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<H1 CLASS="Heading1">
<A NAME="pgfId=33486">
</A>
4.9 <A NAME="30736">
</A>
Problems</H1>
<P CLASS="Exercise">
<A NAME="pgfId=22369">
</A>
* = Difficult, ** = Very difficult, *** = Extremely difficult</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=4333">
</A>
4.1 (Antifuse properties, 20 min.) In this problem we examine some of the physical and electrical features of the antifuse programming process.</P>
<UL>
<LI CLASS="ExercisePartFirst">
<A NAME="pgfId=12874">
</A>
a. If the programming current of an antifuse is 5 mA and the link diameter that is formed is 20 nm, what is the current density during programming?</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=12875">
</A>
b. If the average antifuse resistance is 500 <SPAN CLASS="Symbol">
W</SPAN>
after programming is complete and the programming current is 5 mA, what is the voltage across the antifuse at completion of programming?</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=12876">
</A>
c. What power is dissipated in the antifuse link at the end of programming?</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=31927">
</A>
d. Suppose we wish to reduce the antifuse resistance from 500 <SPAN CLASS="Symbol">
W</SPAN>
to 50 <SPAN CLASS="Symbol">
W </SPAN>
. If the antifuse link is a tall, thin cylinder, what is the diameter of a 50 <SPAN CLASS="Symbol">
W</SPAN>
antifuse?</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=12878">
</A>
e. Assume we need to keep the power dissipated per unit volume of the antifuse link the same at the end of the programming process for both 500 <SPAN CLASS="Symbol">
W</SPAN>
and 50 <SPAN CLASS="Symbol">
W</SPAN>
antifuses. What current density is required to program a 50 <SPAN CLASS="Symbol">
W</SPAN>
antifuse? </LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=12879">
</A>
f. With these assumptions what is the required programming current for a 50 <SPAN CLASS="Symbol">
W</SPAN>
antifuse? Comment on your answer and the assumptions that you have made.</LI>
</UL>
<P CLASS="ExerciseHead">
<A NAME="pgfId=3899">
</A>
4.2 (Actel antifuse programming, 20 min.) In this problem we examine the time taken to program an antifuse-based FPGA.</P>
<UL>
<LI CLASS="ExercisePartFirst">
<A NAME="pgfId=12881">
</A>
a. We have stated that it takes about 5 to 10 minutes to program an Actel part. Given the number of antifuses on the smallest Actel part, and the number of antifuses that need to be blown on average, work out the equivalent time it takes to blow one antifuse. Does this seem reasonable?</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=12882">
</A>
b. Because of a failure process known as electromigration, the current density in a metal wire on a chip is limited to about 50 k Acm<SUP CLASS="Superscript">
–2</SUP>
. You can exceed this current for a short time as long as the time average does not exceed the limit. Suppose we want to use a minimum metal width to connect the programming transistors: Would these facts help explain your answer to part a?</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=12883">
</A>
c. What other factors might be involved in the process of blowing antifuses that may help explain your answer to part a?</LI>
</UL>
<P CLASS="ExerciseHead">
<A NAME="pgfId=4001">
</A>
4.3 (*Xilinx cell) Estimate the area components of a Xilinx cell as follows:</P>
<UL>
<LI CLASS="ExercisePartFirst">
<A NAME="pgfId=12884">
</A>
a. (30 min.) Assume the two inverters in the cross-coupled SRAM cell are minimum size (they are not, the <SPAN CLASS="EmphasisPrefix">
p-</SPAN>
channels—or <SPAN CLASS="EmphasisPrefix">
n-</SPAN>
channels—in one inverter need to be weak—long and narrow—but ignore this). Assume the read–write device is minimum size. Estimate the size of the SRAM cell including an allowance for wiring (state your assumptions clearly). </LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=12885">
</A>
b. (15 min.) Assume a single <SPAN CLASS="EmphasisPrefix">
n-</SPAN>
channel pass transistor is connected to the SRAM cell and has an on-resistance of 500 <SPAN CLASS="Symbol">
W</SPAN>
(equal to the average Actel ACT 1 antifuse resistance for comparison; the actual Xilinx pass transistors have closer to 1 k<SPAN CLASS="Symbol">
W</SPAN>
on-resistance). Estimate the transistor size. Assume the gate voltage of the pass transistor is at 5 V, and the source and drain voltages are both at 0 V (the best case). <SPAN CLASS="Emphasis">
Hint:</SPAN>
Use the parameters from <A HREF="/Humuhumu/from Antibes/Prof.htm#24209" CLASS="XRef">
Section 3.1</A>
, “<A HREF="/Humuhumu/from Antibes/Prof.htm#24209" CLASS="XRef">
Transistors as Resistors</A>
.”</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=12887">
</A>
c. (15min.) Compare your total area estimates of the cell with other FPGA technologies. Explain why the assumptions you made may be too simple, and suggest ways to make more accurate estimates.</LI>
</UL>
<P CLASS="ExerciseHead">
<A NAME="pgfId=11581">
</A>
4.4 (FPGA vendors, 60 min.) Update the information shown in <A HREF="CH04.8.htm#15424" CLASS="XRef">
Table 4.7</A>
using the online information provided by FPGA vendors.</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=29764">
</A>
4.5 (Prices) <A NAME="42757">
</A>
Adjustment factors, calculated from averages across the Xilinx price matrix, are shown in <A HREF="CH04.9.htm#10129" CLASS="XRef">
Table 4.8</A>
(the adjustment factors for the Xilinx military and MIL-STD parts vary so wildly that it is not possible to use a simple model to predict these prices). </P>
<UL>
<LI CLASS="ExercisePartFirst">
<A NAME="pgfId=32514">
</A>
a. (5 min.) Estimate the price of a XC3042-70PG132I in 100+ quantity, purchased in 1H92. </LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=32515">
</A>
b. (30min.) Use the 1992 prices in <A HREF="CH04.9.htm#23802" CLASS="XRef">
Figure 4.9</A>
to derive as much of the information shown in <A HREF="CH04.9.htm#10129" CLASS="XRef">
Table 4.8</A>
as you can, explaining your methods. </LI>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFigTitleSide">
<A NAME="pgfId=34346">
</A>
FIGURE 4.9 <A NAME="23802">
</A>
Xilinx XC3042 prices (1992). Problem <A HREF="CH04.9.htm#42757" CLASS="XRef">
4.5</A>
reconstructs part of <A HREF="CH04.9.htm#10129" CLASS="XRef">
Table 4.8</A>
from this data.</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFigure">
<A NAME="pgfId=34358">
</A>
<IMG SRC="CH04-9.gif" ALIGN="BASELINE">
</P>
</TD>
</TR>
</TABLE>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="7">
<P CLASS="TableTitle">
<A NAME="pgfId=34395">
</A>
TABLE 4.8 <A NAME="10129">
</A>
Xilinx price adjustment factors (1992) for Problem <A HREF="CH04.9.htm#42757" CLASS="XRef">
4.5</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="6">
<P CLASS="TableLeft">
<A NAME="pgfId=34412">
</A>
<SPAN CLASS="TableHeads">
Purchase quantity, all types</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34424">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34426">
</A>
(1–24)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34428">
</A>
(25–99)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34430">
</A>
(100+)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34432">
</A>
(5000+)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34434">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34436">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34438">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=39202">
</A>
100 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34443">
</A>
91 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34445">
</A>
77 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34447">
</A>
70 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34449">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34451">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34453">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="6">
<P CLASS="TableLeft">
<A NAME="pgfId=34455">
</A>
<SPAN CLASS="TableHeads">
Purchase time, in (100–999) quantity</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34467">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34469">
</A>
1H92</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34471">
</A>
+18 months</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34473">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34475">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34477">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34479">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34481">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34483">
</A>
100%</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34486">
</A>
60%</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34488">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34490">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34492">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34494">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34496">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="6">
<P CLASS="TableLeft">
<A NAME="pgfId=34498">
</A>
<SPAN CLASS="TableHeads">
Qualification type, same package</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34510">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34512">
</A>
Commercial</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34514">
</A>
Industrial</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34516">
</A>
Military</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34518">
</A>
883-B</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34520">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34522">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34524">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34526">
</A>
100%</P>
<P CLASS="TableLeft">
<A NAME="pgfId=34527">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34529">
</A>
130%</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34531">
</A>
varies</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34533">
</A>
varies</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34535">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34537">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34539">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="6">
<P CLASS="TableLeft">
<A NAME="pgfId=34541">
</A>
<SPAN CLASS="TableHeads">
Speed bin</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34553">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34555">
</A>
50</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34557">
</A>
70</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34559">
</A>
100</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34561">
</A>
125</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34563">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34565">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34567">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34569">
</A>
100 %</P>
<P CLASS="TableLeft">
<A NAME="pgfId=34570">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34572">
</A>
110 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34574">
</A>
130 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34576">
</A>
220 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34578">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34580">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34582">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34584">
</A>
<SPAN CLASS="TableHeads">
Package type</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="6">
<P CLASS="TableLeft">
<A NAME="pgfId=34586">
</A>
<SPAN CLASS="TableHeads">
</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34598">
</A>
3020:</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34600">
</A>
PC68</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34602">
</A>
PC84</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34604">
</A>
PQ100</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34606">
</A>
PG84</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34608">
</A>
CQ100</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34610">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34612">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34614">
</A>
100 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34616">
</A>
106 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=34618">
</A>
127 %</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
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