Software Tools for Microwave Research, Design, and Education Dejan V. Tošić Milka Potrebić School of Electrical Engineering Belgrade.

Software Tools for Microwave Software Tools for Microwave Research, Design, and EducationResearch, Design, and Education

Dejan V. Tošić

Milka PotrebićSchool of Electrical Engineering

Belgrade

OverviewOverview

• Introduction

• Microwave Office

• WIPL-D Microwave

• Ansoft Designer

• Simulation example

• Benefits

• Conclusion

ObjectiveObjective

• Compare software tools for microwave circuit simulation from the research, design, and educational view point

• Identify a candidate tool for each category

• Highlight teaching aspects

Considered Microwave ToolsConsidered Microwave Tools

• AWR Microwave OfficeMicrowave Office – MWO

• WIPL-D MicrowaveWIPL-D Microwave

• Ansoft DesignerAnsoft Designer

Introduction (1)Introduction (1)

• As we move towards a learner-oriented, self-paced, asynchronous system for higher and continuing education, the traditional course-based curriculum structure must be examined for its efficiency

• Courses can be restructured into primary concept modules that are interlinked to reflect the logical development of knowledge in the domain of the discipline being studied

Introduction (2)Introduction (2)

• With the wireless revolution, brought on mostly by cellular radio technologies, microwave applications have come to dominate the industry

• Cost, time to market, and manufacturing capacity are much stronger influences within the microwave engineering

• Cost versus performance will always be a trade-off within any engineering project, however, the weighting coefficients have shifted

Why is it important ?Why is it important ?

Software tools are indispensable in microwave engineering, so R & D, design, and the corresponding courses should always address• computer aided designcomputer aided design

• simulation prior to manufacturingsimulation prior to manufacturing

Who is using Who is using microwave software tools ?microwave software tools ?

• Engineers

• Practitioners

• Researchers

• Academia

AWR Microwave OfficeAWR Microwave Office(MWO)(MWO)

What is MWO? What is MWO? • Popular microwave software

environments in both academia and industry

• Professional design tool• LinearLinear & nonlinearnonlinear solution for

microwave hybrid, module and MMIC design

• Includes linearlinear, harmonic-balanceharmonic-balance, time-domaintime-domain, electromagneticelectromagnetic (EM) simulation, physical layoutphysical layout

• FrequencyFrequency domain simulator

2.5D EM Layered Structures2.5D EM Layered Structures

• EM simulation is based on 2.5D solver2.5D solver for layered structureslayered structures (microstrip filters & antennas) with predefined objects (rectangle, polygon, path, ellipse, drill hole, edge port, via, ...)

• Only automatic mashingautomatic mashing in three levels

1 21 2

Layout viewLayout view

• Layout viewLayout view can be generated from the schematic to take into account mutual coupling, parasitics, discontinuities, …

• Layout structure can be analyzed by 2.5D EM solverMTRACEID=X1W=Wo milL=Lo milBType=2M=0.6

1 2

3

MTEE$ID=TL1

MLINID=TL3W=Connectwidth1 milL=Connectlength1 mil

1 2

3

MTEE$ID=TL4

1 2

3

MTEE$ID=TL7

1 2

3

MTEE$ID=TL10

MSUBEr=9.8H=11.811 milT=1.9685 milRho=1Tand=0ErNom=9.8Name=SUB1

MTRACEID=X2W=Wo milL=Lo milBType=2M=0.6



MLEFID=TL2W=Stubwidth1 milL=Stublength1 mil




PORTP=1Z=50 Ohm

PORTP=2Z=50 Ohm


1 2

3

MTEE$ID=TL1


1 2

3

MTEE$ID=TL4

1 2

3

MTEE$ID=TL7

1 2

3

MTEE$ID=TL10

MSUBEr=9.8H=11.811 milT=1.9685 milRho=1Tand=0ErNom=9.8Name=SUB1








PORTP=1Z=50 Ohm

PORTP=2Z=50 Ohm

OptimizationOptimization

• OptimizerOptimizer for circuit model parameters without possibility to optimize physical structure

• TuningTuning – manual optimization

MSUBEr=9.8H=25 milT=0.1 milRho=1Tand=0.001ErNom=9.8Name=SUB1

MCFILID=TL1W=W0 milS=S0 milL=L0 mil






MSTEPX$ID=MS1Offset=-abs(W@2-W@1)/2 mil





PORTP=1Z=50 Ohm

PORTP=2Z=50 Ohm

L0=Len[21]=120

L1=Len[8]=107

L2=Len[15]=114

W0=Wid[1]=10

W1=Wid[6]=15

W2=Wid[1]=10

Len=stepped(100,120,1)Wid=stepped(10,18,1)Gap=stepped(2,10,.5)

Input Return Loss

Insertion Loss

S0=Gap[4]=3.5

S1=Gap[3]=3

S2=Gap[15]=9

Schematic Results from Schematic(window in window)

Layout view of Schematic(window in window)

6 8 10 12 14Frequency (GHz)

Filter Response

-50

-40

-30

-20

-10

0

Input Return Loss

Insertion Loss

Transmission Line CalculatorTransmission Line Calculator

Filter Synthesis WizardFilter Synthesis Wizard

TLINID=TL1Z0=Z00 OhmEL=90 DegF0=10 GHz





PORTP=1Z=50 Ohm

PORTP=2Z=50 Ohm

Z00=29.3206

Z01=26.3811

Z02=27.7633

2.5 3.5 4.5 5.5 6.5 7.5Frequency (GHz)

Filter Response

-60

-50

-40

-30

-20

-10

0

DB(|S(1,1)|)Filter

DB(|S(2,1)|)Filter

What is WIPL-D Microwave?What is WIPL-D Microwave?

• New design and simulation tool for microwave projects involving microwave circuitscircuits, componentscomponents, and antennasantennas • Full wave 3D EM solver

FeaturesFeatures

• Predefined circuit components & arbitrary composite metallic and dielectric structures defined by user

• Circuit parameters of the included 3D EM components are computed on-the-fly

• Intended for engineers, practitioners, researches, academia, and as a teaching tool for microwave engineering curricula

Defining structures by means of Defining structures by means of (non)uniform grids(non)uniform grids

Advanced modeling conceptsAdvanced modeling conceptsUsing symmetry to facilitate analysis

Modeling of the end effect and feed area for thick wires

Coaxial line excitation

Edging & De-embeddingEdging & De-embeddingModeling of layered structures

De-embedding of circuit parameters from the 3D EM analysis

Taking the edge effectsinto account

Ideal Palette Ideal Palette

short circuited endshort circuited endopen-circuited endopen-circuited endamplifieramplifierideal transformer ideal transformer circulatorcirculatorsymmetric power splittersymmetric power splitterquadrature hybrid couplerquadrature hybrid coupler

short circuited endshort circuited endopen-circuited endopen-circuited endamplifieramplifierideal transformer ideal transformer circulatorcirculatorsymmetric power splittersymmetric power splitterquadrature hybrid couplerquadrature hybrid coupler

Contains all basic components for introductory microwave courses

Technology-related palettesTechnology-related palettes

Rectangular

Transitions

Not available in MWOdouble step & patch antennadouble step & patch antenna

Not available in MWOdouble step & patch antennadouble step & patch antenna

Special componentscoaxial taper, band, step, gap, coaxial taper, band, step, gap,

T-junction & crossT-junction & cross

Special componentscoaxial taper, band, step, gap, coaxial taper, band, step, gap,

T-junction & crossT-junction & cross Special componentsE- and H-post, E- and H-band, E- and H-post, E- and H-band, ET- and HT-junction, ET- and HT-junction, E- and H- coupled waveguides, E- and H- coupled waveguides, rectangular horn antenna & rectangular horn antenna & magic tee junction magic tee junction

Special componentsE- and H-post, E- and H-band, E- and H-post, E- and H-band, ET- and HT-junction, ET- and HT-junction, E- and H- coupled waveguides, E- and H- coupled waveguides, rectangular horn antenna & rectangular horn antenna & magic tee junction magic tee junction

Special componentstransitions from coaxial to rectangular transitions from coaxial to rectangular or microstrip technology or microstrip technology

Special componentstransitions from coaxial to rectangular transitions from coaxial to rectangular or microstrip technology or microstrip technology

Microstrip

Coaxial

Electrical length of portsElectrical length of ports

• Ports of each component can be electrically extended – equivalent transmission lines can be added to ports

• Schematic can contain fewer elements and one can experiment with shifting reference planes which define component ports

3D EM models3D EM models• 3D EM modeling provides predefined objectspredefined objects

dielectric domains, wires, plates,

sphere, circle, reflector, and body of revolution

•transition between two coaxial cables•half-sphere with a hole•ring with circular cross •ring with a square cross sections

• Symbolic parameters of 3D EM models can be optimizedoptimized

Ideal, analytical, and Ideal, analytical, and 3D EM component characterization 3D EM component characterization

• 3D EM analysis enables to explore differences between the results generated by analytical closed-formanalytical closed-form equations and accurate EM numerical simulationsaccurate EM numerical simulations

• 3D EM models can be made when the component parameters are out of the range over which the analytical model is valid

• Multiple componentMultiple component characterization:ideal or analytical or 3D electromagnetic

Analytical (Recommended):

%5

1/,5.3/5.1,10 221

thenlesserrorfor

hwwwr

Versatile input options Versatile input options

PhysicalPhysicaldimensionsdimensions

PhysicalPhysicaldimensionsdimensions

Characteristic Characteristic impedance &impedance &

Normalized lengthNormalized length

Characteristic Characteristic impedance &impedance &

Normalized lengthNormalized length

What is Ansoft Designer ? What is Ansoft Designer ? High-performance RF/mW Design & Analog/RFIC VerificationHigh-performance RF/mW Design & Analog/RFIC VerificationHigh-performance RF/mW Design & Analog/RFIC VerificationHigh-performance RF/mW Design & Analog/RFIC Verification

• Ansoft Designer provides an integrated schematicintegrated schematic and design management front-enddesign management front-end for complex analog, RF and mixed-signal applications • By leveraging advanced electromagnetic-field simulators dynamically linked to powerful circuit and system simulation, Ansoft Designer enables engineers to design, optimizedesign, optimize and validate validate component, circuit, and system performance long before building a prototype in hardware

Features (1)Features (1)

• Digital-communication-systemDigital-communication-system simulation• NonlinearNonlinear circuit simulation, frequency frequency domain,

and transient transient analyses

• Planar 3D EM3D EM simulation • Integrated IC and PCB layout editor with Java and

Visual Basic scripting• Impulse invariance convolution engine• Swept parameter analysis

Features (2)Features (2)

• Support of parameterized subcircuits, global variables, and parameter scoping

• Support of compiled and interpretive user-defined models (UDMs & SDDs)

• Design utilities, including real-time tuning filter and TRL synthesis and load-pull analysis

• Advanced design environment with dynamic project manager and solution caching

• Dynamic link with HFSS, 3D electromagnetic structure simulator

Circuit, Physical Layout, and Circuit, Physical Layout, and Planar EM modelPlanar EM model

Port1Port2

1 23

W1=WportW2=WLL

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

1 23

W1=WLLW2=Wport

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

P=L2W=WLL

P=L4W=WLL

P=3mmW=1.1348mm

P=3mmW=1.1348mm

P=L1W=Wc

P=L3W=Wc

P=L1W=Wc

P=L3W=Wc

P=L2W=WLL

Port1 Port2

Port1 Port2

CircuitCircuit

Physical Layout

Physical Layout

Planar EM model

Planar EM model

Circuit librariesCircuit libraries

http://www.ansoft.com/products/hf/ansoft_designer/designkits.cfmhttp://www.ansoft.com/products/hf/ansoft_designer/designkits.cfmhttp://www.ansoft.com/products/hf/ansoft_designer/designkits.cfmhttp://www.ansoft.com/products/hf/ansoft_designer/designkits.cfmOnlineOnlineOnlineOnline

Example component parametersExample component parameters

Port1Port2

1 23

W1=WportW2=WLL

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

1 23

W1=WLLW2=Wport

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

P=L2W=WLL

P=L4W=WLL

P=3mmW=1.1348mm

P=3mmW=1.1348mm

P=L1W=Wc

P=L3W=Wc

P=L1W=Wc

P=L3W=Wc

P=L2W=WLL

Port1Port2

1 23

W1=WportW2=WLL

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

1 23

W1=WLLW2=Wport

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

P=L2W=WLL

P=L4W=WLL

P=3mmW=1.1348mm

P=3mmW=1.1348mm

P=L1W=Wc

P=L3W=Wc

P=L1W=Wc

P=L3W=Wc

P=L2W=WLLMicrostrip Transmission Line, Physical Length - MSTRLMicrostrip Transmission Line, Physical Length - MSTRL

Planar EM modelPlanar EM model• Full 3D EM simulation• Predefined objects:

circle, rectangle, arc, line, polygon, void, hole, via (2.5D or 3D), cavity, …

• Symbolic parameters of 3D EM models3D EM models can be optimizedoptimized

• Estimate ModuleEstimate Module – Planar EM Calculator Microstrip line Quarter-wave transformer Tuning stub Rectangular patch Circularly polarized (CP) patch

Port1 Port2Port1 Port2

Meshing Meshing

• Fixed meshing with edge meshing

• Adaptive meshing

Port1 Port2

OptimizationOptimization

Optimetrics changesOptimetrics changes the design parameter values the design parameter values

to meet the goal to meet the goal

Optimetrics changesOptimetrics changes the design parameter values the design parameter values

to meet the goal to meet the goal

… … to determine how each to determine how each design variation affectsdesign variation affects

the performance of the design the performance of the design

… … to determine how each to determine how each design variation affectsdesign variation affects

the performance of the design the performance of the design

… … to determine the sensitivity of to determine the sensitivity of the design to small changes the design to small changes

in variables in variables

… … to determine the sensitivity of to determine the sensitivity of the design to small changes the design to small changes

in variables in variables Optimetrics determines Optimetrics determines the distribution of the distribution of

a design's performancea design's performance

Optimetrics determines Optimetrics determines the distribution of the distribution of

a design's performancea design's performance

Filter Design WizardFilter Design Wizard

Transmission Line CalculatorTransmission Line Calculator

Simulation exampleSimulation exampleSimulation exampleSimulation example

Microstrip lowpass filterMicrostrip lowpass filter

SpecificationSpecification

Source/load impedanceSource/load impedance 500Z 500Z

RealizationRealization

CAPID=C1C=3.76 pF

CAPID=C2C=6.674 pF

CAPID=C3C=3.76 pF

INDID=L1L=11.32 nH

INDID=L2L=11.32 nH

CAPID=C4C=6.674 pF

INDID=L3L=12.52 nH

PORTP=1Z=50 Ohm

PORTP=2Z=50 Ohm

CAPID=C1C=3.76 pF

CAPID=C2C=6.674 pF

CAPID=C3C=3.76 pF

INDID=L1L=11.32 nH

INDID=L2L=11.32 nH

CAPID=C4C=6.674 pF

INDID=L3L=12.52 nH

PORTP=1Z=50 Ohm

PORTP=2Z=50 Ohm

Seven-pole lowpass filter with Chebyshev response

ImplementationImplementation

1100Z

mm5CW

mm1.0LW

• Microstrip technology, fabricated on substrate with relative dielectric constantrelative dielectric constant and thicknessthickness without losses

• Open-circuited stubs implementation is chosen with high impedance lines as and a line width

• Open-circuited stub has a line width

1.27,h

CW

LW

1l2l

3l4l

5l6l

7l

mm86.571 ll

mm32.1362 ll

mm54.953 ll

mm09.154 l

,8.10r

Simulation modelsSimulation models

An important issue is to demonstrate

differences between various simulation models AnalyticalAnalytical 2.5D EM2.5D EM (MWO) 3D EM3D EM (WIPL-D Microwave, Ansoft Designer)

Example in MWOExample in MWO

MLINID=TL2W=Wl mmL=13.32 mm


MSUBEr=10.8H=1.27 mmT=0.036 mmRho=3Tand=0ErNom=10.8Name=SUB1

1 2

3

MTEE$ID=TL4

MLEFID=TL1W=Wc mmL=5.86 mm

1 2

3

MTEE$ID=TL5

1 2

3

MTEE$ID=TL6


1 2

3

MTEE$ID=TL9




MLINID=TL8W=1.126 mmL=13.88 mm


PORTP=1Z=50 Ohm

PORTP=2Z=50 Ohm

Wc=5

Wl=0.1



MSUBEr=10.8H=1.27 mmT=0.036 mmRho=3Tand=0ErNom=10.8Name=SUB1

1 2

3

MTEE$ID=TL4


1 2

3

MTEE$ID=TL5

1 2

3

MTEE$ID=TL6


1 2

3

MTEE$ID=TL9






PORTP=1Z=50 Ohm

PORTP=2Z=50 Ohm

Wc=5

Wl=0.1

1 21 2

1 21 2

SchematicSchematic

2.5D model2.5D model

Example in WIPL-D MicrowaveExample in WIPL-D Microwave

3D model 3D model

Schematic Schematic

Example in Ansoft DesignerExample in Ansoft Designer

Port1Port2

1 23

W1=WportW2=WLL

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

1 23

W1=WLLW2=Wport

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

P=L2W=WLL

P=L4W=WLL

P=3mmW=1.1348mm

P=3mmW=1.1348mm

P=L1W=Wc

P=L3W=Wc

P=L1W=Wc

P=L3W=Wc

P=L2W=WLL

Port1Port2

1 23

W1=WportW2=WLL

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

1 23

W1=WLLW2=Wport

W3=Wc

1 23

W1=WLLW2=WLL

W3=Wc

P=L2W=WLL

P=L4W=WLL

P=3mmW=1.1348mm

P=3mmW=1.1348mm

P=L1W=Wc

P=L3W=Wc

P=L1W=Wc

P=L3W=Wc

P=L2W=WLL

Port1 Port2Port1 Port2

3D model 3D model

Schematic Schematic

Simulation results (1)Simulation results (1)

0.1 0.6 1.1 1.6 2.1 2.6 3Frequency (GHz)

Analytical S21dB

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

DB(|S(1,2)|)Analytical _ MWO

DB(|S(1,2)|)Analytical _ WIPL_D

DB(|S(2,1)|)Analytical_Ansoft Designer

WIPL-D WIPL-D MWMW

WIPL-D WIPL-D MWMW

MWOMWOMWOMWO

AnsoftAnsoftDesignerDesigner



0.1 0.6 1.1 1.6 2.1 2.6 3Frequency (GHz)

Full 3D EM S21dB

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

DB(|S(1,2)|)2_5D EM _ MWO

DB(|S(2,1)|)Full 3D EM_Ansoft Designer

DB(|S(2,1)|)Full 3D EM_WIPL_D

WIPL-D WIPL-D MWMW

WIPL-D WIPL-D MWMW

MWOMWOMWOMWO




0.1 0.6 1.1 1.6 2.1 2.6 3Frequency (GHz)

S21dB

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

DB(|S(1,2)|)2_5D EM _ MWO

DB(|S(1,2)|)Analytical _ MWO

DB(|S(1,2)|)Analytical _ WIPL_D

DB(|S(1,2)|)Full 3D EM_WIPL_D circuit

DB(|S(2,1)|)Analytical_Ansoft Designer

DB(|S(2,1)|)Full 3D EM_Ansoft Designer

DB(|S(2,1)|)Full 3D EM_WIPL_D

Amplitude difference measureAmplitude difference measure (of the frequency response)(of the frequency response)

3D3D WIPL-D model & 2.5D2.5D MWO model3D3D WIPL-D model & 2.5D2.5D MWO model

BenefitsBenefits

and potential disadvantages

Benefits (1)Benefits (1)

• WIPL-D Microwave is a candidate tool for implementing efficient microwave education

• From the teaching view point, it has the following benefits Contains all components and microwave circuit models

needed for undergraduate microwave courses Ideal microwave elements are grouped into

a separate toolbar, so the student easily builds idealized microwave circuits


Numerous teaching examples are available and are based on the widely used textbooks adopted in many microwave courses

Comprehensive review of microwave circuit basics is provided, so students can quickly review the scattering matrix properties, element definitions, and other background lessons

Full wave 3D EM analysis is available so the student can compare the results generated by analytical closed-form equations and accurate EM numerical simulations


Multiple component characterization is provided so the student can specify a component as ideal or analytical or 3D electromagnetic

Technology-related components have integrated parameters and technology descriptors

Arbitrary metallic-dielectric structures can be characterized by, for example, scattering parameters and incorporated into the schematic when the components parameters are out of the range over which the analytical model is valid


WIPL-D optimizer can optimize all schematic parameters including the parameters of the embedded 3D EM models

Ports consist of transmission lines with adjustable length that can be set to an arbitrary value, so a schematic can be built with fewer elements

WIPL-D is affordable for students because of its low price

Potential disadvantages Potential disadvantages

Time response can not be computed Nonlinear circuits can

not be simulated Subcircuits are not available Graphical presentation of the

simulation results by default smoothes data (fitting tool) that might lead to unexpected curves (peaks); this might confuse students and cause them to misinterpret the results

BenefitsBenefits

Provides nonlinear microwave circuits and systems Physical layout representation is assigned to

each component in a schematic, but this option does not always give correct layout

Arbitrary 2.5 D EM multi-layer structures can be incorporated into the schematic

MWO can not optimize physical structure, but it has a powerful manual and automatic optimizer for circuit model parameters

Computes the time-domain response Subcircuits can be used in the schematic realization Filter design wizard

Potential disadvantagesPotential disadvantages

Numerous components and their grouping sometimes might be confusing for undergraduate students

Layered EM structures can be modeled but cannot be optimized

Abundant advanced examples may not be suitable for undergraduate teaching process

MWO is not so affordable for students because of its high price


Provides nonlinear microwave circuits and systems Physical layout representation is assigned to

each component in a schematic and it can be automatically exported to planar electromagnetic model

Full wave 3D EM analysis with possibility to incorporate arbitrary 3D EM multi-layer structures into the schematic

Ansoft Designer has a powerful manual and automatic optimizer for circuit and 3D EM model parameters


Multiple component characterization is provided as analytical or 3D electromagnetic

Technology-related components have predefined global substrates

Computes the time-domain response Subcircuits can be used in the schematic realization Calculators:

• EM estimator

• Transmission line calculator

Filter design wizard

Potential disadvantagesPotential disadvantages

• No transition components (release 2004)

• Might be over-sophisticated for students

• Comparatively high prize

LowVery highPriceCos

tC

ost

NoYesYesTime domain reflectometry

Near & FarFarNear/Far field radiation

Not all, such as: G,H, ABCDYesS, Y, Z, G, H, ABCD, V, I, P

Mea

sure

sM

easu

res

NoYesYesFunctional blocks (systems) NoYesYesLayout (implementation) view

YesYesYesCircuit optimization

YesYesYesSymbolic variable

YesOnly idealTransitions

NoYesYesNonlinear components

Cir

cuit

s &

C

ircu

its

&

Sys

tem

sS

yste

ms

Automatic & ManualAutomaticAutomaticEdging

YesYesYesDe-embedding

YesYesYesAutomatic check

YesNoNoSymmetry planes

YesNoOptimizationYesYesNoSymbolic variables

Uniform & Non-uniformUniformUniformUniform/Non-uniform grid (EM model)

Basic & ComplexBasicBasicPredefined object

YesYesYesYesNoFull 3D simulationFull 3D simulation2.

5D &

3D

2.5D

& 3

D

WIPL-DWIPL-DMWOMWOFeatureFeature AnsoftAnsoft

Yes

Near & Far

EM estimator Yes NoNo

Transmission line calculator Yes BasicFilter design wizard Yes Yes, complex

Yes

No

Yes

Very high

Only ideal

Conclusion (1)Conclusion (1)

• We have evaluated and comparedmicrowave software tools

• Two professional tools: Microwave Office (7.0 beta 2006)Microwave Office (7.0 beta 2006) Ansoft designer (release 2004)Ansoft designer (release 2004)

• New software tool: WIPL-D Microwave (December 2005) WIPL-D Microwave (December 2005)

• Research, design, and teaching aspects were considered

Conclusion (2)Conclusion (2)

• WIPL-D Microwave: WIPL-D Microwave: Teaching, Introductory microwave courses

• Ansoft Designer:Ansoft Designer:

The most versatile from all view points• Microwave Office:Microwave Office:

The most convenient user interface, Suitable for research, design, and advanced microwave courses

Software Tools for Microwave Research, Design, and Education Dejan V. Tošić Milka Potrebić School of Electrical Engineering Belgrade.

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