![Page 1: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/1.jpg)
Effects of Inductance on the Propagation Delayand Repeater Insertion in VLSI Circuits
Yehea I. Ismail and Eby G. Friedman, Fellow, IEEE
![Page 2: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/2.jpg)
Agenda
Introduction
Propagation Delay Formula
Comparison to an RC Model
Dependence of Delay on wire Length
Repeater Insertion for an RLC Interconnect
Conclusions
![Page 3: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/3.jpg)
Introduction
![Page 4: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/4.jpg)
Propagation Delay Formula
npd wet /48.135.19.2
![Page 5: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/5.jpg)
Close Form
2212......8202 1
0
nnn
x
x nnx
2/)1(......2100
nnnxn
x
![Page 6: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/6.jpg)
Interconnect Model-RCL
![Page 7: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/7.jpg)
A gate driving an RLC transmission line
![Page 8: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/8.jpg)
The transfer function-a lossy transmission line
l
L
sl
L
sin
out
eZ
Z
Z
Ze
Z
Z
Z
ZsV
sV
1111
2
)(
)(
0
0
0
0
t
t
t
t
sL
R
C
LZ 10
t
ttt sL
RCLsl 1
trs RZ L
L sCZ
1
Zs is source impedance, ZL is load impedance
γ is propagation constant, Z0 is characteristic impedance
![Page 9: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/9.jpg)
Laplace transform-1
Ltt
nCCL
W
1
'SWs n
Tline
t
CsC
sl
1
'
21
1
''
'
Tline
T
t CsC
LZZ 1
'
21'00
T
T
T
tLL C
C
sC
LZZ
1
'
1'
t
ttline
t
LT
L
CR
C
CC
2
![Page 10: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/10.jpg)
Laplace transform-2
t
trT R
RR
t
LT C
CC
t
ttline L
CR
2
![Page 11: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/11.jpg)
The parameter ζ
TTTTT
t
tt
C
CRCR
L
CR
1
5.0
2
TTTTT
lineC
CRCR
1
5.0
Three parameter:ζ,RT,CT
![Page 12: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/12.jpg)
Laplace transform-3
The scaled 50% propagation delay t`pd can be calculated by solving
Thus, the propagation delay of an RCL line with a source Resistance Rtr and a load capacitance CL has the form
![Page 13: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/13.jpg)
AS/X [20] simulations
the maximum error is 4.6% and the average error is 1.65%
![Page 14: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/14.jpg)
AS/X [20] simulations
npd wet /48.135.19.2 Eq.(18):
![Page 15: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/15.jpg)
Delay function is more accurate
npd wet /48.135.19.2
When CT And RT are high and ζ is lowEq(18) suffers high errors
This case can only occur for unreasonably high values of the inductance per unit length of the line as compared to the resistance and capacitance per unit lengthSuch a case does not exist in a practical VLSI circuit.
![Page 16: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/16.jpg)
ζ characterize inductance effects
![Page 17: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/17.jpg)
ζ characterize inductance effects
![Page 18: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/18.jpg)
ζ characterize inductance effects
![Page 19: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/19.jpg)
ζ characterize inductance effects
![Page 20: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/20.jpg)
The Factor of Inductance
npd wet /48.135.19.2
TTTTT
t
tt
C
CRCR
L
CR
1
5.0
2
![Page 21: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/21.jpg)
Comparison to an RC model
npd wet /48.135.19.2
![Page 22: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/22.jpg)
Comparison to an RC model
![Page 23: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/23.jpg)
copper interconnect line
![Page 24: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/24.jpg)
copper interconnect line
![Page 25: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/25.jpg)
copper interconnect line
![Page 26: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/26.jpg)
Dependence of Delay on Interconnect Length
αasym is the asymptotic value at high frequencies of the attenuation per unit length of the signals
L 0 tpd =0.37RCl2
R 0 tpd = l(LC)0.5
![Page 27: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/27.jpg)
![Page 28: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/28.jpg)
Repeater Insertion for an RLC Interconnect
The buffer output impedance Rtr is R0/hThe input capacitance of the buffer CL is hC0
![Page 29: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/29.jpg)
![Page 30: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/30.jpg)
Curve Fitting Method
![Page 31: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/31.jpg)
highly accurate
The error is less than 0.05%If Lt 0 hopt(RLC) = hopt(RC) kopt(RLC) = kopt(RC)
![Page 32: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/32.jpg)
Comparison with RC model
![Page 33: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/33.jpg)
Total delay in RC & RLC
When TL/R=3 ,tpdtotal increase by 10%When TL/R=5 ,tpdtotal increase by 20%When TL/R=10 ,tpdtotal increase by 30%
![Page 34: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/34.jpg)
Repeater Insertion in RC & RLC
![Page 35: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/35.jpg)
Area in RC & RLC
Amin is the area of a minimum size buffer
=
When TL/R=3 ,Area increase by 154%When TL/R=5 ,Area increase by 435%
![Page 36: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/36.jpg)
conclusion
Propagation delay --- 35%
propagation delay has linear dependence on the length of the line.
![Page 37: Effects of Inductance on the Propagation Delay and Repeater Insertion in VLSI Circuits](https://reader035.vdocuments.net/reader035/viewer/2022062217/56815736550346895dc4da03/html5/thumbnails/37.jpg)
Conclusion for repeater insertion
Insert less buffer
Reduce delay
Reduce buffer area