ch06.a.htm
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Figure 6.10</A>
(c) so that the Thévenin equivalent voltage source is 1.6 V?</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=55363">
</A>
b. What current does a driver have to sink if we want <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
OLmax</SUB>
= 0.4 V?</LI>
<LI CLASS="ExercisePart">
<A NAME="pgfId=55364">
</A>
c. What current does a driver have to source if we want <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
OHmin</SUB>
= 2.4 V?</LI>
</UL>
<P CLASS="ExerciseHead">
<A NAME="pgfId=24199">
</A>
6.12 (Ground resistance, 10 min.) Calculate the resistance of an aluminum GND net that is 0.5 mm long and 10 <SPAN CLASS="Symbol">
m</SPAN>
m wide.</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=37551">
</A>
6.13 (*Temperature) <SPAN CLASS="Bold">
(a)</SPAN>
(30 min.) You are about to ship a product and you have a problem with an FPGA. A high case temperature is causing it to be slower than you thought. You calculated the power dissipation, but you forgot that the InLet microprocessor is toasting the next door FPGA. You have no easy way to calculate T<SUB CLASS="Subscript">
J</SUB>
now, so we need to measure it in order to redesign the FPGA with fixed I/O locations. You remember that a diode forward voltage has a temperature coefficient of about –2 mV°C<SUP CLASS="Superscript">
–1</SUP>
and there are clamp diodes on the FPGA I/O. Explain, using circuit diagrams, how to measure the T<SUB CLASS="Subscript">
J</SUB>
of an FPGA in-circuit using: a voltage supply, DVM, thermometer, resistors, spoon, and a coffee maker. <SPAN CLASS="Bold">
(b)</SPAN>
(**120 min.) Try it. </P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=16068">
</A>
6.14 (Delay measurement, 10 min.) Sumo Silicon has a new process ready before we do and Sumo’s data book timing figures are much better than ours. Explain how to reduce our logic delays by changing our measurement circuits and trip points.</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=37725">
</A>
6.15 (Data sheets, 10 min.) In the 1994 data book Xilinx specifies <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
ILmin</SUB>
= 0.3 V (and <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
ILmax</SUB>
= 0.8 V) for the XC2000L. Why does this surprise you and what do you think the value for <SPAN CLASS="EquationNumber">
VILmin</SPAN>
really is? FPGA vendors produce thousands of pages of data every year with virtually no errors. It is important to have the confidence to question a potential error.</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=37732">
</A>
6.16 (GTL, 60 min.) Find the original reference to Gunning transistor logic. Write a one-page summary of its uses and how it works.</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=37749">
</A>
6.17 (Thresholds, 10 min.) With some FPGAs it is possible to configure an output at TTL thresholds and an input (on the same pad) at CMOS thresholds. Can you think of a reason why you might want to do this?</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=37755">
</A>
6.18 (Input levels, 10 min.) When we define <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
IHmin</SUB>
= 0.7<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DD</SUB>
, why do we calculate the <SPAN CLASS="Emphasis">
minimum</SPAN>
value of <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
IH</SUB>
using <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
DDmax</SUB>
= 5.5 V?</P>
<P CLASS="ExerciseHead">
<A NAME="pgfId=16065">
</A>
6.19 (Metastability equations, 30 min.)</P>
<UL>
<LI CLASS="ExercisePartFirst">
<A NAME="pgfId=55375">
</A>
a. From Eq. <A HREF="CH06.4.htm#18779" CLASS="XRef">
6.4</A>
show that if we make two measurements of <SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
r</SUB>
and MTBF then: </LI>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=107527">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107529">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107531">
</A>
<SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
r</SUB>
<SUB CLASS="Subscript">
1</SUB>
– <SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
r</SUB>
<SUB CLASS="Subscript">
2</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107515">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=107517">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=107533">
</A>
<SPAN CLASS="Symbol">
t</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107535">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107537">
</A>
–––––––––––––––––– ,</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107519">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=107521">
</A>
(6.14)</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=107539">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107541">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107543">
</A>
ln MTBF<SUB CLASS="Subscript">
1</SUB>
– ln MTBF<SUB CLASS="Subscript">
2</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107523">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=107525">
</A>
</P>
</TD>
</TR>
</TABLE>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=107547">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107549">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107551">
</A>
exp <SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
r</SUB>
<SUB CLASS="Subscript">
1</SUB>
/<SPAN CLASS="Symbol">
t</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107553">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=107555">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=107557">
</A>
T<SUB CLASS="Subscript">
0</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107559">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107561">
</A>
–––––––––––––––––– .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107563">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=107565">
</A>
(6.15)</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=107567">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107569">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107571">
</A>
ln MTBF<SUB CLASS="Subscript">
1</SUB>
<SPAN CLASS="EquationVariables">
f</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
<SPAN CLASS="EquationVariables">
f</SPAN>
<SUB CLASS="SubscriptVariable">
d</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107573">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=107575">
</A>
</P>
</TD>
</TR>
</TABLE>
<LI CLASS="ExercisePart">
<A NAME="pgfId=18340">
</A>
b. MTBU is extremely sensitive to variations in <SPAN CLASS="Symbol">
t</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
, show that: </LI>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107640">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107595">
</A>
d MTBU</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107597">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107599">
</A>
– <SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
r</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=107601">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=107603">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107642">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107605">
</A>
-––––––––</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107607">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107609">
</A>
–––––</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=107611">
</A>
.</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=107613">
</A>
(6.16)</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107644">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107615">
</A>
d <SPAN CLASS="Symbol">
t</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107617">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107619">
</A>
<SPAN CLASS="Symbol">
t</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
<SUP CLASS="Superscript">
2</SUP>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=107621">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=107623">
</A>
</P>
</TD>
</TR>
</TABLE>
<LI CLASS="ExercisePart">
<A NAME="pgfId=37687">
</A>
c. Show that the variation in MTBU is related to the variation in <SPAN CLASS="Symbol">
t</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
by the following expression: </LI>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107658">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107660">
</A>
<SPAN CLASS="Symbol">
D</SPAN>
MTBU</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107662">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107664">
</A>
– <SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
r</SUB>
<SPAN CLASS="Symbol">
Dt</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=107666">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=107668">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107670">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107672">
</A>
-––––––</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107674">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107676">
</A>
–––––––</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=107678">
</A>
.</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=107680">
</A>
(6.17)</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107682">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=107684">
</A>
MTBU</P>
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