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Transcript of Design and Analysis of RF and Microwave Systems IMPEDANCE TRANSFORMERS AND TAPERS Lecturers: Lluís...
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
IMPEDANCE TRANSFORMERS
AND TAPERS
Lecturers: Lluís Pradell ([email protected])
Francesc Torres ([email protected])
March 2010
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
The quarter-Wave Transformer* (i)
Zin
Z1 ZLZ0
A quarter-wave transformer can be used to match a real impedance ZL to Z0
40
L
in Z
ZZ
21
tjZZ
tjZZZZ
L
Lin
1
11
tgtgt
If The matching condition at fo is 01 ZZZ L
At a different frequency and the input reflection coefficient is
00
0
0
0
20 ZZtjZZ
ZZ
ZZ
ZZ
LL
L
in
inZin
220
0
cos
41
1
ZZ
ZZ
L
Lin
The mismatch can be computed from:
0ZZ in
*Pozar 5.5
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
The quarter-Wave Transformer (ii)
If Return Loss is constrained to yield a maximum value , the
0
0
2
2
1cos
ZZ
ZZ
L
L
m
mm
frequency that reaches the bound can be computed from:
m
Where for a TEM transmission line
00
0
24
2
4 f
f
f
v
v
f
vp
pp
And the bound frequency is related to the design frequency as:
02 f
f mm
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
The quarter-Wave Transformer (iii)
Finally, the fractional bandwdith is given by
0,05m
02
fl
f
0/ 10LZ Z
0/ 4LZ Z
0/ 2LZ Z
18,1 %BW
4,5 %BW
0
0
2
1
0
0 2
1cos
42
2
ZZ
ZZ
f
fff
L
L
m
mm
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Multisection transformer* (i)
That is, in the case of small reflections the permanent reflection is dominated by the two first transient terms: transmission line discontinuity and load
The theory of small reflections
01
010 ZZ
ZZ
1
1
ZZ
ZZ
L
LL
In the case of small reflections, the reflection coefficient can be approximated taking into account the partial (transient) reflection coefficients:
jLe 2
0
L
L0
40
*Pozar 5.6
20
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
0
1Z2Z LZNZ0Z
1 2
N
Multisection transformer (ii)The theory of small reflections can be extended to a multisection transformer
2 4 2 10 1 2
1
... ; ( 0,1,..., )j j jN i iN i
i i
Z Ze e e i N
Z Z
It is assumed that the impedances ZN increase or decrease monotically
( 2) ( 2)0 1 ...jN jN jN j N j Ne e e e e
0 1 1 2 2, , ,...N N NSymmetric
The reflection coefficients can be grouped in pairs (ZN may not be symmetric)
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
0 1 / 2
12 cos cos( 2) ... cos( 2 ) ...
2jN
i Ne N N N i for N even
0 1 ( 1) / 22 cos cos( 2) ... cos( 2 ) ... cosjNi Ne N N N i
for N odd
Finite Fourier Series: periodic function (period: )
Multisection transformer (iii)
The reflection coefficient can be represented as a Fourier series
Any desired reflection coefficient behaviour over frequency can be synthesized by properly choosing the coefficients and using enough sections:
•Binomial (maximally flat) response
•Chebychev (equal ripple) response
i
L
02
F
0
0
ZZ
ZZ
L
LL
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Binomial multisection matching transformer (i)
2(1 ) 2 cosNj N N jNA e Ae
0
0
2 N L
L
Z ZA
Z Z
Binomial function
AN2)0(
The constant A is computed from the transformer response at f=0:
The transformer coefficients are computed from the response expansion:
n
N
n
jnNn eCA
0
2)( !!
!
nnN
NC N
n
The transformer impedances Zn are then computed, starting from n=0, as:
0
1 ln2lnZ
ZC
Z
Z LNn
N
n
n
Nnn AC
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Binomial multisection matching transformer (ii)
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Binomial multisection matching transformer (iii)
11/
1arccos arccos
2
NN
m mm
LA
Bandwidth of the binomial transformer
mNN
m A cos2
The maximum reflection at the band edge is given by:
02
fl
f
1
0/ 2LZ Z
71 %
( 3)
BW
N
m
05.0The fractional bandwitdh is then:
1/
0
0 0
2( ) 4 4 12 2 arccos
2
N
mm mf f f
f f A
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Chebyshev multisection matching transformer
1( ) cos( cos ), 1nT x n x for x 1( ) cosh( cosh ), 1nT x n x for x
0
0
1
1cos
L
LN
m
Z ZA
Z ZT
1
11 0
0
cosh1
cos11 1 coshcosh cosh
cos
L
m
L
mm L
m NZ Z
N Z Z
cos
cosjN
Nm
A e T
Chebyshev polynomial
02
fl
f
0,05m
0/ 2LZ Z
102 %
( 3)
BW
N
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Chebyshev transformer design
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Chebyshev transformer design
Application: Microstrip to rectangular wave-guide transition: both source and load impedances are real.
Rectangular guide
Ridge guide: five λ/4 sections: Chebychev design
Steped ridge guideMicrostrip line
Ridge guidesection
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
TRANSFORMER EXAMPLE (1):ADS SIMULATION
S_ParamSP1
Step=10 MHzStop=20 GHzStart=0 GHz
S-PARAMETERS
MSUBMSub1
Rough=0 umTanD=9e-4T=17.5 umHu=1.0e+036 umCond=5.8e+7Mur=1Er=2.17H=257 um
MSub
TermTerm2
Z=100 OhmNum=2
TermTerm1
Z=50 OhmNum=1
MLINTL5
L=5509.460000 umW=767.037000 umSubst="MSub1"
MLINTL3
L=5678.81 umW=283.802 umSubst="MSub1"
MSTEPStep3
W2=207.139 umW1=283.802 umSubst="MSub1"
MSTEPStep1
W2=429 umW1=616.935 umSubst="MSub1"
MSTEPStep2
W2=283 umW1=429.655 umSubst="MSub1"
MLINTL2
L=5611.44 umW=429.655 umSubst="MSub1"
MLINTL1
L=5548.47 umW=616.935 umSubst="MSub1"
MSTEPStep4
W2=616 umW1=767.037 umSubst="MSub1"
MLINTL4
L=5725.100000 umW=207.139000 umSubst="MSub1"
Chebyshev transformer, N = 3, |M|=0.05 (ltotal = 3/4)
87,14 70,71 100 57,37 50
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
TRANSFORMER EXAMPLE (2):ADS SIMULATION
2 4 6 8 10 12 14 16 180 20
-40
-30
-20
-10
-50
0
freq, GHz
dB
(S(1
,1))
2 4 6 8 10 12 14 16 180 20
-0.6
-0.4
-0.2
-0.8
0.0
freq, GHz
dB
(S(1
,2))
CHEBYSCHEV N=3
2 4 6 8 10 12 14 16 180 20
0.1
0.2
0.3
0.0
0.4
freq, GHz
mag(S
(1,1
))
BW = 102 %0,05m
microstrip loss
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Tapered lines (i)
LZ
zL0
0Z Z z
zz z z
Z Z Z
In the limit, when z 0:
Taper: transmission line with smooth (progressive) varying impedance Z(z)
Z
Z
ZZZ
ZZZ
2
zZdZ
zd2
1
The transient ΔΓ for a piece Δz of transmission line is given by:
dz
zfd
zfdz
zfLd n
)(
1
dzdz
zfLdzfd
zfn
2
1
)(2
1
This expression can be developed taking into account the following property:
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Tapered lines (ii)
dz
dz
zZLdzd n
2
1
Taking into account the theory of small reflections, the input reflection coefficient is the sum of all differential contributions, each one with its associated delay:
Fourier Transform
LnzjzjL
in dzdz
zZLdeezd
0
22
0 2
1
L Taper electrical length
zZ•Exponential taper
•Triangular taper
•Klopfenstein taper
dz
zZLd n
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Exponential Taper
0zZ z Z e
for 0 <z < L
0
1ln LZ
L Z
0ln / sin( )
2j LLZ Z L
L eL
(sinc function)
L
LZLZ
ZZ 00
dz
zZLd n
L zj
in dze0
2
2
1
Fourier Transform
Lmin2max
L
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Triangular taper
22
ln2 0
024 2
1 ln2 0
0
Zz LZL
Zz z LL ZL
Z e
Z e
Z z
20
20
4ln
0
4( ) ln
lnL
L
Lz Z
ZL
ZL z
ZL
Zd
Z
dz
0 / 2
/ 2
z L
L z L
0 / 2
/ 2
z L
L z L
2
0
1 sin( / 2)ln
2 / 2j L LZ L
L eZ L
(squared sinc function)
- lower side lobes- wider main lobe L
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Klopfenstein Taper
2 2cos
coshj L
L
L AL e
A
:passband L A
0
0 0
1ln
2L L
LL
Z Z Z
Z Z Z
coshL
m A
LShortest length for a specified |M|
Lowest |M| for a specified taper length
( )L A
ltaper =
0/ 2LZ Z
Based on Chebychev coefficients when n→∞. Equal ripple in passband
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Microstrip to rectangular wave-guide transition
Example of linear taper: ridged wave-guide
Microstrip line
Ridgedguide
Rectangularguide
SECTION A-A’
SECTION B-B’SECTION C-C’
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Rectangular wave-guide to finline to transition
Example of taper: finline wave guide
Finline mixer configuration
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TAPER EXAMPLE (1):ADS SIMULATION
TermTerm2
Z=100 OhmNum=2
TermTerm1
Z=50 OhmNum=1
MTAPERTaper1
L=LtotW2=W11W1=W1Subst="MSub1"
MSUBMSub1
Rough=0 milTanD=9e-4 T=17.5 umHu=3.9e+34 milCond=5.8e7 Mur=1.0 Er=2.17 H=10.0 mil
MSub
ADS taper model
S_ParamSP1
Step=10 MHzStop=20 GHzStart=0 GHz
S-PARAMETERS
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TAPER EXAMPLE (2):ADS SIMULATION
Aproximation to exponential taper using ADS : 10 sections of
MLINTL10
L=L11W=W11Subst="MSub1"
MLINTL9
L=L10W=W10Subst="MSub1"
MLINTL7
L=L8W=W8Subst="MSub1"
MLINTL8
L=L9W=W9Subst="MSub1"
MLINTL6
L=L7W=W7Subst="MSub1"
MSTEPStep4
W2=W5W1=W4Subst="MSub1"
MSTEPStep2
W2=W3W1=W2Subst="MSub1"
MLINTL15
L=L2W=W2Subst="MSub1"
MSTEPStep1
W2=W2W1=W1Subst="MSub1"
MLINTL14
L=L1W=W1Subst="MSub1"
MLINTL19
L=L6W=W6Subst="MSub1"
MLINTL18
L=L5W=W5Subst="MSub1"
TermTerm4
Z=100 OhmNum=4
MSTEPStep9
W2=W11W1=W10Subst="MSub1"
MSTEPStep8
W2=W10W1=W9Subst="MSub1"
MSTEPStep7
W2=W9W1=W8Subst="MSub1"
MSTEPStep6
W2=W8W1=W7Subst="MSub1"
MSTEPStep5
W2=W7W1=W6Subst="MSub1"
MSTEPStep11
W2=W6W1=W5Subst="MSub1"
MLINTL17
L=L4W=W4Subst="MSub1"
MLINTL16
L=L3W=W3Subst="MSub1"
TermTerm3
Z=50 OhmNum=3
MSTEPStep3
W2=W4W1=W3Subst="MSub1"
50 53,59 57,44 61,56 65,97 70,71
75,79 81,22 87,05 93,30 100
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
TAPER EXAMPLE (3):ADS SIMULATION
Aproximation to exponential taper using ADS : 10 sections of
50 53,59 57,44 61,56 65,97
70,71 75,79 81,22 87,05 93,30
100 VARVAR11Ltot=L1+L2+L3+L4+L5+L6+L7+L8+L9+L10
EqnVar
VARVAR23L11=2.290040 mm
EqnVar
VARVAR22W11=207.139000 um
EqnVar
VARVAR6L3=2.219510 mm
EqnVar
VARVAR5W3=615.883000 um
EqnVar
VARVAR4L2=2.211550 mm
EqnVar
VARVAR3W2=688.516000 um
EqnVar
VARVAR1W1=767.037000 um
EqnVar
VARVAR2L1=2.203780 mm
EqnVar
VARVAR8W4=548.755000 um
EqnVar
VARVAR7L4=2.227670 mm
EqnVar
VARVAR10W6=429.647000um
EqnVar
VARVAR9L6=2.244580 mm
EqnVar
VARVAR13W7=377.052000 um
EqnVar
VARVAR12L7=2.253330 mm
EqnVar
VARVAR15W5=486.783000 um
EqnVar
VARVAR14L5=2.236020 mm
EqnVar
VARVAR17W8=328.727000 um
EqnVar
VARVAR16L8=2.262270 mm
EqnVar
VARVAR19W9=284.432000 um
EqnVar
VARVAR18L9=2.271390 mm
EqnVar
VARVAR21W10=243.966000 um
EqnVar
VARVAR20L10=2.280660 mm
EqnVar
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
TAPER EXAMPLE (4):ADS SIMULATION
m3freq=m3=-32.452
9.980GHzm1freq=m1=-22.116
7.170GHz
2 4 6 8 10 12 14 16 180 20
-60
-40
-20
-80
0
freq, GHz
dB(S
(1,1
))
9.880G-32.36
m3
dB(S
(3,3
))
7.170G-22.12
m1
EXPONENTIAL / ADS TAPER
− 10 section approx.− ADS model
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
TAPER EXAMPLE (5):ADS SIMULATION
2 4 6 8 10 12 14 16 180 20
0.1
0.2
0.3
0.0
0.4
freq, GHz
mag
(S(1
,1))
mag
(S(3
,3))
Exponential taper
0,05m
ltaper = @ 10 GHz
− 10 section approximation− ADS model
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
TAPER EXAMPLE (6):ADS SIMULATION
m1freq=m1=-9.824
49.41GHz
m2freq=m2=-65.843
9.980GHz
20 40 60 800 100
-60
-40
-20
-80
0
freq, GHz
dB(S
(1,1
))dB
(S(3
,3))
48.85G-9.995
m1
9.980G-65.84
m2
10 section taper: periodicity in frequency
(li=/2)
(li=/10)
− ADS model − 10 section approximation is periodic.
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
MATCHING NETWORKS
LEVY DESIGN
Lecturers: Lluís Pradell ([email protected])
Francesc Torres ([email protected])
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
MatchingNetwork
(passive lossless)
Z0
fVs
22 21
11
11 1dL d
tavS avS
P PG
P P M
f
Minimize |1 (f)| Maximize Gt(2)
Pd1 PdL
MATCHING NETWORKS
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
CONVENTIONAL CHEBYSHEV FILTER (1)
20
0
0
0 0
1si si pi pi
isi
ipi
L C L C
g ZL
w
gC
w Z
20 0 0
020 0
1,
1,
sisi i
pipi i
wC
L g Z
wZL
C g
' 0
0
2 1 2 1
0 0
20 2 1
1
w
f fw
f
0Z
1SL 1SC
2PL 2PC
3SL 3SC
PNL PNC
1 1 0.N NR g Z
Conversion from Low-Pass to Band-
Pass filter
1g 3g
1 1n ng R 0g
2g ng
LC low-pass filter
Center frequency
Relative bandwidth
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CONVENTIONAL CHEBYSHEV FILTER (2)
( 0)
( 1)
22 2
2
2
1'
1 '
1
1
1
10log 10log 1
MAX Tn
MIN Tn
MAX
MIN
tn n
t
tn
tn
t
GT
G
G
Gr dB
G
1
' 2( )Gt
1'
2( )Gt
2
1
1 n
1
1 0 2
20 1. 2
1
1
cos cos , 1
cosh cosh , 1n
n x xT x
n x x
Pass-band ripple
Chebychev polynomials
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CONVENTIONAL CHEBYSHEV FILTER (3) 0
1
12 2
1
1
2 • sin( ) 12 , sinh( ) ,sinh( )
2 1 2 14 • sin( ) • sin( )
2 2•sin ( )
( 1,2,...., 1)
2 • sin( )2
n
i i
n n
g
ng x ax na
i in ng g
ix
n
i n
ng gx
Fix pass-band ripple and filter order “n”
g0, g1,.., gn+1 are the low-pass LC filter coefficients: 1'1 w
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APPLICATION TO A MATCHING NETWORK
1 1 1
1
1 1
1
' '
''
'
,
,
s s e s e
e ss s e
e s
L L L L L
C CC C C
C C
1
1 1
e1 e
0 0
20
2.sin .R.R 2. . .
1
s
s s
g nLw x w
L C
eR
'1SL '
1SC
2PL2PC
eLeC
PNL PNC
1 1.N N eR g R
TransistorM odel
1 1 ?n s e
rgiven a x g L L
n
Solution (?): increase n (n constant) a, x decrease
or increase n (n constant) a, x decrease
Transistor modeled with a dominant RLC behaviour in the pass-band to be matched
The final design may be out of specifications: n too high (too many sections) or r too large
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LEVY NETWORK (1)
( 0)
( 1) 2
2
1
10log 10log 1
MAX Tn
MIN Tn
MAX
MIN
t n
nt
n
tn
t
G K
KG
Gr dB
G
1
1
cos cos , 1
cosh cosh , 1n
n x xT x
n x x
2
2 2' ( 1)
1 'n
t nn n
KG K
T
' 2( )Gt
1'
2( )Gt
21n
n
K
1 0 2
20 1. 2
21n
n
K
nK
nK
SOLUTION: An additional parameter is introduced: Kn<1
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK (2)
0
1
12 2 2
1
1
2.sin2
2 1 2 14.sin .sin
2 2 , ( 1,2...., 1)sin 2. . .cos
2.sin2
i i
n n
g
ngx y
i in ng g i n
i ix y x y
n n
ng gx y
2
2
sinh ( )
sinh
1
sinh
sinh1 , ( 1)
sinhn n
n
x a
n
y b new freedom degree
nbK K
a
na
0
1
2 2 21
32
1
2.sin4
1 2·
1
2.sin1 4·
g
gx y
gg x y
gg x y
Example: n = 2
2
2
2 22
sinh ( )
sinh
1
sinh 2
sinh 21 , ( 1)
sinh 2
y b new freedom degree
bK
a
a
K
x
a
SOLUTION: Additional design equations
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LEVY NETWORK (3)
1 1 1 1
1 1 1 1
2 20
2 20
1 1
1 1
s s e e s e s ee
s s e e s e s ee
If L C L C take C C L L
If L C L C take L L C C
Design procedurea) Choose Cs1 or Ls1 taking into account the load to be matched
c) Compute x-y from the parameter g1
b) Choose network order (n) and compute g1
1
2.sin2nx y
g
1
1
01 1
e 0 e
. .
. .s
s
L w wg or g
R C R
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK (4)
2 2
cosh cosh
tgh a tgh b
a b
OPTIMAL DESIGN: minimize
2
2
2
1
cosh1 1
1 coshMAX
t
ntMIN
n
G
nbKG
na
0MAX
b
sinh sinha b x y ct
cosh cosh
tgh na tgh nb
a b
22 2 2
2
C Cx
For n=2: 2C x y
Select Ls1 (or Cs1) and n. Compute g1. and x-y. Then determine x, y and Kn, n:
x y b
a nnK
d) Choose x, compute y, max
Example: usual case n=2: Optimum x
The matched bandwith can be increased from ~5% to ~20% with n=2, with moderate Return Loss requirements (~20 dB)
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LEVY NETWORK EXAMPLE (1)
M atch ingN etwork
LeC e
R e R
15,2
0,528,86
0,62
50
e
ee
e
R
L nHf GHz
C pF
R
10
2
5,56,4226
7,5
f GHzf GHz
f GHz
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE (2)
dBRL 75.17min
dBRL 98.23min
0
20
10
21
22 2
2
3
0,62 ( )
10,99
0,8195
2sin( )4 1,7257
21,978 1,434
20,2535 0,2509
0,996 0,015
0,114 0,071
0,4903 2,57 , 0,239
1
S e e
SS
S e
n tMAX
n tMIN
p p
C C pF f f
L nHC
wg
C R
C x yg
C Cx a
y b
K G dB
G dB
g C pF L nH
g
3 3, 2928 19,65eR g R
1
2
0
5,5
7,5
6,4226
20,3114
6,4226
f Ghz
f Ghz
f GHz
w
dBRL 75.17min
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE (3):ADS SIMULATION
5 6 7 84 9
-20
-15
-10
-5
-25
0
freq, GHz
dB
(S(2
,1))
dB
(S(2
,2))
5 6 7 84 9
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
-1.0
0.0
freq, GHz
dB
(S(2
,1))
LEVY NETWORK (LUMPED COMPONENTS)
TFTF1T=1.5951
S_ParamSP1
Step=100 MHzStop=9.0 GHzStart=4 GHz
S-PARAMETERS
LLs
R=L=0.99 nH
TermTerm2
Z=50 OhmNum=2
TermTerm1
Z=15.2 OhmNum=1
CC2C=2.57 pF
LLp
R=L=0.239 nH
CCeC=0.62 pF
A transformer is necessary since g3≠1 (R3≠50 Ω). This transformed must be eliminated from the design
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
Norton Transformer equivalences
STEPS:1) the capacitor C2 is pushed towards the load through the transformer2) The transformer is eliminated using Norton equivalences
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE (4):ADS SIMULATION
5 6 7 84 9
-20
-15
-10
-5
-25
0
freq, GHz
dB
(S(2
,1))
dB
(S(2
,2))
5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.54.5 9.0
-0.8
-0.6
-0.4
-0.2
-0.0
-1.0
0.2
freq, GHz
dB
(S(2
,1))
S_ParamSP1
Step=100 MHzStop=9.0 GHzStart=4 GHz
S-PARAMETERS
LLe
R=L=0.52 nH
LL2
R=L=0.23 nH
CC2C=1.02 pF
LLp
R=L=0.38 nH
LLs
R=L=0.33 nH
TermTerm2
Z=50 OhmNum=2
TermTerm1
Z=15.2 OhmNum=1
CCeC=0.62 pF
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
SMALL SERIES INDUCTANCES AND PARALLEL CAPACITANCES IMPLEMENTED USING SHORT TRANSMISSION LINES
L l
Z0h 0 0 0 00
2 h h
lf L Z l f L Z
C
l
Z0l 0 0 0 00
2 l l
lf C Y l f C Y
L, C elements are then synthesized by means of short transmission lines:
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
SMALL SERIES INDUCTANCES AND PARALLEL CAPACITANCES IMPLEMENTED USING SHORT
TRANSMISSION LINES: EXAMPLE
10
0
10,33 106
50S h
lL nH Z for
22 0
0
10,23 73,85
50h
lL nH Z for
32 0
0
11,02 15,26
10l
lC pF Z for
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE ADS SIMULATION (5):
5 6 7 84 9
-25
-20
-15
-10
-5
-30
0
freq, GHz
dB(S
(1,1
))dB
(S(2
,1))
5.5 6.0 6.5 7.0 7.55.0 8.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
-1.2
0.2
freq, GHz
dB(S
(2,1
))
MSUBMSub3
Rough=0 milTanD=9e-4 T=0.689 milHu=3.9e+34 milCond=5.8e7 Mur=1.0 Er=2.17 H=10.0 mil
MSub
MLINTL8
L=715.898000 umW=178.873000 umSubst="MSub3"
MLSCTL4
L=948.7005301751 umW=262 umSubst="MSub3"
MLINTL10
L=3278.680000 umW=3586.240000 umSubst="MSub3"
TermTerm2
Z=50 OhmNum=2
MLINTL9
L=701.096000 umW=396.160000 umSubst="MSub3"
S_ParamSP1
Step=10 MHzStop=9 GHzStart=4 GHz
S-PARAMETERS
LLe
R=L=0.52 nH
CCeC=0.62 pF
TermTerm1
Z=15.2 OhmNum=1
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE: ADS SIMULATION (6):
5 6 7 84 9
-10
-5
-15
0
freq, GHz
dB
(S(1
,1))
dB
(S(1
,2))
5.5 6.0 6.5 7.0 7.55.0 8.0
-2.0
-1.5
-1.0
-0.5
-2.5
0.0
freq, GHz
dB
(S(2
,1))
MTEETee1
W3=262.0 umW2=0.39616 mmW1=0.178873 mmSubst="MSub3"
MSTEPStep1
W2=3586.24 umW1=396.16 umSubst="MSub3"
MSUBMSub3
Rough=0 milTanD=9e-4 T=0.689 milHu=3.9e+34 milCond=5.8e7 Mur=1.0 Er=2.17 H=10.0 mil
MSub
MLINTL8
L=715.898000 umW=178.873000 umSubst="MSub3"
MLSCTL4
L=948.7005301751 umW=262 umSubst="MSub3"
MLINTL10
L=3278.680000 umW=3586.240000 umSubst="MSub3"
TermTerm2
Z=50 OhmNum=2
MLINTL9
L=701.096000 umW=396.160000 umSubst="MSub3"
S_ParamSP1
Step=10 MHzStop=9 GHzStart=4 GHz
S-PARAMETERS
LLe
R=L=0.52 nH
CCeC=0.62 pF
TermTerm1
Z=15.2 OhmNum=1
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE (7):
ADS SIMULATION: optimization
VARVAR4L4=3213.73 um opt{ 2000 um to 4000 um }
EqnVar
VARVAR3L3=1074.12 um opt{ 500 um to 1400 um }
EqnVar
VARVAR2L2=368.083 um opt{ 300 um to 1200 um }
EqnVar
VARVAR1L1=553.743 um opt{ 300 um to 1200 um }
EqnVar
OptimOptim1
SaveCurrentEF=noUseAllGoals=yes
UseAllOptVars=yesSaveAllIterations=noSaveNominal=yesUpdateDataset=yesSaveOptimVars=noSaveGoals=yesSaveSolns=noSeed= SetBestValues=yesNormalizeGoals=noFinalAnalysis="SP1"StatusLevel=4DesiredError=0.0MaxIters=25OptimType=Random
OPTIM
MLINTL10
L=L4W=3586.240000 umSubst="MSub3"
MLSCTL4
L=L3W=262 umSubst="MSub3"
MLINTL9
L=L2W=396.160000 umSubst="MSub3"
MLINTL8
L=L1W=178.873000 umSubst="MSub3"
GoalOptimGoal2
RangeMax[1]=7.5 GHzRangeMin[1]=5.5 GHzRangeVar[1]="freq"Weight=Max=Min=-0.5SimInstanceName="SP1"Expr="insertion_loss"
GOAL
GoalOptimGoal1
RangeMax[1]=7.5 GHzRangeMin[1]=5.5 GHzRangeVar[1]="freq"Weight=Max=-10Min=SimInstanceName="SP1"Expr="matching"
GOALMeasEqnMeas1
insertion_loss=dB(S(2,1))matching=dB(S(1,1))
EqnMeas
MTEETee1
W3=262.0 umW2=0.39616 mmW1=0.178873 mmSubst="MSub3"
MSTEPStep1
W2=3586.24 umW1=396.16 umSubst="MSub3"
MSUBMSub3
Rough=0 milTanD=9e-4 T=0.689 milHu=3.9e+34 milCond=5.8e7 Mur=1.0 Er=2.17 H=10.0 mil
MSub
TermTerm2
Z=50 OhmNum=2
S_ParamSP1
Step=10 MHzStop=9 GHzStart=4 GHz
S-PARAMETERS
LLe
R=L=0.52 nH
CCeC=0.62 pF
TermTerm1
Z=15.2 OhmNum=1
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE (8):ADS SIMULATION: optimization
5 6 7 84 9
-20
-15
-10
-5
-25
0
freq, GHz
dB
(S(1
,1))
dB
(S(2
,1))
5.0 5.5 6.0 6.5 7.0 7.54.5 8.0
-1.0
-0.5
0.0
0.5
1.0
-1.5
1.5
freq, GHz
dB
(S(2
,1))
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE (9):ADS SIMULATION: optimization
VARVAR2L2=554.494 um opt{ 200 um to 1200 um }
EqnVar
VARVAR4L4=2193.75 um opt{ 2000 um to 4000 um }
EqnVar
VARVAR3L3=1332.32 um opt{ 500 um to 1400 um }
EqnVar
VARVAR1L1=485.326 um opt{ 300 um to 1200 um }
EqnVarGoal
OptimGoal1
RangeMax[1]=7.5 GHzRangeMin[1]=5.5 GHzRangeVar[1]="freq"Weight=Max=-18Min=SimInstanceName="SP1"Expr="matching"
GOAL
GoalOptimGoal2
RangeMax[1]=7.5 GHzRangeMin[1]=5.5 GHzRangeVar[1]="freq"Weight=Max=Min=-0.2SimInstanceName="SP1"Expr="insertion_loss"
GOAL
OptimOptim1
SaveCurrentEF=noUseAllGoals=yes
UseAllOptVars=yesSaveAllIterations=noSaveNominal=yesUpdateDataset=yesSaveOptimVars=noSaveGoals=yesSaveSolns=noSeed= SetBestValues=yesNormalizeGoals=noFinalAnalysis="SP1"StatusLevel=4DesiredError=0.0MaxIters=25OptimType=Random
OPTIM
MLINTL10
L=L4W=3586.240000 umSubst="MSub3"
MLSCTL4
L=L3W=262 umSubst="MSub3"
MLINTL9
L=L2W=396.160000 umSubst="MSub3"
MLINTL8
L=L1W=178.873000 umSubst="MSub3"
MeasEqnMeas1
insertion_loss=dB(S(2,1))matching=dB(S(1,1))
EqnMeas
MTEETee1
W3=262.0 umW2=0.39616 mmW1=0.178873 mmSubst="MSub3"
MSTEPStep1
W2=3586.24 umW1=396.16 umSubst="MSub3"
MSUBMSub3
Rough=0 milTanD=9e-4 T=0.689 milHu=3.9e+34 milCond=5.8e7 Mur=1.0 Er=2.17 H=10.0 mil
MSub
TermTerm2
Z=50 OhmNum=2
S_ParamSP1
Step=10 MHzStop=9 GHzStart=4 GHz
S-PARAMETERS
LLe
R=L=0.52 nH
CCeC=0.62 pF
TermTerm1
Z=15.2 OhmNum=1
Design and Analysis of RF and Microwave SystemsEuropean Master of Researchon Information TechnologyEuropean Master of Researchon Information Technology
LEVY NETWORK EXAMPLE (10):ADS SIMULATION: optimization
5 6 7 84 9
-20
-15
-10
-5
-25
0
freq, GHz
dB(S
(1,1
))dB
(S(2
,1))
dB(le
vy3_
amb_
T_o
ptim
..S(1
,1))
dB(le
vy3_
amb_
T_o
ptim
..S(2
,1))
5.0 5.5 6.0 6.5 7.0 7.5 8.04.5 8.5
-0.8
-0.6
-0.4
-0.2
0.0
-1.0
0.2
freq, GHzdB
(S(2
,1))
dB(le
vy3_
amb_
T_o
ptim
..S(2
,1))