The
proposed filter structure is shown
in
Fig. 2.
To
have an
attenuation pole
at
1.2 GHz, electromagnetic coupling between two
resonators is controlled and capacitance pattems are added.
The
designed inter-resonators coupling constant is
k=
0.129. Fig.
3
compares
the
simulated and measured results
of
the proposed
filter.
The
3-D
field simulation is carried out with
HFSS
(Ansoft Co., Ltd.).
The measured results show good agreement with the simulatation.
The
measured passband insertion
loss
is
0.9
dB
at the passband and the
attenuation
at
1.2
GHz
is
60
dB
and
at
5
GHz
is 70
dB.
This filter is
distinctive
in
the feature
of
its attenuation pole positions and this great
performance is very favourable for wireless and Bluetooth applications.
dielectric
sheets
shield
layer
coupling
and
loaded
capacitor
layer
planar
line
resonator
layer
coupling
and
loaded
capacitor
layer
Fig.
2
Filter
structure
shield
layer
frequency,
GHz
Fig.
3
Response
of
proposedjilter
Conclusions:
A
novel laminated filter using tapped resonators
is
proposed
which has attenuation poles
at
both
sides of passband.
Minimum
50
dB attenuations
are achieved at the attenuation pole
positions. This
performance is applicable
to
wireless and Bluetooth
applications.
0
IEE
2002
Electronics Letters Online
No:
20020995
DOI: 10.1049/el:20020995
B.H. Lee,
S.S.
Park and J.H.
Yoon
(CAE
Team,
R&D
Center:
Sumsung
Electro-Mechnics
Co.,
Ltd,
31
4,
Maetan-3Dong,
Paldal-Gu,
Suwon,
Kyunggi-Do,
442-743,
Korea)
D.S. Park
(MLCC
Lab. Electronic
Device
Business,
Sumsung
Electro-Mechnics
Co.,
Ltd,
31
4,
Maetan-SDong,
Paldal-Gu,
Suwon,
Kyunggi-Do,
442- 743,
Korea)
E-mail:
as89@samsung.co.kr
I7
April 2002
References
1
ISHIZAKI, T.,
FUJITA.
M.,
GAGATA,
H.,
UWANO,
T.,
and
MIYAKE,
H.:
‘A
very
small
dielectric planar filter
for
portable telephones’,
IEEE
Trans.
Microw.
Theory
Tech.,
1994,
42,
pp.
2017-2022
ISHIZAKI,
T.,
UWANO,
T.,
and
MIYAKE,
H.:
‘An
extended
configuration
of
a
stepped impedance comb-line
filter’,
IEICE
Trans.
Electron.,
1996,
E79-
C,
pp.
671477
2
Phase
noise
in
distributed
oscillators
C.J.
White
and
A.
Hajimiri
The
phase noise
of
a distributed
oscillator
is evaluated
very
simply
by
identifying
an
effective capacitance equal
to
the total capacitance
distributed
along
the transmission
lines.
The
contributions
of
the
various passive
and
active noise sources
to
the total phase noise are
calculated revealing several
guidelines
for
improved
distributed oscil-
lator designs.
Introduction:
Distributed
oscillators have various
applications
includ-
ing
multi-gigahertz integrated voltage-controlled oscillators
[I,
21
and
broadly
tunable
microwave oscillators
[3].
Calculating
the
phase
noise
of
a
distributed
oscillator
appears to
be a much
more
complicated
problem than the lumped
case;
however,
we
demonstrate that
once
the
basic
equation for
phase noise in distributed oscillators is established,
the
techniques for calculating phase
noise in
lumped
circuits
[4-61
are
easily
adapted to
the distributed
case.
One example
of
a
distributed oscillator is the forward gain mode
oscillator shown in Fig.
1.
The oscillator consists
of
two
transmission
lines connecting the gate and drain
of
several evenly spaced transistors.
The
output
at the right
of
the drain line is
AC
coupled to the input at the
left
of
the gate line. Matched terminations
on
the opposite
ends of
each
transmission line absorb the reverse waves.
The
operation
of
the
oscillator is given
in
more detail
in
[l].
-1
I
I
-J
i(t)=qS(t)
0
F
V
gate
rt-r
Fig.
1
Forward
mode
distributed oscillator (biasing not shown)
Einstein relation:
The conjecture
behind the results presented in this
Letter
is based
on
the phase
noise theory
developed
in
[6].
The phase
noise
of
a
lumped
LC
oscillator can
be
calculated using
the
Einstein
relation
for
the phase diffusion
constant
[6].
For
a sinusoidal
oscil-
lator,
the
phase diffusion
due to
passive,
white
noise
sources
is
In
(1)
C
is the tank capacitance,
V,
is
the
oscillation amplitude,
k
is
Boltzman’s constant,
Tis
temperature,
o,
is the centre frequency and
Q
is the loaded quality factor
of
the resonator. The factor
of
1/2
accounts
for
time-varying effects. The corresponding phase noise is
[6]
(2)
For
the distributed oscillator,
we
will show later that the lumped
capacitance
C
is
replaced
by
the total capacitance distributed along
the transmission lines.
The
Q
of
the distributed oscillator is calculated
using the general definition
(0,
times the energy stored in the oscilla-
tion divided
by
the average power dissipated).
For
the oscillator in Fig. 1
Q
is essentially
n,
because the
sum
of
the power dissipated
in
the gate
and drain lines and
the
power lost
to
the matched terminations does not
depend
on
the attenuation coefficient
of
the lines.
Langevin
equation:
The
detailed calculation
of
the phase noise
of
a
distributed
oscillator
is established by deriving the Langevin equation
for
the
phase
diffusion
[4].
Consider
a current impulse
q6(t)
injected
at the input
of the
distributed oscillator,
as
shown in Fig.
1.
The
voltage
at the input
is
the sum of
the oscillation
(with amplitude
5)
ELECTRONICS
LETERS
7th
November
2002
Vol.
38
No.
23
1453
and the
impulse (represented
as
a Fourier series):
Vi”(t)
=
V“
cos
27[
-
t
+
0
(
(22
1
In
this expression,
Z,
is the characteristic impedance,
v
is the phase
velocity, and
nl
is the total length
of
each transmission line. The voltage
along
the
gate line is similar
to
the waveform
in
Fig.
2,
where the
dashed line shows
the sum of
the oscillation and the fundamental
component
of
the
injected current.
The
phase shift is
(4)
assuming that the amplitude
of
the fundamental component
(gZ0v/2nl)
is much smaller than
the
oscillation. The parasitic capacitances
of
the
transistors filter the higher harmonics
of
the impulse,
so
that the total
amplitude
of
the noise signal at the gate
of
the transistors is small.
To
first order, the injected noise does not change the operating point
of
the
oscillator, except for the phase perturbation calculated above.
6
........................................
\
...._.........
.................................................................
\
-
-1
.o
0
1
2
3
distance
along
gate line, rad
Fig.
2
Voltage
along gate line, showing oscillation and
fundamental
component
of
injected impulse
Comparing
the
Langevin equation for the phase
of
a distributed
oscillator,
(4),
to
the standard equation for a sinusoidal oscillator (c.f.
[41),
the equations are
the
same except that the capacitance
of
the tank
circuit is replaced by the total capacitance
C,
=
2nl/vZ,
distributed
along the transmission lines.
The
phase noise of a distributed oscillator
in
response to a white noise current source with power spectral density
(PSD)
i;/Af
injected
at
the input
is therefore
L(Aw)
=
10 log
(
(2n1;:)2v2%)
in
the 1
/f
region, where the factor
of
1/2
is the average
of
the impulse
sensitivity function (ISF) for
a
sinusoidal oscillation
[5].
Noise
sources:
For
the distributed oscillator
shown in Fig.
1,
the
thermal noise
from
the drain line and
left
termination
is
always
4kT/Z,.
This can
be
calculated from the usual Nyquist equation for
the
thermal
noise of
a resistor,
because the impedance of the
matched
transmission line
is
Z,.
As
a result,
the phase noise
of
the oscillator
must
be
greater
than
L{Ao)
>
10
log
(;
-Z
.E2)
~
For other designs, it may be useful
to
calculated the noise generated
by
the
transmission line only
[7,
81.
Thermal noise generated by the gate line adds
to the
total phase noise
of the
distributed oscillator in Fig.
1.
The
details
of
the calculation are
omitted.
Noise
from
the transistors is cyclostationary, and needs to be adjusted
by
(rLVms),
the
rms
value
of the
product
of
the noise modulation
function
(NMF)
and
the
impulse sensitivity function
(ISF,),
as
discussed
in
[5,
61.
The noise power from each transistor that reaches the input
is
reduced
by
the power
loss
along the drain line, depending
on
the
position
of
the transistor.
The
overall phase noise for the distributed oscillator in Fig.
1
is
therefore
where
the sum
is over all the passive
and
active noise sources, and
&,,
is
determined
by
the cyclostationary properties
of
the noise
sources.
Conclusion:
We
have
presented
a general
method for calculating the
phase noise
of
a
distributed
oscillator.
The
total
capacitance distrib-
uted
along the transmission
lines
enters into the Langevin equation for
the phase diffusion
in
place of the lumped capacitance
of
the
resonator.
To
design an
improved
distributed
oscillator,
the
power
loss
to the terminations must
be
eliminated to increase the
overall
Q.
In
the current design (Fig.
I),
the phase noise
is largely
independent
of the
loss
in
the transmission lines.
Acknowledgments:
The
authors appreciate discussions
with
D.
Ham.
C.J.
White
would like
to acknowledge the
support
of an Intel
Fellow-
ship.
0
IEE
2002
Electronics
Letters Online
No:
20020982
DOL
IO.
1049/e1:20020982
C.J.
White
and
A.
Hajimiri
(Department
of
Electrical
Engineering,
California
Institute
of
Technology,
Pasadena,
CA
91
125,
USA)
E-mail: cjwhite@caltech.edu
References
30
August
2002
WU,
H.,
and
HAJIMIRI,
A,:
‘Silicon-based distributed voltage-controlled
oscillators’,
IEEE
J.
Solid-state Circuits,
2001,
36,
(3),
pp.
493-502
wONG,
S.S.:
‘Monolithic
CMOS
distributed amplfier and oscillator’.
IEEE
TSSCC
Dig.
Tech.
Papers, February
1999,
pp.
70-71
DIVMA,
L.,
and
SKVOR,
z.:
‘The distributed oscillator at
4
GHz’,
IEEE
Trans. Microw.
Theory
Tech.,
1998,
46,
pp.
2240-2243
LAX, M
:
‘Classical noise.
V.
noise
in
self-sustained oscillators’,
Phys.
HAJIMIRI,
A,,
and
LEE,
T.H.:
‘A
general theory
of
phase noise
in electrical
oscillators’,
.I
Solid-State Circuits,
1998,
33,
(2),
pp.
179-194
HAM,
D.,
and
HAJIMIRI,
A,:
‘Virtual damping
in oscillators’. Proc. Custom
Integrated Circuits Conf., Orlando,
FL,
USA,
May
2002
BOSMA,
H.:
‘On
the theory
of
linear
noisy
systems’,
Philips Res. Rep.
Suppl.,
1967, (10)
RUTLEDGE,
D.B.,
and
WEDGE,
S.W.:
‘Noise
waves and
passive linear
multiports’,
IEEE
Microw.
Guid.
Wave
Lett.,
1991,
1,
(5),
pp.
11 7-1
19
KLEVELAND,
C.,
DIAZ,
C.H.,
DIETER,
D.,
MADDEN,
L., LEE, T.H.,
and
Rev.,
1967,
CAS-160,
pp.
290-307
Improvement
of
iterative
decoding
algorithm
for linear block codes
G.
Drolet
Two
parameters are
introduced
into
a
popular algorithm
for
the
iterative
decoding
of
information encoded
with
a binary linear code
and
transmitted
over
the
additive
white Gaussian noise channel
to
improve the coding
gain.
Theoretical
justification
supported
by
simu-
lation
results
are
presented.
Introduction:
Let
F2
GF(2) denote the binary
field
and
C
C
F;
a(n,
k,
dmin)
binary linear
block
code with
(n,
n
-
k,
d;,”)
dual
code
CL
c
FZ.
One
codeword
c
=
(cl,
c2,
.
. .
,
c,)
E
C
is
chosen
at
random
among the
2k
equiprobable codewords
of
C.
The
bits of
c
are
transmitted
over
the (memoryless)
AWGN
channel using (normalised
energy)
binary
antipodal modulation:
F2
+
(fl)
C
R
b
+
(-l)b
1454
ELECTRONICS LETTERS
7th
November
2002
Vol.
38
No.
23