IMPEDANCE TRANSFORMERS AND TAPERS

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


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


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


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


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


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)


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


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


Binomial multisection matching transformer (ii)


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


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


Chebyshev transformer design


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


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


MSTEPStep3

W2=207.139 umW1=283.802 umSubst="MSub1"

MSTEPStep1

W2=429 umW1=616.935 umSubst="MSub1"

MSTEPStep2


MLINTL2


MLINTL1


MSTEPStep4


MLINTL4


Chebyshev transformer, N = 3, |M|=0.05 (ltotal = 3/4)

87,14 70,71 100 57,37 50


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


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:


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


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


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


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


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’


Rectangular wave-guide to finline to transition

Example of taper: finline wave guide

Finline mixer configuration


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


S-PARAMETERS



Aproximation to exponential taper using ADS : 10 sections of

MLINTL10

L=L11W=W11Subst="MSub1"

MLINTL9


MLINTL7


MLINTL8


MLINTL6


MSTEPStep4

W2=W5W1=W4Subst="MSub1"

MSTEPStep2


MLINTL15


MSTEPStep1


MLINTL14


MLINTL19


MLINTL18


TermTerm4

Z=100 OhmNum=4

MSTEPStep9


MSTEPStep8


MSTEPStep7


MSTEPStep6


MSTEPStep5


MSTEPStep11


MLINTL17


MLINTL16


TermTerm3

Z=50 OhmNum=3

MSTEPStep3


50 53,59 57,44 61,56 65,97 70,71

75,79 81,22 87,05 93,30 100



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


EqnVar

VARVAR3W2=688.516000 um

EqnVar

VARVAR1W1=767.037000 um

EqnVar


EqnVar

VARVAR8W4=548.755000 um

EqnVar


EqnVar

VARVAR10W6=429.647000um

EqnVar


EqnVar

VARVAR13W7=377.052000 um

EqnVar


EqnVar

VARVAR15W5=486.783000 um

EqnVar


EqnVar

VARVAR17W8=328.727000 um

EqnVar


EqnVar

VARVAR19W9=284.432000 um

EqnVar


EqnVar

VARVAR21W10=243.966000 um

EqnVar

VARVAR20L10=2.280660 mm

EqnVar



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



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



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.


MATCHING NETWORKS

LEVY DESIGN

Lecturers: Lluís Pradell ([email protected])

Francesc Torres ([email protected])


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


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


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


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


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


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


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


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


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)


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


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


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


Norton Transformer equivalences

STEPS:1) the capacitor C2 is pushed towards the load through the transformer2) The transformer is eliminated using Norton equivalences


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


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:


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


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


MLSCTL4

L=948.7005301751 umW=262 umSubst="MSub3"

MLINTL10


TermTerm2

Z=50 OhmNum=2

MLINTL9


S_ParamSP1


S-PARAMETERS

LLe

R=L=0.52 nH

CCeC=0.62 pF

TermTerm1

Z=15.2 OhmNum=1


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


MSUBMSub3


MSub

MLINTL8


MLSCTL4

L=948.7005301751 umW=262 umSubst="MSub3"

MLINTL10


TermTerm2

Z=50 OhmNum=2

MLINTL9


S_ParamSP1


S-PARAMETERS

LLe

R=L=0.52 nH

CCeC=0.62 pF

TermTerm1

Z=15.2 OhmNum=1


LEVY NETWORK EXAMPLE (7):

ADS SIMULATION: optimization

VARVAR4L4=3213.73 um opt{ 2000 um to 4000 um }

EqnVar


EqnVar


EqnVar


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


MLINTL8


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


MSTEPStep1


MSUBMSub3


MSub

TermTerm2

Z=50 OhmNum=2

S_ParamSP1


S-PARAMETERS

LLe

R=L=0.52 nH

CCeC=0.62 pF

TermTerm1

Z=15.2 OhmNum=1


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))




EqnVar


EqnVar


EqnVar


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


MLSCTL4

L=L3W=262 umSubst="MSub3"

MLINTL9


MLINTL8


MeasEqnMeas1

insertion_loss=dB(S(2,1))matching=dB(S(1,1))

EqnMeas

MTEETee1


MSTEPStep1


MSUBMSub3


MSub

TermTerm2

Z=50 OhmNum=2

S_ParamSP1


S-PARAMETERS

LLe

R=L=0.52 nH

CCeC=0.62 pF

TermTerm1

Z=15.2 OhmNum=1



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))

Documents

IMPEDANCE TRANSFORMERS AND TAPERS