ch17.6.htm

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=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=84843">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
a</SUB>
 + <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
b</SUB>
 .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=84845">
 </A>
&nbsp;</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=84847">
 </A>
(17.14)</P>
</TD>
</TR>
</TABLE>
<P CLASS="ExerciseNoIndent">
<A NAME="pgfId=20328">
 </A>
where <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
a</SUB>
 represents the contribution from two parallel plates and <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
b</SUB>
 is the fringing capacitance (for both edges). The following equation then takes into account the coupling capacitance to a neighbor conductor separated horizontally by a gap <SPAN CLASS="EquationVariables">
G </SPAN>
between the edges of the conductors:  </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=85069">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
2</SUB>
/<SPAN CLASS="Symbol">
e</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=85071">
 </A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=85073">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
/<SPAN CLASS="Symbol">
e</SPAN>
 + [0.03(<SPAN CLASS="EquationVariables">
W</SPAN>
/<SPAN CLASS="EquationVariables">
H</SPAN>
) + 0.83 (<SPAN CLASS="EquationVariables">
T</SPAN>
/<SPAN CLASS="EquationVariables">
H</SPAN>
) &#8211; 0.07 (<SPAN CLASS="EquationVariables">
T</SPAN>
/<SPAN CLASS="EquationVariables">
H</SPAN>
)<SUP CLASS="Superscript">
0.222</SUP>
](<SPAN CLASS="EquationVariables">
G</SPAN>
/<SPAN CLASS="EquationVariables">
H</SPAN>
)<SUP CLASS="Superscript">
&#8211;1.34</SUP>
 .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=85075">
 </A>
(17.15)</P>
</TD>
</TR>
</TABLE>
<P CLASS="ExerciseNoIndent">
<A NAME="pgfId=20333">
 </A>
This equation is of the form,  </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=85175">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
2</SUB>
<SPAN CLASS="Symbol">
</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=85177">
 </A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=85179">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
 + <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
 .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=85181">
 </A>
&nbsp;</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=85183">
 </A>
(17.16)</P>
</TD>
</TR>
</TABLE>
<P CLASS="ExerciseNoIndent">
<A NAME="pgfId=15165">
 </A>
<SPAN CLASS="EquationVariables">
</SPAN>
where <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
 is the coupling capacitance from the conductor to one neighbor. For a conductor having two neighbors (one on each side), the total capacitance will be  </P>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=85202">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
2</SUB>
<SPAN CLASS="Symbol">
</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=85204">
 </A>
=</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=85206">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
 + 2<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="SubscriptVariable">
c</SUB>
 .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnLeft">
<A NAME="pgfId=85208">
 </A>
&nbsp;</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=85210">
 </A>
(17.17)</P>
</TD>
</TR>
</TABLE>
<P CLASS="ExerciseNoIndent">
<A NAME="pgfId=15168">
 </A>
<SPAN CLASS="EquationVariables">
</SPAN>
<A HREF="CH17.6.htm#29648" CLASS="XRef">
Table&nbsp;17.3</A>
 shows the result of evaluating these equations for different values of <SPAN CLASS="EquationVariables">
T/H</SPAN>
, <SPAN CLASS="EquationVariables">
W/H</SPAN>
, and <SPAN CLASS="EquationVariables">
S/H</SPAN>
 for <SPAN CLASS="Symbol">
l</SPAN>
 = 0.5 <SPAN CLASS="Symbol">
m</SPAN>
m.</P>
<UL>
<LI CLASS="ExercisePartFirst">
<A NAME="pgfId=21827">
 </A>
a.&nbsp;Calculate the corresponding values for <SPAN CLASS="Symbol">
l</SPAN>
 = 0.125 <SPAN CLASS="Symbol">
m</SPAN>
m assuming quasi-ideal scaling. </LI>
<TABLE>
<TR>
<TD ROWSPAN="1" COLSPAN="3">
<P CLASS="TableTitle">
<A NAME="pgfId=15606">
 </A>
TABLE&nbsp;17.3&nbsp;<A NAME="29648">
 </A>
Calculated fringing capacitance (per unit length and normalized by permittivity) using quasi-ideal scaling and the Sakurai&#8211;Tamaru equations. Problem <A HREF="CH17.6.htm#13391" CLASS="XRef">
17.10</A>
 completes this table.</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=15486">
 </A>
<SPAN CLASS="TableHeads">
Parameter</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=15488">
 </A>
<SPAN CLASS="Symbol">
l</SPAN>
 =  0.5 <SPAN CLASS="Symbol">
m</SPAN>
m</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableFirst">
<A NAME="pgfId=15490">
 </A>
<SPAN CLASS="Symbol">
l</SPAN>
 = 0.125 <SPAN CLASS="Symbol">
m</SPAN>
m</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15498">
 </A>
<SPAN CLASS="EquationVariables">
T</SPAN>
 (<SPAN CLASS="Symbol">
m</SPAN>
m)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15500">
 </A>
0.5</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15502">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15504">
 </A>
<SPAN CLASS="EquationVariables">
W</SPAN>
 (<SPAN CLASS="Symbol">
m</SPAN>
m)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15506">
 </A>
1.5</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15508">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15510">
 </A>
<SPAN CLASS="EquationVariables">
S</SPAN>
 (<SPAN CLASS="Symbol">
m</SPAN>
m)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15512">
 </A>
1.5</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15514">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15516">
 </A>
<SPAN CLASS="EquationVariables">
H</SPAN>
 (<SPAN CLASS="Symbol">
m</SPAN>
m)</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15518">
 </A>
0.5</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15520">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15522">
 </A>
<SPAN CLASS="EquationVariables">
T</SPAN>
/<SPAN CLASS="EquationVariables">
H</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15524">
 </A>
1</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15526">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15528">
 </A>
<SPAN CLASS="EquationVariables">
W</SPAN>
/<SPAN CLASS="EquationVariables">
H</SPAN>
, <SPAN CLASS="EquationVariables">
S</SPAN>
/<SPAN CLASS="EquationVariables">
H</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15530">
 </A>
3</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15532">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15534">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
 = <SPAN CLASS="EquationVariables">
Ca</SPAN>
 + <SPAN CLASS="EquationVariables">
Cb</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15536">
 </A>
6.25</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15538">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15540">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
2</SUB>
 = <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
 + <SPAN CLASS="EquationVariables">
Cc</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15542">
 </A>
6.44</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15544">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15546">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
3</SUB>
 = <SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
1</SUB>
 +2 <SPAN CLASS="EquationVariables">
Cc</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15548">
 </A>
6.63</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15550">
 </A>
&nbsp;</P>
</TD>
</TR>
<TR>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableLeft">
<A NAME="pgfId=15552">
 </A>
<SPAN CLASS="EquationVariables">
C</SPAN>
<SUB CLASS="Subscript">
a</SUB>
 = parallel plate</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="Table">
<A NAME="pgfId=15554">
 </A>
3.45</P>
</TD>