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1.7 Problems</H1>
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1.1 (Break-even volumes, 60 min.) You need a spreadsheet program (such as Microsoft Excel) for this problem.</P>
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a. Build a spreadsheet, “Break-even Analysis,” to generate Figure 1.11.</LI>
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b. Derive equations for the break-even volumes (there are three: FPGA/MGA, FPGA/CBIC, and MGA/CBIC) and calculate their values.</LI>
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c. Increase the FPGA part cost by $10 and use your spreadsheet to produce the new break-even graph. <SPAN CLASS="Emphasis">
Hint:</SPAN>
(For users of Excel-like spreadsheets) use the XY scatter plot option. Use the first column for the <SPAN CLASS="EmphasisPrefix">
x</SPAN>
-axis data.</LI>
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d. Find the new break-even volumes (change the volume until the cost becomes the same for two technologies).</LI>
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e. Program your spreadsheet to automatically find the break-even volumes. Now graph the break-even volume (for a choice between FPGA and CBIC) for values of FPGA part costs ranging from $10–$50 and CBIC costs ranging from $2–$10 (do not change the fixed costs from Figure 1.12).</LI>
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f. Calculate the sensitivity of the break-even volumes to changes in the part costs and fixed costs. There are three break-even volumes and each of these is sensitive to two part costs and two fixed costs. Express your answers in two ways: in equation form and as numbers (for the values in Section 1.4.2 and Figure 1.11).</LI>
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g. The costs in Figure 1.11 are not unrealistic. What can you say from your answers if you are a defense contractor, primarily selling products in volumes of less than 1000 parts? What if you are a PC board vendor selling between 10,000 and 100,000 parts?</LI>
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1.2 (Design productivity, 10 min.) Given the figures for the SPARCstation 1 ASICs described in Section 1.3 what was the productivity measured in transistors/day? and measured in gates/day? Compare your answers with the figures for productivity in Section 1.4.3 and explain any differences. How accurate do you think productivity estimates are?</P>
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1.3 (ASIC package size, 30 min.) Assuming, for this problem, a gate density of 1.0 gate/mil<SUP CLASS="Superscript">
2</SUP>
(see Section 15.4, “Estimating ASIC Size,” for a detailed explanation of this figure), the maximum number of gates you can put in a package is determined by the maximum die size for each of the packages shown in Table 1.4. The maximum die size is determined by the package cavity size; these are <SPAN CLASS="Definition">
package-limited</SPAN>
ASICs. Calculate the maximum number of I/O pads that can be placed on a die for each package if the pad spacing is: (i) 5 mil, and (ii) 10 mil. Compare your answers with the maximum numbers of pins (or leads) on each package and comment. Now calculate the minimum number of gates that you can put in each package determined by the minimum die size.</P>
<TABLE>
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<P CLASS="TableTitle">
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TABLE 1.4 Die size limits for ASIC packages.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
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<SPAN CLASS="TableHeads">
Package<A HREF="#pgfId=36873" CLASS="footnote">
1</A>
</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="2">
<P CLASS="TableFirst">
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<SPAN CLASS="TableHeads">
Number of pins or leads</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
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<SPAN CLASS="TableHeads">
Maximum die size<A HREF="#pgfId=36881" CLASS="footnote">
2</A>
(mil</SPAN>
<SUP CLASS="Superscript">
2</SUP>
<SPAN CLASS="TableHeads">
)</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=36883">
</A>
<SPAN CLASS="TableHeads">
Minimum die size<A HREF="#pgfId=36886" CLASS="footnote">
3</A>
(mil</SPAN>
<SUP CLASS="Superscript">
2</SUP>
<SPAN CLASS="TableHeads">
)</SPAN>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
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PLCC</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=36890">
</A>
44</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
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</A>
</P>
</TD>
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<P CLASS="Table">
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320 <SPAN CLASS="Symbol">
¥</SPAN>
320</P>
</TD>
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<P CLASS="Table">
<A NAME="pgfId=36894">
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94 <SPAN CLASS="Symbol">
¥</SPAN>
94</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
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PLCC</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
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68</P>
</TD>
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<P CLASS="TableLeft">
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</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36900">
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420 <SPAN CLASS="Symbol">
¥</SPAN>
420</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36902">
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154 <SPAN CLASS="Symbol">
¥</SPAN>
154</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36904">
</A>
PLCC</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=36906">
</A>
84</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=44349">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36908">
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395 <SPAN CLASS="Symbol">
¥</SPAN>
395</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36910">
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171 <SPAN CLASS="Symbol">
¥</SPAN>
171</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
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PQFP</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=36914">
</A>
100</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=44351">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36916">
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338 <SPAN CLASS="Symbol">
¥</SPAN>
338</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36918">
</A>
124 <SPAN CLASS="Symbol">
¥</SPAN>
124</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36920">
</A>
PQFP</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=36922">
</A>
144</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=44353">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36924">
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350 <SPAN CLASS="Symbol">
¥</SPAN>
350</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36926">
</A>
266 <SPAN CLASS="Symbol">
¥</SPAN>
266</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36928">
</A>
PQFP</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=36930">
</A>
160</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=44355">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36932">
</A>
429 <SPAN CLASS="Symbol">
¥</SPAN>
429</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36934">
</A>
248 <SPAN CLASS="Symbol">
¥</SPAN>
248</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36936">
</A>
PQFP</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=36938">
</A>
208</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=44357">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36940">
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501 <SPAN CLASS="Symbol">
¥</SPAN>
501</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36942">
</A>
427 <SPAN CLASS="Symbol">
¥</SPAN>
427</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=36944">
</A>
CPGA</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=36946">
</A>
68</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=44359">
</A>
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