ECE 497 JS Lecture - 13 Projectsjsa.ece.illinois.edu/ece497js/Lect_13.pdfTitle: Microsoft PowerPoint...
Transcript of 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]
2Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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.
3Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
4Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
5Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
−•
−−
=−
−−
−−
−−
)(
)()(
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
6Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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.
7Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
• 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
8Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
9Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
( , ') ( ') '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
10Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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∑
11Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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:
P2 - METHOD OF MOMENTS
12Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
lmn[ ]=w1, Lf1 w1, Lf2 ...w2 , Lf1 w2, Lf2 ............. ............. ...
αn[ ]=α1
α2
.
gm[ ]=w1,gw2,g
.
Solution for weight coefficients
αn[ ]= lnm−1[ ] gm[ ]
P2 - METHOD OF MOMENTS
13Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
http://jsa6.ece.uiuc.edu/ece497js/projects/p2.pdf
14Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
15Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
( )( 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
16Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
17Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
• 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
18Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
• 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
19Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
20Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
21Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
22Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
http://jsa6.ece.uiuc.edu/ece497js/projects/p3.pdf
23Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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.
24Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
25Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
26Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
27Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
http://jsa6.ece.uiuc.edu/ece497js/projects/p4.pdf
28Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
PowerClamp
Threshold&
EnableLogic
GNDClamp
GNDClamp
GNDClamp
PowerClamp
PowerClamp
InputPackage
EnablePackage
OutputPackage
PullupRamp
PulldownRamp
PullupV/I
PulldownV/I
P5 – IBIS Diagram
Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
P5 – IBIS Input Topology
Power_Clamp
GND_Clamp
Vcc
R_pkg
C_pkg
L_pkg
C_comp
GNDGND
30Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
Vcc Vcc
Power_ClampGND_Clamp
GND GND
C_pkgL_pkg
R_pkg
C_omp
PullupPulldownRamp
P5 – IBIS Output Topology
31Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
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
32Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004
Visit http://www.eigroup.org/ibis/ibis.htm
P4 – IBIS References