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Simulation and Modeling ofLarge Microwave and

Millimeter-Wave Systems,

Part 1Michael Steer

with

Nikhil Kriplani, Carlos Christofferson

and Shivam Priyadarshi

1

Copyright 2009 to 2011 by M. Steer, N. Kriplani and S. Priyadarshi

Not to be posted on the web or distributed electronically without permission.

http://www.freeda.org

http://www.freeda.org/http://www.freeda.org/

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fREEDA

3

Open Source / Open

LicensingBSD License (Open to

companies to do what they

want), well almost there.

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Essential Concepts for

Multi-Physics Modeling

Integration of multi physics problem into the circuitmodeling domain

Object Oriented Approach

Global Modeling EM Interconnect Modeling Digital Macromodeling Opto Electronic Modeling Quantum Modeling Molecular Modeling

Materials Modeling Bio / Chemical Modeling

Interfaces

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Universal Error Concept (Energy Norm)

Universal error concept:AT A TERMINAL

FLUX = 0

All Potent ials are the SAME

MECHANICAL

THERMAL

ELECTRICAL

FORCE

HEAT

CURRENT

I

Flow

POSITION

TEMPERATURE

V

Effort

INERTIAL REFERENCE FRAME

ABSOLUTE ZERO

LOCAL GROUND

LOCAL REFERENCE NODE

For each state variable xthere must be a flow and an effort

contribution.

i(t) v(t)

5

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Many Unique Models

EM Interface (TD and FD) Electro-Thermal

Dynamic Range

Time Delay

Large Signal Noise

Electro-Optic

Molecular Diode

n+ poly

STI STI

tox

Vg

oxide

L

p type

Jg (tunneling)

V_ref

MOSCAPWorlds first implementation

E.G. The tunnel process cannot be expressed as a

current-charge-voltage expression as Spice

requires. Instead use state variables to implement

tunneling correctly. 6

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Circuit Theory

7

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Background Reading

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Background Reading

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Microstrip Model In a Field Simulator Voltages Are Determined By

Integrating The Electric Field Along a Path

In Microstrip Problems the Field is Integrated OverThe Paths Shown to Obtain V

The Path of Integration Matters

The Dashed Path Yields a Different Value of V2

V1

V2

Not the same

point electrically.

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Microstrip Model

Network Model:11 12

21 22

S S

S S

V1 V2

REFREF

REF REF

V2V1

But a (SPICE) Circuit

does not have two

reference terminals.

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Global Reference Node

Perfect Ground Plane Assumed (No Retardation Effects)

In A Field Simulator Voltages Are Determined ByIntegrating The Electric Field Along a Path

In Microstrip Problems the Field is IntegratedOver The Paths Shown to Obtain

The Path of Integration Matters The Dashed Path Yields a Totally Different

Value

of

12

Conventional Microwave Circuits(e.g. Microstrip)

V1

V2

V and1 V2

V2

Current Microwave

Simulators (Linear, Harmonic

Balance, Transient) are

Based on Nodal VoltageDescriptions

To Use Nodal Voltages There

Must Be a Common

Reference Node

Field Simulators Currently

Require A Common

Reference Ground

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Local reference node concept This avoids non-physical connections and therefore is

fundamental for the analysis of spatially distributed

circuits as well as for simultaneous thermal-electricalsimulations.

V1 V2REFREF

LOCAL REFERENCE

TERMINAL

How to extend this beyond two terminal ports?

Our common view of

a port is that it has

two terminals

i1

i1

i2

i2

1 2

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Non- fREEDA fREEDA

Circuit

Circuit

14

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Circuit vs. Network Graph

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Circuit Graph

Network Graph

Concept of Spice

CIRCUIT GRAPH

NETWORK GRAPH

Concept of fREEDA

Must use two circuit graphs to

represent a general circuit

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Network Graph

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A

N

U

TS

R

Q

P

O

F

L

G

H

IB

C

J

D

KE

A node

a edgea

b

Information is stored in fREEDA as a Network Graph but the

difference between a terminal and an element is retained.

c

d

e

f

A

B

C

D

E

F

G

H

I

J

L

M

K

N

O

P

Q

R

S

T

U

ab

c

d

ef

hg

g

h

NETWORK GRAPH

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Modeling Concept

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SPATIALLY

DISTRIBUTED

CIRCUIT

LINEAR

CIRCUITNONLINEAR

NETWORK

THERMAL

NETWORK

LINEAR NETWORK

Nonlinear Analysis Must be Point of Integration

UseSPICE-like & HARMONIC BALANCE analyses

Use Existing Domain Specific Analyses

E.G. Thermal, Field

Behavioral Modeling Is the Key to Using Results of

One Simulator In Another

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Modeling Scope

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Can handle

11

2 32 31 12 2 3 3

1 1 1

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

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

( ), , ( )

nn

n n

n

dx tdx tx t x t

dt dt

d x t d x t d x t d x t y t F

dt dt dt dt x t x t

=

Where y(t) is either an i(t) or a v(t).

Also in any type of analysis we want dy/dx The exact derivatives (w.r.t. t imeor frequency etc.) we want depend on the type of analysis we are doing

(transient, wavelet, harmonic balance). The derivatives needed are calculated

using ADOL-C under control of the analysis rout ines. This is why the same

model can be used in any type of analysis.

ADOL-C is one of the many support libraries.

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fREEDAUnique Feature:

Nonlinear devices models based onstate variables:

This provides great flexibility forthe design of new models. All ofthe analyses are state-variable-based, including a time marchinganalysis (different integration

methods available) and a uniquewavelet transient analysis.

The state variables can be chosento achieve robust numericalcharacteristics.

The calculation of derivatives arefree of truncation errors at a small

multiple of the run time requiredto evaluate the original functionwith little additional memoryrequired. (ADOLC)

CONVENTIONAL DIODE MODEL

STRONG NONLINEARITY

v

i

v

x

x

NEW

NEW

MODERATE NONLINEARITY

+

ix

v

=

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Bottom

DBR

TopDBRp-contact

Oxide

Light

Output

Active

Regionn-contact

VCSEL Modeling

Single Mode Rate Equations

Carrier density

dN(t)/dt =i(I(t)-IL(T))/ N(t)/nr G(T)(N(t)-N0(T))S(t)/(1+S(t))

Photon densitydS(t)/dt = -S(t)/p+ N(t)/r+ G(T)(N(t)-N0(T))S(t)/(1+S(t))

Temperature

dT(t)/dt = -T(t)/th+ (T0+(I(t)V(t)-P0(t))Rth)/th

Leakage Current

IL = IL0exp[(-a0+ a1N0 + a2N0T- a3/N0)/T]

Temperature dependence of Gain and Transparency

G(T) = G0(ag0+ ag1T +ag2T2) / (bg0+ bg1T +bg2T

2)

N0(T) = Nt0(cn0+cn1T+cn2T2)

Transim Power vs Current

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Current(amps)

Power(watts)

Power@298K

Power@323K

Power@338K

Leakage @298K

Leakage(mA)

0

10

20

30

Transient Optical Output

Power

Time(10ns)

drive current

Time(ns)

Wavelength Chirp

DC Optical Power versus Drive Current

Rollover from leakage

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Power and Wavelength degradation due to two components

Electro-Optics

Optical PowerWavelength

z=12m z=12m

m

f1=12mm, R=0.04 f2=12mm, R=0.04

Detector

Lens2Lens

1

Vcsel

No feedback

L1 feedback

L1+L2 feedback

No feedback

L1 feedback

L1+L2 feedback

Output power

degradation due

to single and

double lens feedback

Output wavelength

degradation due

to single and

double lens feedback

With:

Mark Niefeld

Ravi Pant

Univ. of Arizona

Feedback Results:

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Time Delays

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Spice handles only short (< 4 time step) time delays.

TWTA used to validated fREEDAs

ability to handle models with long

time delays. Also implemented in

many transistor models.

100

101

102

103

104

100

101

102

103

104

Specified delay (ns)

Observeddelay(ns)

0 2000 4000 6000 8000 10000 12000 14000

-1

-0.5

0

0.5

1

Time (ps)

InputTerminalVoltage(volts)

0 2000 4000 6000 8000 10000 12000 14000-3

-2

-1

0

1

2

3

Time (ps)

OutputTerminalVoltage(volts)

fREEDA has no limit

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Choice of Time Step to keep error below a set tolerance.

Conventional

approachResult obtained

with linear

extrapolation

Result from

nonlinear

iteration

(Trapezoidal /

Backward

Euler)

Tn+1TnTn-1

Error

estimate

Poor estimate of error leads to

inappropriate choice of time step

ConventionalTime Stepping Algorithm

IDEAL

RESULT

The difference between

the nonlinear iteration and

the straight line extrapolation is

taken as an estimate of error.

If the error is too large the

time step is reduced bya factor of 2.

If the error is very low the

time step is increased by

A factor of 2.

This results in excessively

short time steps around curves

and limits dynamic range.

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fREEDA Time Stepping Algorithm

New

approach

Error

estimate

Tn+1TnTn-1

Better estimate of error leads to

a better choice of time step

Result from

Backward Euler

Result from trapezoidalIDEAL

RESULT

The difference between

the Backward Euler and

trapezoidal estimates is

an incredibly good estimate

of error. If the error is too

large the time step isreduced by a factor of 2.

If the error is very low the

time step is increased by

A factor of 2.

The half way point is

taken as the answer.

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0

Tolerance

0.002 0.004 0.006 0.008 0.01

Error

0.01

0.02

0

0.03

0.04

0.05

CONVENTIONAL

NEW

High Dynamic Range

Through Error Control

The new approachis a better

estimate of error.

Better time point

selection.

160 dBc

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fREEDA, Transient Simulation

and Frequency-DomainModeling

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Three Milestones for Interfacing EM and

Circuits

D. Winkelstein, M. B. Steer, and R. Pomerleau, Simulation of arbitrary transmiss ion line networks w ith nonlinear

terminations, IEEE Trans. on Circui ts and Systems, April 1991, pp.418-422. See also, IEEE Trans. on Circui ts and

Systems, Vol. 38, Oct. 1991.

Impulse response and convolut ion

Time and f requency bounded

C. S. Saunders, J. Hu, C. E. Christoffersen, and M. B. Steer, Inverse singu lar value method for enforc ing passivi ty

in reduced-order models of distribu ted structures for transient and steady-state simulation, IEEE Trans.

Microwave Theory and Techniques, April 2011, pp. 837847.

S parameters to Foster Model

Passivity, causality

C. S. Saunders and M. B. Steer, Passivity enforcement for admittance models of distributed networks using an

inverse eigenvalue method, IEEE Transactions on Microwave Theory and Techniques, In Press.

y parameters to Foster Model

Passivity, causality What is needed for ci rcuit s imualtpors which are y parameter based

ALL CONVERTERS NEED SOME HUERITIC KNOWLEDGE

Did the user provide sufficient data

If not how to extrapolate

What i s the basic response (what to emphasize)

Low pass, Bandpass

29

http://wolftech.ad.ncsu.edu/ece/centers/muri_mbs/mbs%20CV/Publications/vitae_papers/X2010/saunders_hu_singular_2010.pdfhttp://wolftech.ad.ncsu.edu/ece/centers/muri_mbs/mbs%20CV/Publications/vitae_papers/X2010/saunders_hu_singular_2010.pdf

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SINCGARS

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Output Waveforms

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Summary

Most robust circuit simulator technology

Interfaces with TD and FD EM solvers.

Will be supported commercially.

fREEDA papers athttp://people.engr.ncsu.edu/mbs/Publications/mbs_publications.html

35

http://people.engr.ncsu.edu/mbs/Publications/mbs_publications.htmlhttp://people.engr.ncsu.edu/mbs/Publications/mbs_publications.html