Title: EE201C Chapter 3 Interconnect RLC Modeling
1EE201C Chapter 3 Interconnect RLC Modeling
- Prof. Lei He
- LHE_at_ee.ucla.edu
2Chapter 3 Interconnect RLC Model
- Efficient capacitance model
- Efficient inductance model
- RC and RLC circuit model generation
3Reading Assignments
- J. Cong, L. He, A. B. Kahng, D. Noice, N. Shirali
and S. H.-C. Yen, "Analysis and Justification of
a Simple, Practical 2 1/2-D Capacitance
Extraction Methodology", ACM/IEEE Design
Automation Conference, June 1997, pp.627-632 - http//eda.ee.ucla.edu/pub/c7.pdf
- L. He, N. Chang, S. Lin, and O. S. Nakagawa, "An
Efficient Inductance Modeling for On-chip
Interconnects", (nomination for Best Paper
Award)IEEE Custom Integrated Circuits Conference,
San Diego, CA, pp. 457-460, May 1999. - http//eda.ee.ucla.edu/pub/c11.pdf
- M. Xu and L. He, "An efficient model for
frequency-based on-chip inductance," IEEE/ACM
International Great Lakes Symposium on VLSI, West
Lafayette, Indiana, pp. 115-120, March 2001. - http//eda.ee.ucla.edu/pub/c18.pdf
4Is RC Model still Sufficient?
- Interconnect impedance is more than resistance
- Z ? R j?L
- ? ? 1/tr
- On-chip inductance should be considered
- When ?L becomes comparable to R as we move
towards Ghz designs
5Candidates for On-Chip Inductance
- Wide clock trees
- Skews are different under RLC and RC models
- Neighboring signals are disturbed due to large
clock di/dt noise - Fast edge rate (100ps) buses
- RC model under-estimates crosstalk
- P/G grids (and C4 bumps)
- di/dt noise might overweight IR drop
6Resistance vs Inductance
Length 2000, Width 0.8 Thickness 2.0,
Space 0.8
Ls and Lx for two parallel wires
R and ?L for a single wire
7Impact of Inductance
6000u
10u
5u
5u
Gnd
Gnd
Clk
RC model
RLC model
8Inductance Extraction from Geometries
- Numerical method based on Maxwells equations
- Accurate, but way too slow for iterative physical
design and verification - Efficient yet accurate models
- Coplanar bus structure He-Chang-Shen-et al,
CICC99 - Strip-lines and micro-strip bus lines
Chang-Shen-He-et al, DATE2K - Used in HP for state-of-the-art CPU design
9Definition of Loop Inductance
Ii
Ij
Vj
Vi
10Loop Inductance for N Traces
Tw
TwL
TwR
Tw
Tw
Ts
Ts
TsL
TsR
tL
t1
t2
t3
tR
11Table in Brute-Force Way is Expensive
Tw
Tw
TwL
TwR
Tw
1.73 1.15 0.53 1.15 1.94 1.24 0.53 1.24
1.92
Ts
Ts
TsL
TsR
tL
t1
t2
t3
tR
- Self inductance has nine dimensions
- (n, length, location,TwL,TsL,Tw,Ts,TwR,TsR)
- Mutual inductance has ten dimensions
- (n, length, location1, location2,TwL,TsL,Tw,Ts,Tw
R,TsR) - Length is needed because inductance is not
linearly scalable
12Definition of Partial Inductance
Vj
Vi
- Partial inductance is the portion of loop
inductance for a segment when its current returns
via the infinity - called partial element equivalent circuit (PEEC)
model - If current is uniform (no skin effect), the
partial inductance is
13Partial Inductance for N Traces
Tw
Tw
TwL
TwR
Tw
6.17 5.43 5.12 4.89 4.66 5.43 6.79 6.10
5.48 5.04 5.12 6.10 6.79 6.10 5.33 4.89
5.48 6.10 6.79 5.77 4.66 5.04 5.33 5.77
6.50
Ts
Ts
TsL
TsR
tL
t1
t2
t3
tR
- Treat edge traces same as inner traces
- lead to 5x5 partial inductance table
- Partial inductance model is more accurate
compared to loop inductance model - Without pre-setting current return loop
14Foundation I
- The self inductance under the PEEC model for a
trace depends only on the trace itself (w/ skin
effect for a given frequency).
Tw
TwL
TwR
Tw
Tw
Ts
Ts
TsL
TsR
tL
t1
t2
t3
tR
15Foundation II
- The mutual inductance under the PEEC model for
two traces depends only on the traces themselves
(w/ skin effect for given frequency).
Tw
TwL
TwR
Tw
Tw
Ts
Ts
TsL
TsR
tL
t1
t2
t3
tR
16Foundation III
- The self loop inductance for a trace on top of a
ground plane depends only on the trace itself
(its length, width, and thickness)
Tw
Tw
TwL
TwR
Tw
4.8 2.5 1.3 0.7 0.14 2.5 5.5 2.9 1.5
0.7 1.3 2.9 5.7 2.9 1.3 0.7 1.5 2.9
2.5 2.5 0.14 0.7 1.3 2.5 4.8
Ts
Ts
TsL
TsR
t1
t2
t3
tR
tL
4.8
tR
17Foundation IV
- The mutual loop inductance for two traces on top
of a ground plane depends only on the two traces
themselves (their lengths, widths, and thickness)
Tw
TwL
TwR
Tw
Tw
4.8 2.5 1.3 0.7 0.14 2.5 5.5 2.9 1.5
0.7 1.3 2.9 5.7 2.9 1.3 0.7 1.5 2.9
2.5 2.5 0.14 0.7 1.3 2.5 4.8
Ts
Ts
TsL
TsR
tL
t1
t2
t3
tR
0.14
4.8
tL
tR
4.8
0.14
18Validation and Implication of Foundations
- Foundations I and II can be validated
theoretically - Foundations III and IV were verified
experimentally
- Problem size of inductance extraction can be
greatly reduced w/o loss of accuracy - Solve 1-trace problem for self inductance
- Reduce 9-D table to 2-D table
- Solve 2-trace problem for mutual inductance
- Reduce 10-D table to 3-D table
19Analytical Solutions to Inductance
Not suitable for on-chip interconnects
- Without considering skin effect and internal
inductance - Self inductance
- kf(w,t) 0 lt k lt 0.0025
- Mutual inductance
- Inductance is not sensitive to width, thickness
and spacing - No need to consider process variations for
inductance
20Extension to Random Nets Xu-HE, GLSVLSI01
21Accuracy
- Table versus FastHenry
- 400 random displaced parallel wires cases
22Error Distribution
- ?5 most cases
- Bigger error only found in smaller inductance
values
23Full RLC Circuit Model
Ls(wire12)
Self inductance L11 N11 N12 val L12
N13 N14 val L21 N21 N22 val L22 N23 N24
val mutual inductance K1 L11 L21
val K2 L12 L22 val K3 L11 L12 val K4
L21 L22 val K5 L11 L22 val K6 L21 L12
val
N13
N11
N14
N12
N23
N21
N24
N22
- For n wire segments per net
- RC elements n
- self inductance n
- mutual inductance n(n-1)
Lm(wire21, wire12) / sqrt(L21 L12)
24Normalized RLC Circuit Model
Ls(net1)
Self inductance L11 N11 N12 val L12
N13 N14 val L21 N21 N22 val L22 N23 N24
val mutual inductance K1 L11 L21
val K2 L12 L22 val
N13
N11
N14
N12
N23
N21
N24
N22
Lm(net1, net2) / sqrt(net1 net2)
- For n segments per wire
- RC elements n
- Self inductance n
- Mutual inductance n
25Full Versus Normalized
- Two waveforms are almost identical
- Running time
- Full 99.0 seconds
- Normalized 9.1 seconds
26Application of RLC modelShielding Insertion
- To decide a uniform shielding structure for a
given wide bus - Ns number of signal traces between two
shielding traces - Ws width of shielding traces
Ws
Ws
Ws
...
...
1
2
3
1
2
Ns
3
Ns
27Trade-off between Area and Noise
- Total 18 signal traces
- 2000um long, 0.8um wide
- separated by 0.8um
- Drivers -- 130x Receivers -- 40x
- Power supply 1.3V
Ns Ws Noise(v) Routing Area (um) Wire Area (um)
18 -- 0.71 61.1(0.0) 46.4(0.0) 6 0.8 0.38 64.
8 48.0 6 1.6 0.27 66.4 49.6 6 2.4 0.22 68.0
51.2 3 0.8 0.17 69.6(13) 50.4(8.8)
28Conclusions
- Inductance is a long-range effect
- Inductance can be extracted efficiently use PEEC
model - Normalized RLC circuit model with a much reduced
complexity can be used for buses - Full RLC circuit model should be used for random
nets - Model reduction or sparse inductance model may
reduce circuit complexity - RLC circuit model may be simulated for
interconnect optimization