Iwashita - Laminated conductor structure for rf in normal conducting case

Laminated Conductor Structure
for RF in Normal Conducting Case

Y. Iwashita, Kyoto U.
AccLab BmSci ICR
KyotoUniversity

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

Normal vs Super
Nc Sc

resistance

depth

E Limit Break down Cold Emission?

H Limit Heat (melt?) Hc

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KyotoUniversity


preparation of this paper.
In this paper we have attempted to present what is We are also much indebted to J. A. Morton for his
known about the circuit performance of n-p-n transis- encouragement and helpful guidance, and to M. Sparks
tors. Since these devices are still undergoing exploratory for providing most of the transistors which have been
development and since only a limited number have studied. We wish to thank L. 0. Schott, L. C. Geiger,
A. M. Clogston, Reduction of Skin-Effect Losses by the Use of
been produced, it is obviously impossible to give sta-
tistical data on reproducibility or on such reliability
and K. D. Smith for taking some of the data presented,
and G. Raisbeck and L. G. Schimpf for proofreading and
factors as the effect of ambient temperature. correcting the manuscript.
Laminated Conductors, Proc. of the IRE, 39-7, July 1951, pp.767-782
Reduction Skin-Effect Losses by the
of 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 to where a is the conductivity of the material, ju is its per-
reduce skin effect losses in transmission Iines by properly laminating meability, and X is 2wx times the frequency f under con-
the conductors and adjusting the velocity of transmission of the
waves. The theory for such laminated transmission lines is pre- sideration. Throughout this paper rationalized mks
sented in the case of planar systems for both infinitesimally thin units are used.
laminae and laminae of finite thickness. A transmission line com- From one point of view, skin effect serves a most use-
pletely filled with lamimated material is discussed. An analysis is ful purpose; for instance, in shielding electrical equip-
given of the modes of transmission in a laminated line, and of the ment or reducing cross talk between communication
problem of terminating such a line. circuits. On the other hand, the effect severely limits
I. INTRODUCTION the high-frequency performance of many types of
T HAS LONG been recognized that an electro- electrical apparatus, including in particular the various
magnetic wave propagating in the vicinity of an kinds of transmission lines. has been discovered that it
electrical conductor can penetrate only a limited is Surprisingly enough, it to increase the distance to
possible, within limits,
distance into the interior of the material. This phenom- which an electromagnetic wave penetrates into a con-
enon is known as "skin effect" and is usually measured
is done essentially by
by a so-called "skin depth" 6. If y is measured from the ducting conductorThismany insulated laminaefabricat-
material.
ing the
surface of a conductor into its depth, the amplitude ments of conducting material arranged of or fila-
of the electromagnetic wave and the accompanying parallel to the
current density decreases as e-vJa, provided the con- direction
of current flow. If the transverse dimensions
ductor is several times 6 in thickness, so that for y=8 skin of the laminae or filaments are small compared to the
the amplitude has fallen to 1/e=0.367 times its value depth 8 at the frequency under consideration, and
at the surface. The skin depth 8 is given by if the velocity of the electromagnetic wave along the
conductor is close to a certain critical value, the wave
/2 will penetrate into the composite conductor a distance
a- /{/-} ~~~~~(1)great enough to include a thickness of conducting ma-
terial many skin depths deep. Physically speaking, the
But no product...
* This is one of a
class of papers published through arrangements lateral change of the wave through the conducting
with certain other journals. It is appearing also in the July, 1951, regions is very nearly cancelled by the change through
issue of the Bell System Technical Journal.
t Bell Telephone Laboratories, Inc., Murray Hill, N. J. the insulating regions.
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KyotoUniversity


1+ i iωt
−(1+i)x
j(x) = H z (0)e e δ
δ
J = ∞j (x) dx = H (0)e iωt
∫ 0
z

2
€ ∞ 2 H z (0) ωµ
Pbulk = ∫ 0
j σ dx =
σδ
=
2σ
H z (0) 2

€

j(x)

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KyotoUniversity
4

Current Distribution in Conductor
1+ i −(1+i)x
iωt δ
j(x) = H z (0)e e
δ
1.0
Abs(j/jmax)
Re(j/jmax)

Relative values
0.5 Im(j/jmax)

€ 0.0

-0.5
0 1 2 3 4 x/δ
5

δ : Skin Depth
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KyotoUniversity

The 4th International WS on Thin Films and New Ideas for pushing the 5
limits of RF Sc, 2010 Oct.4, Legnaro National Laboratories (Padua) ITALY

EM Field in a Thin Foil Conductor
vacuum Y vacuum
Hz=H0eiωt Hz=ξH0eiωt

αδ X

j(x) = H z (0) j f e ( −(1+i)x /δ
– jbe
+ −(1+i)(αδ −x )/δ
)
jf =
(1+ i)e (1+i)α
(e (1+i)α
−ξ ),j =
(1 + i)e (1+i)α
(ξe (1+i)α
−1 ).
b
€ δe ( 2(1+i)α
−1 ) δe ( 2(1+i)α
−1 )
Superposition of left and right traveling waves.
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6

Current Distribution
Conductor Conductor

HL j j HR HL j j HR

HL=HR HL>HR

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


Current Distribution in a Thin Foil
1.5 1.5

ξ=1 ξ=0.5
ξ=1, α=8 ξ=1, α=1
ξ=1, α=4 ξ=0.5, α=1
1.0 ξ=1, α=2 1.0 ξ=0.5, α=2
ξ=1, α=1.5 ξ=0.5, α=4
ξ=1, α=1
0.5 ξ=1, α=0.5 0.5
Im( j ) Im( j )
Thick Thick
0.0 0.0

-0.5 -0.5
Thin Thin
-1.0 -1.0

-1.5 -1.5
-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
Re( j ) Re( j )

Same B: Zero net Current Half strength at right
Thinner→Real part vanishes quickly Thinner→Uniform real part
while imaginary part remains Linear in imaginary part
Net current in imaginary part is Zero. AccLab BmSci ICR
KyotoUniversity
8

Magnetic Field(current)distribution

Conductor

Foil
Conductor

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Conductor

Foil
Conductor

How to re-distribute the currents? AccLab BmSci ICR
KyotoUniversity


Example: Dielectric Resonator

>>
1.50

Ez (r) = Ez (0) J 0 (kr), k = x1' R 1.00
Ez
Hθ
rHθ
0.50

0.00

-0.50
0 0.5 1 1.5 2 2.5 3 3.5 4
r

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10

Example: Dielectric Resonator

>>
1.50

Ez (r) = Ez (0) J 0 (kr), k = x1' R 1.00
Ez
Hθ
rHθ

r2 0.50

˙
∫ r1
D 2πrdr = 0 0.00

-0.50
0 0.5 1 1.5 2
r
2.5 3 3.5 4

Spacer r1 r2
Dielectric R
material r
€
Conductor
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10

Equivalent Circuit

E B E

L Raise freq. by
reducing L and C

C
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11

Experiment with coaxial cavity
(Simple Cavity Structure)

Second Mode has current λ/4
peak at the center
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
E

Z
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KyotoUniversity
12

Inner Conductor

Outer Conductor

PE mesh End Plates AccLab BmSci ICR
KyotoUniversity


Measurements and CFISH

Length of
insulated 10%
conductor
1.0

CFISH Complex version of SUPERFISH
Agrees within a few %.
Only 1/4 area was covered.
corresponds to 1.4 times local effect
n (n=2) AccLab BmSci ICR
KyotoUniversity
14


Conductor

This gap is
essential to bring
Foil
Conductor magnetic ﬂux.

AccLab BmSci ICR
KyotoUniversity


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.

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KyotoUniversity


Limitations
0.46!c~
!c/2

low Q

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Coax Cavity Case
CFISH: MLcoax with Lossy Dielectric as conductor 1um F = 2990.32 MHz
4100 4100

λ/4
4050
Including losses 70%
4050

4000 4000

0 50 100 150 200 250 300 350 400 450 500

FISH: MLcoax with Lossy Dielectric as conductor 1um F = 3003.8031 MHz
4100 4100

4050
Lossless 4050

4000 4000
0 50 100 150 200 250 300 350 400 450 500

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Possible Conﬁguration

C
L

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19

Possible Conﬁguration

C
L

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20

Summary
The 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...
AccLab BmSci ICR
KyotoUniversity


Iwashita - Laminated conductor structure for rf in normal conducting case

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