ece 497 js lecture - 14 projects: fdtd & lvdsjsa.ece.illinois.edu/ece497js/lect_14.pdf ·...

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

ECE 497 JS Lecture - 14Projects: FDTD & LVDS

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. LVDS versus single-ended designP9. 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.


o Model signal coupling and distortion in high speed circuit

o Predict propagation characteristics beyond TEM

o Extract frequency dependence of circuit parameters

o Full wave simulation is necessary

MOTIVATION


FullFull--Wave MethodsWave Methods

∇×

r E = − ∂

r B ∂t

∇×

r H =

r J + ∂

r D ∂t

∇⋅r B = 0

∇⋅r D = ρv

FDTD: Discretize equations and solve with appropriate boundary conditions


Finite Difference Time Domain

Ey

Ey

Ey

Ey

HyHy

Ex Ex

ExEx

Hx

Hx

Ez

Ez

Ez

Hz

Hz

x

y

zYee AlgorithmExn(i, j,k )= Ex

n−1+cε∆t∆y

Hzn−1/ 2 (i, j, k) − Hz

n −1/2(i, j − 1,k)( )−c

ε∆t

∆zHyn−1/ 2 (i, j, k )− Hy

n−1/ 2(i, j,k −1)( )

Hxn+1/ 2(i, j,k )= Hxn−1/ 2 −cµ∆t∆y

Ezn (i, j + 1,k)− Ezn(i, j,k )( )+cµ∆t∆z

Eyn(i, j,k +1) − Eyn(i, j,k)( )


2D-FDTD

Ex

Ey

Hz

x

y

Exn i + 1

2, j

= Ex

n−1 i + 12

, j

+

∆tε o∆y

Hzn−1/2 i + 1

2, j+ 1

2

−Hz

n−1/2 i+ 12

, j− 12

Eyn i, j+ 1

2

= Ey

n−1 i, j+ 12

−

∆tεo∆x

Hzn−1/2 i+ 1

2, j+ 1

2

− Hz

n−1/2 i − 12

, j+ 12

Hzn+1/2 i+ 1

2, j+ 1

2

= Hz

n−1/2 i + 12

, j + 12

+

∆tµo∆y

Exn i + 1

2, j+1

− Ex

n i + 12

, j

- ∆tµo∆x

Eyn i +1, j+ 1

2

− Ex

n i, j + 12


2D-PML Formulation

x

y

Simulation Medium PML Medium

No reflection from PML interface

εo∂Ex∂t

=∂Hz∂y

εo∂Ey

∂t= −

∂Hz∂x

µo∂Hz∂t

=∂Ex∂y

−∂Ey

∂x

εo∂Ex∂t

+ σEx =∂Hz∂y

εo∂Ey

∂t+ σEy = −

∂Hz∂x

µo∂Hz∂t

+σ* Hz =∂Ex∂y

−∂Ey

∂x

σεo

=σ*µo


o artificial lossy medium

o reflectionless absorption of EM waves

o independent of frequency or angle of incidence

o characterized by electrical conductivity and magneticconductivity

The above relation ensures that the wave impedance of thePML medium is matched to that of the adjacent physical medium

PML-FDTD Formulation

σε =

σ∗µ

Perfectly Matched Layer (PML)


o Modified Maxwell’s equations:

and

where and

o The above equations contain twelve scalar equations with twelve split field unknowns.

For example,


i= x,y,z

E = Esx +Esy +Esz H = Hsx +Hsy +Hsz

µ∂Hsxz∂t +σ x

∗Hsxz =−∂Ey∂x

ε∂Esi∂t +σiEsi =

∂∂i i ×H

µ∂Hsxz∂t +σ x

∗Hsxz =−∂Ey∂x


The FDTD implementation of these scalar equations on aYee grid is straightforward.

where


Hsxzn i, j,k

=αmHsxz

n−1 i, j,k

− βm

Eyn−1 i +1, j,k

− Ey

n−1 i, j,k

∆x

αm =µ∆t −

σ x∗2

/ µ

∆t +σ x∗2

βm =µ∆t +

σ x∗2

−1


CIRCUIT MODEL

o EM fields are simulated by the FDTD, where the PML is used as ABC

o The fields at sample positions are recorded

o The current and voltage on the line are caculated by the followingintegrations

o After FFT, get the voltage and current matrices ,

o Calculate the circuit parameters ,

V(z,ω)[ ]L(ω) C(ω)

I(z,ω)[ ]

i(z,t) = H •dlc∫

v(z,t) = E∫ •dl


CIRCUIT MODEL

Quasi-TEM mode of propagation in MTL’s consisting of M lossless lines

, are the × per unit length inductance and capacitanceparameter matrices, respectively.

, are the line voltage and current vectors.The circuit parameter matrices can be caculated by

, are the line voltage and current vector matrices(M excitations)

L(ω) C(ω) M M

V(z,ω) I(z,ω)

V(z,ω)[ ] I(z,ω)[ ]

− ddzV(z,ω)= jωL(ω)I(z,ω)

− ddzI(z,ω)= jωC(ω)V(z,ω)

L(ω) = − 1jω ( ddz V(z,ω)[ ]I(z,ω)[ ]−1)

C(ω)= − 1jω ( ddz I(z,ω)[ ]V(z,ω)[ ]−1)


Numerical Results

Verification of the FDTD-PML code

o The conductivities in PML are chosen with parabolic profiles

o The fields are excited with a single frequency source (18 GHz)

-1

-0 .5

0

0 .5

1

2 1 0 3 4 1 0 3 6 1 0 3

Nor

mal

ized

cur

rent

s

Time steps


Numerical Results

Coupled lossless transmission lines

h

w s

t

y

z

Parameters: w=s=0.3 mm, t=0.05 mm and h=0.25 mm


.

Coupled Lines

h

w s w

Parameters: w=0.3mm, h=0.25mm. Dielectric constant is 4.5.

0 .1 0 2

0 .1 0 3

0 .1 0 4

0 .1 0 5

0 .1 0 6

0 .1 0 7

0 5 1 0 1 5 2 0 2 5

s / h=0 .8

s / h=1 .0

s / h=1 .2

Frequency (GHz)

-0 .0 1 7

-0 .0 1 6

-0 .0 1 5

-0 .0 1 4

-0 .0 1 3

-0 .0 1 2

-0 .0 1 1

-0 .0 1

0 5 1 0 1 5 2 0 2 5

s / h=0 .8

s / h=1 .

s / h=1 .2

Frequency (GHz)

3 3 5

3 4 0

3 4 5

3 5 0

3 5 5

3 6 0

0 5 1 0 1 5 2 0 2 5

s / h=0 .8

s / h=1 .0

s / h=1 .2

Frequency (GHz)6 5

7 0

7 5

8 0

8 5

9 0

9 5

1 0 0

1 0 5

0 5 1 0 1 5 2 0 2 5

s / h=0 .8

s / h=1 .0

s / h=1 .2

Fr equency( GHz)

C12

(nF/

m)

C11

(nF/

m)

L 12(n

H/m

)

L 11(n

H/m

)


.

EMI Simulations

W

h

4

3

21

w=1.2mm, h=1mm , εr = 4.5

- 1 1 0

- 1 0 0

- 9 0

- 8 0

- 7 0

- 6 0

0 2 4 6 8 1 0

1

32

4

Frequency (GHz)

- 9 0

- 8 0

- 7 0

- 6 0

- 5 0

- 4 0

0 1 0 2 0 3 0 4 0 5 0

1

32

4

Frequency (GHz)

Prop

agat

ing

signa

l (dB

)

Prop

agat

ing

signa

l (dB

)


2D-FDTD for Interconnects

* Take advantage of single mode propagation

* Reduce computational domain

* Formulate FDTD problem in transverse direction

Use βz as input and obtain transverse field profiles fordifferent values of βz

MOTIVATION

STRATEGYE(x,y,z)H(x,y,z)

→

E(x, y)H(x, y)

e− jβzz

∂∂z

→ jβz


.

3 5 0

4 0 0

4 5 0

5 0 0

5 5 0

6 0 0

0 5 1 0 1 5 2 0 2 5

L

2 D-FDTD

3 D-FDTD

Frequency (GHz)

2D-FDTDW

h

Parameters: w=h=1mm. The effective dielectric constant is 9.8.

0 .1 6

0 .1 6 5

0 .1 7

0 .1 7 5

0 .1 8

0 .1 8 5

0 .1 9

0 5 1 0 1 5 2 0 2 5

C

2 D-FDTD3 D-FDTD

Frequency (GHz)

Cap

acita

nce

(nF/

m)

Indu

ctan

ce (n

H/m

)


o FDTD-PML provides an accurate method for theextraction of interconnect characteristics.

o Radiation effects can be simulated accurately usingFDTD-PML.

o 2D-FDTD is an efficient method for extractingthe frequency dependence of interconnects.

o Implementation of absorbing boundary conditionis critical to the accuracy of the method.

FDTD/PML Summary


[1] K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media ,” IEEE trans. Antennas Propagat. , vol 14, pp. 302-307, May 1966.

[2] J. P. Berenger, " A perfectly matched layer for the absorption of electromagnetic waves", J. Computational Physics, vol 144, pp. 185-200, Oct. 1994

[3] R. Mittra, W. D. Becker, and P. H. Harms, " A general purpose Maxwell solver for the extraction of equivalent circuits of electric package component for circuit simulation." IEEE Trans. Circuits Syst. I, vol.39, pp964-973, Nov. 1992.

[4] T. Dhaene, S. Criel, and D. D. Zutter, " Analysis and modeling of coupled dispersiveinterconnection lines," IEEE Trans. MTT., vol40, pp2103-2105, Nov.1992.

[5] J. Zhao and Z. F. Li, " A time-domain full-wave extraction method of frequency-dependent equivalent circuit parameters of multiconductor interconnection lines", IEEE Trans. MTT, vol 45, pp23-31, Jan. 1997

[6] T. Daehne and D. De Zutter, " CAD-oriented general circuit description of uniform coupledlossy dispersive waveguide structures, " IEEE Trans. MTT., vol. 40, pp1545-1559, July 1992.

References


Low-Voltage Differential Signaling (LVDS)

Definition: Method to communicate data using a very low voltage swing (about 350mV) differentially over two PCB traces or a balanced cable

- Bandwidth - Low Power- Low Noise

Solution exists for very short and very long distances; however for board-to-board or box-to-box, this is a challenge

Criteria for high-performance communication


Why LVDS?

1. Differential transmission is less susceptible to common mode noise

2. Consequently they can use lower voltage swings

3. In PC board (microstrip) odd-mode propagation is faster


1. Low output voltage swing

2. Slow edge rates

3. Odd-mode operation (magnetic fields cancel)

4. Soft output corner transitions

LVDS Attributes for EMI


LVDS Driver and Receiver

- Majority of current flows across 100-ohm resistor- Switching changes the direction of current - Logic state determined by current direction


RS-422 PECL LVDS Differential Driver Output Voltage ±2 to ±5V ±600-1000 mV ±250-450 mV Receiver Input Threshold ±200 mV ±200-300mV ±100 mV Data Rate <30Mbps >400Mbps >400Mbps Supply Current Quad Driver (no load, static) 60 mA (max) 32-65mA (max) 8.0mA Supply Current Quad Receiver (no load, static) 23mA (max) 40mA (max) 15mA (max) Propagation Delay of Driver 11ns (max) 4.5ns (max) 1.7ns (max) Propagation Delay of Receiver 30ns (max) 7.0ns (max) 2.7ns (max) Pulse Skew (Driver or Receiver) N/A 500ps (max) 400ps (max)

Differential Signaling Technologies


LVDS Standard• Maximum Switching Speed

– Depends on line driver– Depends on selected media (type and length)

• LVDS Saves Power– Power dissipated in load is small – LVDS devices are in CMOS=>low static power– Lowers system power through current-mode

• Design Practices– Matching is critical– Preserve balance


Perform simulation experiments to compare LVDS and single-ended signaling with CMOS driver and receiver. Emphasize speed, power and noise issues to validate the use of LVDS.

Project P8 - LVDS Design

http://jsa6.ece.uiuc.edu/projects/p6

http://www.national.com/appinfo/lvds

ece 497 js lecture - 14 projects: fdtd & lvdsjsa.ece.illinois.edu/ece497js/lect_14.pdf ·...

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