📄 ch03.1.htm
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=<SPAN CLASS="Symbol">
</SPAN>
4 standard loads<SPAN CLASS="Symbol">
</SPAN>
=<SPAN CLASS="Symbol">
</SPAN>
4<SPAN CLASS="Symbol">
¥ </SPAN>
0.034<SPAN CLASS="Symbol">
</SPAN>
pF<SPAN CLASS="Symbol">
</SPAN>
=<SPAN CLASS="Symbol">
</SPAN>
0.136<SPAN CLASS="Symbol">
</SPAN>
pF, </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=295569">
</A>
<SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="SubscriptVariable">
pd </SUB>
(<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
out</SUB>
+ <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
p</SUB>
) = (38 + 817 (0.136)) ps = 149.112 ps .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=295571">
</A>
(3.5)</P>
</TD>
</TR>
</TABLE>
<P CLASS="Body">
<A NAME="pgfId=221610">
</A>
To make a comparison with the simulation we need to use ln<SPAN CLASS="Symbol">
</SPAN>
(1/0.35)<SPAN CLASS="Symbol">
</SPAN>
=<SPAN CLASS="Symbol">
</SPAN>
1.04 and not approximately 1 as we have assumed, so that (with all times in ps) </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=264835">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=420230">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=264837">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=264839">
</A>
–<SPAN CLASS="EquationVariables">
t'</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=264841">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=264843">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=264845">
</A>
<SPAN CLASS="BodyComputer">
v(out1)</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=420232">
</A>
<SPAN CLASS="Symbol">
ª</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=264847">
</A>
3.0 exp</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=264849">
</A>
–––––––––––</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=264851">
</A>
V</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=264853">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=264855">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=420234">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=264857">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=264859">
</A>
149.112/1.04</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=264861">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=264863">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=265113">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=420236">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=265115">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=265117">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=265119">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=265121">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=265059">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=420238">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=265089">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=265091">
</A>
–(<SPAN CLASS="EquationVariables">
t</SPAN>
– 20)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=265093">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=265067">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=265069">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=420240">
</A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=265095">
</A>
3.0 exp</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=265097">
</A>
–––––––––</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=265099">
</A>
for t > 20 ps .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=265077">
</A>
<A NAME="17393">
</A>
(3.6)</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=265079">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=420242">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=265101">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=265103">
</A>
143.4</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=265105">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=265087">
</A>
</P>
</TD>
</TR>
</TABLE>
<P CLASS="Body">
<A NAME="pgfId=184561">
</A>
Equation <A HREF="#17393" CLASS="XRef">
3.6</A>
is plotted in Figure <A HREF="#19386" CLASS="XRef">
3.3</A>
(d). For <SPAN CLASS="BodyComputer">
v(out1)</SPAN>
<SPAN CLASS="Symbol">
</SPAN>
=<SPAN CLASS="Symbol">
</SPAN>
1.05<SPAN CLASS="Symbol">
</SPAN>
V (equal to the 0.35 output trip point), Eq. <A HREF="#17393" CLASS="XRef">
3.6</A>
predicts <SPAN CLASS="EquationVariables">
t</SPAN>
<SPAN CLASS="Symbol">
</SPAN>
=<SPAN CLASS="Symbol">
</SPAN>
20<SPAN CLASS="Symbol">
</SPAN>
+<SPAN CLASS="Symbol">
</SPAN>
149.112<SPAN CLASS="Symbol">
ª </SPAN>
169<SPAN CLASS="Symbol">
</SPAN>
ps and agrees with Figure <A HREF="#19386" CLASS="XRef">
3.3</A>
(b)—it should because we derived the model from these results!</P>
<P CLASS="Body">
<A NAME="pgfId=290708">
</A>
Now we find <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
p</SUB>
. From Figure <A HREF="#19386" CLASS="XRef">
3.3</A>
(c) and Eq. <A HREF="#10713" CLASS="XRef">
3.2</A>
</P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=221812">
</A>
<SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
PDr</SUB>
= (52 + 1281 <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
out </SUB>
) ps thus <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
pr</SUB>
= 52/1281 = 0.041 pF (rising) ,</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=221814">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=221816">
</A>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=221818">
</A>
</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqn">
<A NAME="pgfId=224448">
</A>
<SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
PDf</SUB>
= (38 + 817 <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
out </SUB>
) ps thus <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
pf</SUB>
= 38/817 = 0.047 pF (falling) .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=221822">
</A>
<A NAME="33563">
</A>
(3.7)</P>
</TD>
</TR>
</TABLE>
<P CLASS="BodyAfterHead">
<A NAME="pgfId=187479">
</A>
These intrinsic parasitic capacitance values depend on the choice of output trip points, even though <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
pf </SUB>
<SPAN CLASS="Symbol">
</SPAN>
<SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="SubscriptVariable">
pdf</SUB>
and <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
pr</SUB>
<SPAN CLASS="Symbol">
</SPAN>
<SPAN CLASS="EquationVariables">
R</SPAN>
<SUB CLASS="SubscriptVariable">
pdr</SUB>
are constant for a given input trip point and waveform, because the pull-up and pull-down resistances depend on the choice of output trip points. We take a closer look at parasitic capacitance next.</P>
<HR><P>[ <A HREF="CH03.htm">Chapter start</A> ] [ <A HREF="CH03.htm">Previous page</A> ] [ <A HREF="CH03.2.htm">Next page</A> ]</P></BODY>
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