ece 497 js lecture - 13 projectsjsa.ece.illinois.edu/ece497js/lect_13.pdftitle: microsoft powerpoint...

1Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004

ECE 497 JS Lecture - 13Projects

Spring 2004

Jose E. Schutt-AineElectrical & Computer Engineering

University of [email protected]


P1. Write a program that simulates transients on a uniform lossless line.P2. Write a moment method code to calculate the capacitance per unit length of a single microstrip line.P3. Write a program that predicts the TDR response of a device from the measured s parameters.P4. Write an FDTD program to calculate the frequency dependence of a microstrip lineP5. Develop an IBIS model for a CMOS differential amplifierP6. Write a single TL program that will accept IBIS models at its terminationsP7. TBD on power distributionP8. On signaling techniquesP9. Paper survey on related subjects

ECE 497 JS - Projects

All projects should be accompanied with a short paper (3-5 pages) Paper surveys should be about 10-15 pages.


1) Get L and C matrices and calculate LC product

2) Get square root of eigenvalues and eigenvectors of LC matrix → Λm

3) Arrange eigenvectors into the voltage eigenvector matrix E

4) Get square root of eigenvalues and eigenvectors of CL matrix →Λm

5) Arrange eigenvectors into the current eigenvector matrix H

6) Invert matrices E, H, Λm.

7) Calculate the line impedance matrix Zc → Zc = E-1Λm-1EL

P1 - Procedure for Multiconductor Solution


8) Construct source and load impedance matrices Zs(t) and ZL(t)

9) Construct source and load reflection coefficient matrices Γ1(t) and Γ2(t).

10) Construct source and load transmission coefficient matrices T1(t), T2(t)

11) Calculate modal voltage sources g1(t) and g2(t)

12) Calculate modal voltage waves:

a1(t) = T1(t)g1(t) + Γ1(t)a2(t - τm)

a2(t) = T2(t)g2(t) + Γ2(t)a1(t - τm)

b1(t) = a2(t - τm)

b2(t) = a1(t - τm)

P1 - Procedure for Multiconductor Solution


−•

−−

=−

−−

−−

−−

)(

)()(

a

mod

22mod

11mod

mi

mnnei

mei

mei

ta

tata

t

τ

ττ

τ )(

τmi is the delay associated with mode i. τmi = length/velocity of mode i. The modal volage wave vectors a1(t) and a2(t) need to be stored since they contain the history of the system.

13) Calculate total modal voltage vectors:

Vm1(t) = a1(t) + b1(t)Vm2(t) = a2(t) + b2(t)

14) Calculate line voltage vectors:

V1(t) = E-1Vm1(t)V2(t) = E-1Vm2(t)

P1 - Wave-Shifting Solution


ALS04 ALS240Drive Line 1

Drive Line 2

z=0 z=l

Drive Line 3

Sense Line 4

Drive Line 5

Drive Line 6

Drive Line 7

ALS04

ALS04

ALS04

ALS04

ALS04

ALS240

ALS240

ALS240

ALS240

ALS240

P1 – Example: 7-Line Microstrip

Ls = 312 nH/m; Cs = 100 pF/m;

Lm = 85 nH/m; Cm = 12 pF/m.


• J. E. Schutt-Aine and R. Mittra, "Transient analysis of coupled lossy transmission lines with nonlinear terminations," IEEE Trans. Circuit Syst., vol. CAS-36, pp. 959-967, July 1989.

• J. E. Schutt-Aine and D. B. Kuznetsov, "Efficient transient simulation of distributed interconnects," Int. Journ. Computation Math. Electr. Eng. (COMPEL), vol. 13, no. 4, pp. 795-806, Dec. 1994.

• D. B. Kuznetsov and J. E. Schutt-Ainé, "The optimal transient simulation of transmission lines," IEEE Trans. Circuits Syst.-I., vol. cas-43, pp. 110-121, February 1996.

• W. T. Beyene and J. E. Schutt-Ainé, "Efficient Transient Simulation of High-Speed Interconnects Characterized by Sampled Data," IEEE Trans. Comp., Hybrids, Manufacturing Tech. vol. 21, pp. 105-114, February 1998.

P1 - References

http://jsa6.ece.uiuc.edu/ece497js/projects/p1.pdf


Static Analysis

Integral EquationMethods

Green's Function

- Spectral domain- Closed-form

PEECNo retardation

Solvers

- MOM- CGM- Fast Multipole

Output- Charge distribution

Domain Methods

Matrix Solver

- Sparse matrix techniques- Full matrix techniques

Output- Potential distribution

FEM MOL

Maxwell's Equations: (d/dt =0)

Integral Form Differential Form

R, L, G, C

Circuit models

Physical Model

GeometryPEEC: partial element equivalent circuitMOM: method of momentsMOL: method of linesFEM: finite element methodCGM: conjugate gradient method

Acronyms

Static Static

P2 – Static Field Solver Methods


( , ') ( ') 'g r r r drφ σ= ∫

( )potential knownφ =

( , ') ' (known)g r r Green s function=

( ') arg ( )r ch e distribution unknownσ =

Q=CV

Once the charge distribution is known, the total charge Q can be determined. If the potential φ=V, we have

To determine the charge distribution, use the moment method

P2 - Capacitance Calculation


P2 - METHOD OF MOMENTS

Operator equation

L(f) = g

L = integral or differential operator

f = unknown function

g = known function

Expand unknown function f

f = αnfnn∑


Matrix equation

α n L(fn )n∑ = g

α n wm , Lfnn∑ = wm,g

lmn[ ]αn[ ]= gm[ ]

in terms of basis functions fn, with unknown coefficients αn to get

Finally, take the scalar or inner product with testing of weighting functions wm:



lmn[ ]=w1, Lf1 w1, Lf2 ...w2 , Lf1 w2, Lf2 ............. ............. ...

αn[ ]=α1

α2

.

gm[ ]=w1,gw2,g

.

Solution for weight coefficients

αn[ ]= lnm−1[ ] gm[ ]



One-Portb1(ω)

a1(ω)

Scattering parameter of one-port network can be measured over a wide frequency range. Since incident and reflected voltagewaves are related through the measured scattering parameters, the total voltage can be determined as a function of frequency.

P3 - Using Frequency Domain Data forTime-Domain Simulation

Approach


( )( 0, )2

sf

VV x ωω= =

11( )( 0, ) ( )2

sb

VV x Sωω ω= =

[ ]11( )( 0, ) 1 ( ) ( )2

so

VV x S Vωω ω ω= = + =

Unknown andJunction

Discontinuities

Zo

Zo

Reference Line

Vf

x=0

Vb

Vs(ω)

P3 - One-Port S-Parameter Measurements


2( ) ( ) j fts sV v t e dtπω

∞ −

−∞= ∫

[ ] 211( ) ( ) 1 ( ) j ft

o sv t V S e dtπω ω∞ +

−∞= +∫

S11(ω) is measured experimentally. Assume vs(t) to be an arbitrarytime-domain signal (unit step, pulse, impulse). Vs(ω) is its transform

Since the system is linear, its response in the time domain is the superposition of the responses due to all frequencies

P3 - Frequency-to-Time Analysis


• Measure S11(f)

• Calculate Vs(ω) analytically

• Evaluate Vo(ω)= [1+S11(ω)] .

• Feed Vo(ω) into inverse Fourier transform to get vo(t)

P3 - Transformation Steps


• Discretization: (not a continuous spectrum)

• Truncation: frequency range is band limited

F: frequency rangeN: number of points∆f = F/N: frequency step∆t = time step

P3 - Problems and Issues


1. For negative frequencies use conjugate relation V(-ω)= V*(ω)

2. DC value: use lower frequency measurement

3. Rise time is determined by frequency range or bandwidth

4. Time step is determined by frequency range

5. Duration of simulation is determined by frequency step

P3 - Addressing Frequency and Time Limitations


Problems & Limitations(in frequency domain)

Discretization

Truncation in Frequency

No negativefrequency values

No DC value

Consequences(in time domain)

Solution

Time-domain response will repeat itself periodically (Fourier series) Aliasing effects

Take small frequency steps. Minimum sampling rate must be the Nyquist rate

Time-domain response will have finite time resolution (Gibbs effect)

Take maximum frequency as high as possible

Time-domain response will be complex

Define negative-frequency values and use V(-f)=V*(f) which forces v(t) to be real

Offset in time-domain response, ringing in base line

Use measurement at the lowest frequency as the DC value

P3 - Addressing Frequency and Time Limitations


0 1 2 3-0.5

0.0

0.5

1.0

1.5Simulated Step Response

Time (ns)

Ref

lect

ion

Coe

ffic

ient

P3 – Example: Microstrip Line TDR Simulation


P4 - Study of Microstrip Structures By Using FDTD and PML

-The finite difference time domain (FDTD) method discretizesMaxwell’s equations in both space and time using second-order accurate central difference formulas.

- Arbitrary geometries are described on a uniform rectangular mesh, and the electric and magnetic fields are determined at discrete locations within the mesh as a function of the time

- The electric field values are located on the edges of the rectangular FDTD cells, and the magnetic field values are located at the centers of the faces of the cells.

- The dimensions of each cell are ∆x by ∆y by ∆z, and time step is ∆t.


Exn(i, j,k) = Ex

n−1(i, j, k) + 1ε

∆t∆y

⋅ Hzn−1/ 2(i, j,k ) − Hz

n−1/ 2(i, j − 1,k)( )−

1ε

∆t∆z

⋅ Hyn−1/ 2(i, j, k) − Hy

n−1/2(i, j,k − 1)( )

Hxn+1/ 2(i, j,k) = Hx

n−1/ 2(i, j, k) −1µ

∆t∆y

⋅ Ezn(i, j + 1,k) − Ez

n (i, j, k)( )−

1µ

∆t∆z

⋅ Eyn (i, j,k + 1) − Ey

n(i, j, k)( )

P4 - Yee Algorithm


z

x

y

Ey(i,j,k)

Hz

Ez

Ex

Ey

Ey

HyHy

Hx

Hx

Hz

Ez

Ey

Ex

Ex

Ez

Ez

Ex

P4 - 3D Yee Cell


Dynamic Analysis

- FDTD- TLM

Time-Domain Techniques

Full-WaveTechniques

Frequency Domain Time Domain

R(f), L(f), G(f), C(f)

Dynamiccircuit models

Spectral methods

Output

E(t), H(t)

Visualization

- Matlab- Hoops

Output

E(f), H(f)Fourier

Maxwell's Equations: (d/dt ≠ 0)

Physical Model

Geometry

FDTD: finite difference time domainTLM: transmission line method

Acronyms

P4 – Full-Wave Field Solver Methods


PowerClamp

Threshold&

EnableLogic

GNDClamp

GNDClamp

GNDClamp

PowerClamp

PowerClamp

InputPackage

EnablePackage

OutputPackage

PullupRamp

PulldownRamp

PullupV/I

PulldownV/I

P5 – IBIS Diagram


Vcc Vcc

Power_ClampGND_Clamp

GND GND

C_pkgL_pkg

R_pkg

C_omp

PullupPulldownRamp

P5 – IBIS Output Topology


Create an IBIS modelfrom either simulation

or empirical data

Model fromEmpirical data?

No

Yes

Collect Data

Data in IBIStext file

Run IBIS Parser

Parser Pass

Get SPICE I/Oinfo

No

Yes

Run modelon

Simulator

YesModelvalidated?

No Adoptmodel

Run SPICE to IBISTranslator

P4 – IBIS Model Generation


Visit http://www.eigroup.org/ibis/ibis.htm

P4 – IBIS References

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