WPR3

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İİİssstttaaannnbbbuuulll,,, TTTuuurrrkkkeeeyyy

Işık University MiMicrowave Techniquescrowave Techniques G Grouproup

Newcom WPR3 Contribution Areas

Design of Front-End Building Blocks •Filters, •Matching Networks, •Amplifiers, •Phase Shifters.

Integration of Microwave Front-Ends.

Power Amplifier Linearization.

Işık University

MiMicrowave Techniquescrowave Techniques G Grouproup

http://www.isikun.edu.tr/~microwave/

Prof. Dr. B. Sıddık Yarman (yarman@isikun.edu.tr)

Prof. Dr. Ahmet Aksen (aksen@isikun.edu.tr)

Dr. Ali Kılınç

Dr. Ebru Gürsu Çimen

Hacı Pınarbaşı

Metin Şengül

Microwave Circuits Education at Işık University•Courses

•Microwave Laboratory

•Research Areas

Microwave CoursesMicrowave Courses

EE 475 Microwave Communications (3 hrs/week + Lab.):Transmission line theory, transmission lines and waveguides, impedance transformation and matching techniques, microwave network analysis and matrix representations, generalized scattering parameters, signal flow graphs, modal analysis, power dividers, introduction to microwave communication systems and microwave propagation.

EE 476 Wireless Communications (3 hrs/week ):Design and analysis of wireless communication systems, with an emphasis on understanding the unique characteristics of these systems. Topics include: cellular planning, mobile radio propagation and path loss, characterization of multipath fading channels, modulation and equalization techniques for mobile radio systems, multiple access alternatives, common air protocols and standards.

EE 536 Microwave Circuit Design for Wireless Communication(3hrs/week)

Radio Transceiver Technology Requirements, RF Component Requirements for Transceivers; Filter, Amplifier, Mixer, Frequency Synthesizer and Dublexer Requirements. RF/Microwave Circuit Implementation Options; Semiconductor Devices and Passive Devices. Design of microwave filters and impedance matching networks; Analytic and semi-analytic approaches; Low-Power Radio Frequency ICs for Broadcast Radio Receivers and Wireless Celular Telephone Trancievers

EE 620 Advanced Microwave Circuit Design (3 hrs/week )Characterization of linear circuits at microwave frequencies: Brune functions, Piloty functions, realizability conditions for lossless networks, scattering description of lossless two-ports. Design of microwave filters, distributed Richards frequency transformation and theorem, Kroda’s identities, microwave filter design, broadband matching: Analytic and semianalytic approaches, mixed lumped-distributed network design.

EE 625 Microwave Amplifier Desing (3 hrs/week )Active circuits at microwave frequencies: Noise parameters, SNR, noise figure, noise temperature measurements, microwave transistor amplifier design gain stability, microwave transistor oscillator design, numerical methods for multistage amplifier design.

This laboratory provides facilities in undergraduate and graduate training and research in the field of microwave engineering and antenna systems and applications. Various passive and active microwave components, basic antenna types and measurement setups operating at microwave frequencies of up to 10 GHz are among the basic facilities offered in this laboratory.

Hardware Facilities Lab-Volt Microwave Training Set (10.5 GHz)HP-Agilent Spectrum Analyzer (9 KHz-1.8 GHz)Lab-Volt Gunn Oscillator (10.5 GHz)RF Cable Assemblies and Connectors (10 MHz to 10 GHz)Waveguide Hardware (2 GHz to 10 GHz)RF Components : (800 MHz to 10 GHz) Amplifiers, Mixers, Detectors, Couplers, Power Dividers,Terminations,Attenuators, Horn Antennas

Software FacilitiesAutoCad, PCB Design Software, MATLAB, Microwave Office, SONNET(EM simulation), RFT: Microwave Circuit Design and Optimization,FILPRO(Filter Design) APLAC RF Design Tool

Microwave Microwave LaboratoryLaboratory

Design of Broadband Matching Networks Design of Microwave Amplifiers Multivariable Network Characterization

(Mixed Lumped-distributed Networks) Data Modelling Design of Broadband Phase Shifters CAD Tools for Broadband Microwave Circuit Design

Real Frequency Technique (RFT) ToolboxesRFT) Toolboxes Modelling Toolbox WWideband MMicrowave CCircuit DDesigner (WMCD) (WMCD)

Integrated Toolbox

Research Research AreasAreas

Design of Broadband Matching Networks

•Broadband Matching ProblemBroadband Matching Problem

•Analytic vs Real Frequency Analytic vs Real Frequency TechniquesTechniques

•Real Frequency Broadband Matching TechniquesReal Frequency Broadband Matching Techniques

Lossless

NZ L

P AZ G

E G

+

P L

Power transmission problem between a complex generator and load

A

L

P

PT )(

Gain-Bandwith Optimization

Broadband Matching ProblemBroadband Matching Problem

Analytic Theory An analytic form of transfer function is chosen,

which should include load network Applicable to simple problems

Real frequency techniques No need to choose circuit topology No need to choose transfer function Well behaved numeric Experimental load data is directly processed

Analytic versus Real Frequency Analytic versus Real Frequency TechniquesTechniques in Broadband in Broadband

MatchingMatching

Line Segment Technique (Carlin, 1977) Parametric Approach (Fettweis, 1979) Simplified Real Frequency Technique (Yarman, 1982) Direct Computational Technique (Yarman & Carlin 1983) RFT for Mixed Lumped-Distributed Circuits (Aksen & Yarman, 1994) ....

Real Frequency Broadband Real Frequency Broadband Matching TechniquesMatching Techniques

01

( ) ( )n

i ii

R R a R

,0

,

,1

)(a

1i

i1i1ii

1i

i

i

i

i

dyy

yb

iii

1

ln)(

1)(

1

R

R()

k-1 k n

Rk

Rn=0

Rk-1

1

( ) ( )n

i ii

X b R

Unknown real part R() is represented as a number of straight-line segments

N R

jXRZ

)()( RX H

Optimize TPG

22 ))()(())()(()()(4

)(

LL

L

XXRRRR

T

Line Segment TechniqueLine Segment Technique

Design Parmeters:Ri

•Based on parametric representation of Brune functions, analytic form of the impedance function is directly generated,

•The direct control of transmission zeros is ensured,

•Computational complexity is reduced,

•The gain function is explicit in terms of free parameters.

Parametric ApproachParametric Approach

N R

)( pZZ is minimum reactive

n

ii

i

pp

BB

pd

pnpZ

10)(

)()(

n

ikk

ikni

ii

i

ppDp

pfpfB

1

222 )(

)()(

nfD

nf

B

n

deg,....1

deg,.......0

2

0

f(p) denotes transmission zeros of N

n

1i ippnDpd )()(

d(p) is strictly Hurwitz

Optimize TPG 22 ))()(())()(()()(4

)(

LL

L

XXRRRR

T

Design Parameters:p0,p1,...pn singularities of the network; Roots of the driving point impedance

Simplified Real Frequency Simplified Real Frequency TechniqueTechnique

N

S 1 S 2S LSG

ZG

Z L

R 2=1R 1=1

1 2

E+

)(/)(11

pgphS )(/)(12

pgpfS

)(/)(21

pgpfS )(/)(22

pgphS

g(p)g(-p) = h(p)h(-p) + f(p)f(-p)

Belevitch Representation of Scattering Parameters:

Losslessness Equation:

Initialize f and h g S(p) parameters

contruct contruct

Optimize TPG 2

)()()()(

2)()2

1)(2

1(

jgGS-jhLσSGSjhjg

jfLSGST

Design Parameters:h0,h1,...hn coefficients of the h(p) polynomial

Direct Computational TechniqueDirect Computational Technique

n

n

o

wDwDDA

wR22

10

2 ...)(

N

S

Z L

1 2

1

Z

2

1

Z 2=R2+jX 2

N

Z in

ZG

ZL

1 2

E+

N

Z in

ZG

ZL

1 2

E+

Initialize Di,A0

Generate Z2(p) via Gewertz Procedure

n

n

n

n

pbpbbpapaa

pDpN

pZ

....

....)()(

)(10

10

2

Optimize TPG2

1

2

1

2

|1|)||1)(||1(

)(SS

SST

G

G

11

G

G

G ZZ

S11

L

L

L ZZ

SD

fH

ZZ

ZZ

H

HS

L

L *

2

*2

*1

Design Parameters:A0,D0,D1,...Dn coefficients of the R2(w)=Re[in(jw)]

Design of Distributed Structures

Design of broadband microwave networks; Filters, Matching Networks and Amplifiers with Transmission Line structures.

Available Real Frequency Design techniques can directly be employed for distributed designs by making use of Richards’ transformation

Planar implementation techniques; Microstrip, Stripline,

coplanar line, suspended substrate in MIC and MMIC

ptanh

Network SynthesisNetwork Synthesis

Na Nb

N

• Darlington Synthesis for Lumped Networks• Richards Synthesis for Distributed Networksor • Generalized Network Synthesis via Transfer Matrix Factorization

Decomposing the lossless reciprocal two-port N into two cascade connected lossless two-port Na and Nb.

T=TaTb

bbb

bbb

bb

aaa

aaa

aa gh

hg

fT

gh

hg

fT

*

*

*

* 1,

1

Mixed Lumped-Distributed Mixed Lumped-Distributed CircuitsCircuits

( ( Multivariable Network Characterization )Multivariable Network Characterization )

Multivariable description and insertion loss synthesis of mixed element structures

Parasitics, discontinuities and device to medium interface modelling

Computer aided design and simulation of MIC layouts

,pZZ

,pSS

jp ptanh :Delay length of unit

elements

Scattering Description Scattering Description iin Two n Two VVariableariabless

, , are real polynomials is a Scattering Hurwitz polynomial is monic, is a unimodular constant

),( pg),( pf ),( pg ),( ph

),( ph

gTppg ),(

hTpph ),(

pnT pppp 21 nT 21

nnnn

n

n

g

pppggg

ggg

ggg

10

11110

00100

nnnn

n

n

h

ppphhh

hhh

hhh

10

11110

00100

and

where , and

Boundary Conditions Transmission Zeros : Lumped Prototype : Distributed Prototype : Connectivity Information

2/20 )1)((),( npfpf

)0,(),0,(),0,( phpgpfS p

),0(),,0(),,0( hgfS

),(),(),(),(),(),( pfpfphphpgpg

g g g h f h h f fkk l

l k ll

k

k kk l

l

k

l k l l k l02

0 0 20

1

02

02

0

1

0 0 2 0 0 22 1 2 1, , , , , , , , ,( ) ( ) ( )

( , ,....., )k n0 1

( ) ( ), , , , , ,

1 12 1 2 1 2 1

0000

i j lj l i j k l

i j lj l i j k l j l i j k l

l

k

j

i

l

k

j

i

g g h h f f

( , ,..., , , ,....., )i n k np 1 3 2 1 0 1 1

i

j

k

llkjiljlkjilj

lkkjikjkjikj

jii

j

k

llkjilj

lkkjikj

ji ffhhffhhgggg0

1

02,,2,,,,,,

0

1

02,,,, )1(2)1())1(2()1(

( , ,..., , , ,....., )i n k np 2 4 2 2 0 1

)()1(2)1(2 2,,2,,

1

0

2,

2,

1

02,,

2, lknlnlknln

k

l

lkknkn

k

llknln

lkkn ppppppppp

ffhhfhggg

( , ,....., )k n0 1

Losslessness ConditionLosslessness Condition

Fundamental Equation Set (FES)

ExampleExample : : Low-Pass Ladder with Unit Low-Pass Ladder with Unit ElementsElements

njnigij 0,0,0 Boundary Conditions

1)0,()0,()0,()0,( phphpgpg

n2 )1(),0(h),0(h),0(g),0(g: Strictly Hurwitz

Connectivity Information

1001100111 hhggg

0 klkl hg

klkl gh

1/ 00 pp nn gh

1 nlk nlk ,....1,0,

1 nlk nlk ,....1,0, 11 nn p

),0(),0,( gpgfor

for

if

Multivariable Characterization of Regular Multivariable Characterization of Regular Mixed Element Two-PortsMixed Element Two-Ports

Explicit design equations

Low-Pass,

Symmetrical,

High-Pass,

Band-Pass

Impedance Description in Impedance Description in Two Two VVariableariabless

( , )( , )( , )

Z pn pd p

0 0( , ) ( ) , ( , ) ( )

n ni i

i ii i

n p N p d p D p

0 0( ) , ( )

p pn nj j

i ji i jij j

D p D p N p N p

C1Z1

Z ( p , λ)

LZ1 1ΩC2

Boundary ConditionsBoundary Conditions/ 22

0( , ) ( )(1 )nf p f p Transmission Zeros:

Lumped Prototype:1 0

1

( ,0)( ,0)

( ,0)

pni

ii

Bn pZ p B

d p p p

Distributed Prototype:1 0

1

(0, )(0, )

(0, )

ni

ii

CnZ C

d

0 020

2 2 2

( 1)( )

0 , deg( ) ( ),

1/ ,deg( )

p

pi ii n

n pi n k i

kk i

f nf p f pB B

D f np D p p

/ 22(0, ) (1 )nf

0( ,0) ( )f p f p

Even Part ConditionEven Part Condition

1 1

1

( , ) ( , ) ( , ) ( , )( , )

2 ( , ) ( , )Z p Z p f p f p

Ev Z pd p d p

0( , ) ( )

ni

ii

f p F p

0( )

pnj

i jij

F p F p

Transmission Zeros:

Even Part constraint: ( , ) ( , ) ( , ) ( , )

2 ( , ) ( , )

n p d p n p d p

f p f p

Frequency (GHz)

1 1.2

1.4

1.6

1.8

2

15

16

17

18

19

20

21

Transducer Power Gain (dB)

MATLABAWR

Design Example:Single Stage Amplifier

CAP

C=

ID=

1.3 pF

C2

IND

L=

ID=

1.814 nH

L1 IND

L=

ID=

3.777 nH

L2 IND

L=

ID=

4.32 nH

L3 IND

L=

ID=

3.246 nH

L4

TLIN

F0=

EL=

Z0=

ID=

15.78 GHz

90 Deg

42.36 Ohm

TL1 TLIN

F0=

EL=

Z0=

ID=

15.78 GHz

90 Deg

49.21 Ohm

TL2 TLIN

F0=

EL=

Z0=

ID=

15.78 GHz

90 Deg

58.28 Ohm

TL3 TLIN

F0=

EL=

Z0=

ID=

15.78 GHz

90 Deg

52.56 Ohm

TL4

1 2

SUBCKT

NET=

ID=

"S_Parameters"

AM012MXQF PORT

Z=

P=

50 Ohm

1

PORT

Z=

P=

50 Ohm

2 CAP

C=

ID=

2.3 pF

C1

Front – End Equalizer

22

2

3 22

2 2

22

2

( , )( , )

( , )

( , ) (0.6148 1.3484 1.4053 1)

(2.7302 3.4821 1.8313) (1.765 1.161)

( , ) (0.6474 1.105 1) (2.2035 2.196)

0.8608

n pZ p

d p

n p p p p

p p p

d p p p p

Back – End Equalizer

22

2

3 21

2 2

21

2

( , )( , )

( , )

( , ) (0.7156 0.8858 1.8967 1)

(3.2864 2.9152 2.2168) (1.482 1.1087)

( , ) (0.6592 0.816 1) (2.319 1.809)

0.9019

n pZ p

d p

n p p p p

p p p

d p p p p

Symmetrical Mixed Element Structures

Symmetrical Mixed-Element Lossless Two-Ports Symmetrical Interconnect Models Symmetrical Two-port Characterization Design Example

Symmetrical Lossless Two-Ports Constructed with Mixed Elements

C 2 Z2 C 1 Z1 C 1Z2 C 2

Typical ApplicationsTypical Applications

•MMicrowave amplifiers icrowave amplifiers andand antenna matching networks antenna matching networks,,

•RF front-end interstage RF front-end interstage interconnectinterconnect modelling modelling of high of high

speed, high frequency analog/digital systemsspeed, high frequency analog/digital systems

Symmetrical Interconnect Models

•AAssuressuress the sharp roll-off on the performance the sharp roll-off on the performance

characteristicscharacteristics,,

•FFacilitate the production of the same value elements acilitate the production of the same value elements

employing the MMIC or VLSI technologyemploying the MMIC or VLSI technology,,

•LLeads to savings in both design and manufacturingeads to savings in both design and manufacturing

efforteffort,,

•RReduce the requirededuce the required execution time and memoryexecution time and memory..

Symmetrical Two-port CharacterizationSymmetrical Two-port Characterization

hh((p,p,)) even or odd polynomial even or odd polynomial

hh((p,p,)) polynomial polynomial::

Generate Generate ΛΛHH, , ΛΛGG in terms of properly selected independent in terms of properly selected independent

coefficient set coefficient set hhijij

Construct Construct hh((p, p, )),, gg((p, p, )) and hence and hence S(S(pp, , ))

,, p22

Sp11

S

,, phph

pn

0i

n

0j

jipijhph ,

jifor0

jiforijhijh

is odd

is even

Design Example:Design Example:Two Stage AmplifierTwo Stage AmplifierScattering Parameters of the 0.3m Low-noise Gate GaAs MESFET NE76000 Biased at VDS = 3 V, IDS = 10 mA

Freq.GHz

s11

m p

s21

m p

s12

m p

s22

m p

2.03.04.05.06.07.08.09.0

10.0

0.99 -270.97 -390.95 -500.92 -610.89 -700.87 -780.86 -870.83 -960.81 -104

3.19 1583.08 1482.95 1382.81 1292.67 1202.55 1132.45 1042.33 972.24 90

0.04 740.06 660.07 590.09 510.09 470.10 410.11 360.11 300.12 29

0.67 -160.66 -230.64 -300.62 -360.60 -420.59 -470.58 -530.57 -580.57 -63

Coefficients of Equalizers

8863.105205.0

03784.10H

8863.19817.15205.0

000.14290.20000.1G

6065.204949.0

08592.10H

6065.22715.24949.0

0000.17307.20000.1G

3766.103765.00

09160.305094.0

2332.006678.20

H

3766.14398.13765.00

4782.14621.54263.35094.0

0268.11765.30584.40000.1

G

Input matching network:

Interstage matching network:

Output matching network:

1 2NEC76000

1 2NEC76000

1 2

Input matchingnetwork

1 2

Interstage matchingnetwork

1 2

Output matchingnetwork

Z= 50 Ohm Z= 50 Ohm

Z0

50 Ohm

Z0

C50 Ohm 50 Ohm 50 Ohm

CC

Z1 Z1Z2

Input InterstageZ0= 95.1842Ω C= 0.33136pF

Z0 = 114.7467 ΩC = 0.31506pF

Z1= 95.6074 ΩZ2= 145.0932 ΩC = 0.16215pF

Output

Transducer Power Gain

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

Frequency GHz

Gain dB

Input Gain

Performance of amplifier

Design of Broadband Microwave Amplifiers

•Broadband Amplifier DesignBroadband Amplifier Design

•Design IssuesDesign Issues

• Front and back equalizer designFront and back equalizer design

•Multistage Amplifier Design

•Power Amplifier design

Broadband Amplifier DesignBroadband Amplifier Design

Design Issues

Gain-Bandwidth Constraints

Performance criteria (Gain, Noise Figure, SWR,

Dynamic Range, Linearity )

Numerical transistor data utilization and modelling

Design of front-end, back-end and interstage equalizers

Power amplifier design

Hybrid/MIC/MMIC Implementation

Front and Back Equalizer Design

N 1 A 1E+

S 221

1

N 1 A 1E+

1

N 2

A 22

^

2

2122

2

21

12

2

2

ˆ1 SA

STT

1122

221221

2222

1

1

1 AS

SAAAA

2

1122

2

211

11 AS

ATT G

2

11

2

21 111 SSTG

Multistage Amplifier Design

N k+11 A k-1 A k

S 221^ A 22k

^

N 1

1

E

+

N 1

S 22k^A 22(k-1)

^

2

1122

2

1122

2

21

2

21

1

1

1

ˆ1ˆ1

kkk

kk

SAAS

SATT kk

2

22

/

ˆ1

1

kA

TT kk

Circuit Data Modelling

Data Modeling TasksData Modeling Tasks

Given a numerical data set which measured over a Given a numerical data set which measured over a frequency band as an impedance, admittance or frequency band as an impedance, admittance or reflectance as real-imaginary or magnitude-phasereflectance as real-imaginary or magnitude-phase

Match a network function which satisfies Positive-Realness Match a network function which satisfies Positive-Realness conditionsconditions

Generate network equivalent constructed with passive Generate network equivalent constructed with passive circuit elements.circuit elements.

ApplicationsApplications

Antenna modelingTo analyze their electrical behavior such as the gain bandwidth limitations or power delivering capabilities

Impedance matchingDesign of high speed/high frequency analog/digital mobile communication sub-systems manufactured on VLSI chips

Passive device modelingSuch as components, connectors, power/signal line’s behavior characterization, simulation

Active deviceInput or output port model for impedance matching, noise figure merits

Approaches

Modeling by Immitance functionsusing Non-Linear optimizationusing interpolation techniques

• Polynomial interpolation• Lagrange interpolation

Zin

Rm Xm

Xf

Real Part Data

Imaginary Part Data

ZM : Minimum Reactance Function

ZF : Foster Function

Approaches

Modeling by Scattering parameters using Non-Linear optimization using iterative solution

Sin 1ΩN

Lossless two-ports

)(/)(11

pgphS

)(/)(12

pgpfS

)(/)(21

pgpfS

)(/)(22

pgphS

Belevitch Representation of Scattering Parameters:

An Antenna modeling example

Freq(MHz)

Real part data()

Imaginary part data ()

20 0.6 -6.0

30 0.8 -2.2

40 0.8 0

45 1.0 1.4

50 2.0 2.8

55 3.4 4.6

60 7.0 7.6

65 15.0 8.8

70 22.4 -5.4

75 11.0 -13.0

80 5.0 -10.8

90 1.6 -6.8

100 1.0 -4.4

Given measured impedance data

Program screen

An Antenna modeling example

--- Result of Modelling --- Real Part Modelling Result = Successful Trial number: 60 Error: 3.8979 Function type: Impedance Interp. method: Lagrange Zeros: Chebyshev roots: 3 12 Samples: 2 9 Minimum reactance functions R_w2_nom =0.000000e+000 0.000000e+000 1.000000e+000 R_w2_den =7.812500e+000 -7.544643e+000 1.865737e+000 Z_s_nom =0.000000e+000 4.964006e+000 5.359813e-001 Z_s_den =2.046303e+000 2.209465e-001 1.000000e+000 Synthesis of Minimum reactance functions C1= +4.12228e-001 L2= +4.96401e+000 R3= +5.35981e-001

Foster Modelling Result = Successful Error: 1.3751 Func. type: FF-1, poles at zero, infinity and finite freq. Samples: 1 8 10 13 pole freq. =6.745369e-001 7.745967e-001 Residues =2.534267e-002 3.561921e-002 1.870885e+000 1.489978e+000 Synthesis of Foster functions L1= +5.56982e-002 C2= +3.94591e+001 L3= +5.93654e-002 C4= +2.80747e+001 L5= +1.87088e+000 C6= +6.71151e-001 End of report.

Report of Program

Future WorksFuture Works

A modeling process can be done for •One-port device•Multi-port device

And modeled devices can be•Passive device •Active device

DoneDoneFuture projectFuture project

DoneDonePartially donePartially done

Design of Broadband Phase Shifters

00oo-360-360oo Wide Range Digital Phase Wide Range Digital Phase ShiftersShifters

Current Projects:CAD Tools for Broadband Microwave Circuit Design

RFT Toolboxes:RFT Toolboxes: Modelling ToolboxWMCD WMCD Integrated Toolbox

RFT Matching Network Design RFT Matching Network Design ToolboxesToolboxes

Toolboxes

• Line Segment Technique

• Direct Computational Technique

• Parametric Technique

• Simplifed Real Frequency Technique

• Mixed Lumped-distributed Design

Modelling ToolboxModelling Toolbox

WMCD WMCD Integrated Toolbox

Broadband matching toolbox: Design and optimization of broadband matching networks and amplifiers via real frequency techniquesLumped Element Design

Distributed Element Design

Mixed Lumped-Distributed Design

Multistage Amplifier Design

Options:

• Line Segment Approach

• Direct Computational Technique

• Parametric Approach

• Simplifed Real Frequency Technique

v1.0

WWIDEBANDIDEBAND

MMICROWAVEICROWAVE

CCIRCUITIRCUIT

DDESIGNERESIGNER

Design Example: Double Matching Problem

Bandwidth: 0 w 1 Complexity of equalizer:

n=3 (Low pass)

NE+

1 1H 2H

1F 1

Z(p) LoadGenerator

18520p61860p65030p

22760p44350p68210pZ

23

2

...

...)(

E

+

11H 2H

1F 1C 1

L2

C 3

1:n

0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

- New parametric

_._ SRFT

Frequency

Gain(dB)

w

Comparision of RFT Results (Normalized values)

Min.Gain

Ripple

n C1 L2 C3

Scattering approach

0.922 0.0768 1.188 1.322 2.475 1.113

Parametric approach

0.923 0.06391.119

11.3526

2.3902

1.1676

Impedance approach

0.924 0.06291.119

81.351

2.3941

1.166

Transducer Power Gain

Design Example: Single Stage Amplifier

Scattering Data for HFET 2001

Frequency

GHz

S11m p

S21 m p

S12m p

S22m p

68

10121416

0.88 -650.83 -850.79 -1010.76 -1130.73 -1260.71 -141

2.00 1251.81 1091.64 951.48 841.39 731.32 61

0.05 600.06 530.06 510.06 520.06 540.07 55

0.71 -220.68 -300.66 -370.66 -430.64 -480.63 -56

1

C 1

L 2

C 3

1 1:n1

C 7

L 4

C 5

L 6

HFET 2001

E

+

1:n 2

0.4 0.5 0.6 0.7 0.8 0.9 13

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

Frequency

front-end

back-end

w

Gain(dB)

C1 = 0.0260

L2 = 0.7516

C3 = 1.4

n1 = 0..6298

n2 = 1.53

C4 = 0.3874

L5 = 1.4105

C6 = 1.307

L7 = 1.6386

9444.57p0466.52p1340.1p

4939.36p5549.43p4075.38)p(Z

23

2

1

8543.0p9461.0p8390.2p3988.0p

5583.0p6049.2p0295.1p5812.2)p(Z

234

23

2

Front-End

Back- End

Normalized element values

Transducer Power Gain

Design Example:Two Stage Amplifier

4 4.5 5 5.5 6 6.5 7 7.5 84

5

6

7

8

9

10

11

12

13

14

15

Frequency(GHz)

TP

G (

dB

)

2nd stage gain1st stage gain

L1=42.3pH, L2=165pH, C3=182pF, C1=170pF, C2=52.8pF, L3=60.2pH, Z1=54.23Ω, Z3=20Ω, C4=170.8pF, Z2=30Ω, Z4=200Ω, Z5=40Ω,

Z6=16.82Ω τ1= τ2= 0.2, τ3= τ4=0.2, τ5= τ6=0.25

Scattering Data for HP 1 μm FET

004797.0

05887.20215.0

9181.23663.01706.1

9890.05352.10

H

004797.0

05887.26803.0

9181.26279.26526.1

4065.16776.21

G

01384.02299.0

5375.07650.05099.0

6233.04481.00

H

01384.02299.0

5375.05828.18484.0

1783.11348.21

G

01308.12796.0

0368.70495.14506.0

0087.58473.00

H

01308.12796.0

0368.77581.28731.0

1076.55963.31

G

Front-End Interstage Back-End

Coefficients of Mixed Element Equalizer

Transducer Power Gain

Selected PublicationsSelected Publications Yarman B.S., “Broadband Network”, Wiley Encyclopedia of Electrical and

Electronics Engineering John G.Webster, Editor, Vol 2, pp.589-605, 1999, John Wiley&Sons corp.

A. Aksen, H. Pınarbası,B. S. Yarman ”A Parametric Approach to Construct Two-Variable Positive Real Impedance Functions for the Real Frequency Design of Mixed Lumped-Distributed Matching Networks IEEE MTT- 2004, pp. 1851-1854, 6-11 June 2004

A.Aksen, B.S.Yarman, “A Real Frequency Approach to Describe Lossless Two-Ports Formed with Mixed Lumped and Distributed Elements” ” (Dedicated to Professor Alfred Fettweis on the occasion of his 75 th birthday), Int.J.Electron.Commun.(AEÜ) 55 (2001) No.6, pp.389-396

B.S.Yarman, A.Aksen, A.Kılınç, “An Immitance Based Tool for Modelling Passive One-Port Devices by Means of Darlington Equivalents” (Dedicated to Professor Alfred Fettweis on the occasion of his 75 th birthday), Int.J.Electron.Commun.(AEÜ) 55 (2001) No.6, pp.443-451

A.Aksen, B.S.Yarman, “Cascade synthesis of two-wariable lossless two-port networks with lumped elements and transmission lines”, in Multidimensional Signals, Circuits and Systems, Editors: K.Galkowski and J.Wood, Chapter 12, pp.219-232, Taylor and Francis, New York, 2001

B.S.Yarman, E. G. Çimen, A. Aksen, “Description of symmetrical lossless two-ports in two-kinds of elements for the design of microwave communication systems in MMIC realization”, ECCTD2001 (European Conference on Circuit Theory and Design), Espoo, Finland, 28-31 August, 2001