=1ξ=0.5, α=1ξ=0.5, α=2ξ=0.5, α=4

Im( j )

Re( j )

Thick

Thin

Thinner→Real part vanishes quickly　　　while imaginary part remains

ξ=1

Thinner→Uniform real part　　　Linear in imaginary part

Net current in imaginary part is Zero.8

Thin

Thick

ξ=0.5



Magnetic Field(current)distribution

Conductor

Conductor

Foil




Conductor

Conductor

Foil

How to re-distribute the currents?



Example: Dielectric Resonator

ε >> 1

€

Ez (r) = Ez (0) J 0 (kr), k = x1' R

-0.50

0.00

0.50

1.00

1.50

0 0.5 1 1.5 2 2.5 3 3.5 4

EzHθrHθ

r

10



Example: Dielectric Resonator

ε >> 1

€

Ez (r) = Ez (0) J 0 (kr), k = x1' R

-0.50

0.00

0.50

1.00

1.50

0 0.5 1 1.5 2 2.5 3 3.5 4

EzHθrHθ

r

€

˙ D 2πrdrr1

r2∫ = 0

Dielectric materialConductor

Spacer r1

rR

r2

10



Equivalent Circuit

E EB

Raise freq. byreducing L and C

L

C

11



Experiment with coaxial cavity

Second Mode has current peak at the center

λ/4

E

Z

12

(Simple Cavity Structure)

Y.Tajima, Y.Iwashita, H.Fujisawa, M.Ichikawa, H.Tongu: Reduction of skin effect RF power loss by a thin conductor foil, JAPANESE JOURNAL OF APPLIED PHYSICS, 47, 4765-4768, 2008



Outer Conductor

Inner Conductor

End PlatesPE mesh


The 4th International WS on Thin Films and New Ideas for pushing the limits of RF Sc, 2010 Oct.4, Legnaro National Laboratories (Padua) ITALY14

CFISH：Complex version of SUPERFISHAgrees within a few %.

Measurements and CFISH

Only 1/4 area was covered. corresponds to 1.4 times local effect

1.010%

√n (n=2)

Length of insulated conductor




Conductor

Conductor

Foil

This gap is essential to bring

magnetic flux.



ISSUES•When the insulating layers have

comparable length to the wavelength, they form resonators whose resonances screw up the field distributions.

•The stepped gap structure may help it. But when the gap is too narrow, small stored energy leads to low Q.



Limitations 0.46!c~!c/2

low Q



Coax Cavity Case

Lossless

CFISH: MLcoax with Lossy Dielectric as conductor 1um F = 2990.32 MHz

4000

4050

4100

4000

4050

4100

0 50 100 150 200 250 300 350 400 450 500

FISH: MLcoax with Lossy Dielectric as conductor 1um F = 3003.8031 MHz

4000

4050

4100

4000

4050

4100

0 50 100 150 200 250 300 350 400 450 500

Including lossesλ/4

70%



CMulti-layer Coated Cavity

19

Possible Configuration

L



Possible Configuration

Multi-layer Coated Cavity20

CL



SummaryThe structure can improve Q on some structure.

The insulating layers should have openings for magnetic flux to go through.

An insulating layer between conducting layers forms resonator and the resonance may increase the magnetic field.

Need more study...

Iwashita - Laminated conductor structure for rf in normal conducting case

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