ch02.1.htm

介绍asci设计的一本书

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(2.6)</P>
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The gate capacitance, <SPAN CLASS="EquationNumber">
C</SPAN>
, is given by the formula for a parallel-plate capacitor with length <SPAN CLASS="EquationNumber">
L</SPAN>
, width <SPAN CLASS="EquationNumber">
W</SPAN>
, and plate separation equal to the gate-oxide thickness, <SPAN CLASS="EquationNumber">
T</SPAN>
<SUB CLASS="Subscript">
ox</SUB>
. Thus the gate capacitance is  </P>
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<A NAME="pgfId=376114">
 </A>
<SPAN CLASS="EquationNumber">
WL</SPAN>
<SPAN CLASS="Symbol">
e</SPAN>
<SUB CLASS="Subscript">
ox</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
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&nbsp;</P>
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&nbsp;</P>
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<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnRight">
<A NAME="pgfId=376124">
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<SPAN CLASS="EquationNumber">
C</SPAN>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=376126">
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=</P>
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<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
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<SPAN CLASS="EquationVariables">
&#8211;&#8211;&#8211;&#8211;&#8211;&#8211;</SPAN>
</P>
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=</P>
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<A NAME="pgfId=376132">
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<SPAN CLASS="EquationNumber">
WLC</SPAN>
<SUB CLASS="Subscript">
ox</SUB>
</P>
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<TD ROWSPAN="1" COLSPAN="1">
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<A NAME="pgfId=376134">
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,</P>
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(2.7)</P>
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<A NAME="pgfId=376142">
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<SPAN CLASS="EquationNumber">
T</SPAN>
<SUB CLASS="Subscript">
ox</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
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&nbsp;</P>
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&nbsp;</P>
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&nbsp;</P>
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where e<SUB CLASS="Subscript">
ox</SUB>
 is the gate-oxide dielectric permittivity. For silicon dioxide, Si0<SUB CLASS="Subscript">
2</SUB>
, e<SUB CLASS="Subscript">
ox</SUB>
 <SPAN CLASS="Symbol">
&#170;</SPAN>
 3.45 <SPAN CLASS="Symbol">
&#165;</SPAN>
 10<SUP CLASS="Superscript">
&#8211;11</SUP>
 Fm<SUP CLASS="Superscript">
&#8211;1</SUP>
, so that, for a typical gate-oxide thickness of 100 &Aring; (1 &Aring; = 1 angstrom = 0.1 nm), the gate capacitance per unit area, C<SUB CLASS="Subscript">
ox</SUB>
 <SPAN CLASS="Symbol">
&#170;</SPAN>
 3 f F<SPAN CLASS="Symbol">
m</SPAN>
m<SUP CLASS="Superscript">
&#8211;2</SUP>
.</P>
<P CLASS="Body">
<A NAME="pgfId=200983">
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Now we can express the channel charge in terms of the transistor parameters,  </P>
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 </A>
<SPAN CLASS="EquationVariables">
Q</SPAN>
 = WL<SPAN CLASS="EquationNumber">
C</SPAN>
<SUB CLASS="Subscript">
ox</SUB>
<SPAN CLASS="EquationVariables">
 </SPAN>
[ (<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
 &#8211; V<SUB CLASS="Subscript">
t</SUB>
<SUB CLASS="SubscriptVariable">
n</SUB>
) &#8211; 0.5 <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 ] .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
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(2.8)</P>
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<P CLASS="Body">
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Finally, the drain&#8211;source current is  </P>
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<P CLASS="TableEqnRight">
<A NAME="pgfId=377447">
 </A>
<SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="SubscriptVariable">
DSn</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=377449">
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=</P>
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<A NAME="pgfId=377451">
 </A>
<SPAN CLASS="EquationNumber">
Q/</SPAN>
<SPAN CLASS="EquationVariables">
t</SPAN>
<SUB CLASS="SubscriptVariable">
f</SUB>
</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
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<A NAME="pgfId=377453">
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&nbsp;</P>
</TD>
</TR>
<TR>
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&nbsp;</P>
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<TD ROWSPAN="1" COLSPAN="1">
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=</P>
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(W/L)<SPAN CLASS="Symbol">
m</SPAN>
<SUB CLASS="SubscriptVariable">
n</SUB>
<SPAN CLASS="EquationNumber">
C</SPAN>
<SUB CLASS="Subscript">
ox</SUB>
[ (<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
 &#8211; V<SUB CLASS="Subscript">
t</SUB>
<SUB CLASS="SubscriptVariable">
n</SUB>
) &#8211; 0.5 <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 ]<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 </P>
</TD>
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&nbsp;</P>
</TD>
</TR>
<TR>
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&nbsp;</P>
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<TD ROWSPAN="1" COLSPAN="1">
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=</P>
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<P CLASS="TableEqnLeft">
<A NAME="pgfId=377467">
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(W/L)k<SUP CLASS="Superscript">
'</SUP>
<SUB CLASS="SubscriptVariable">
n</SUB>
 [ (<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
 &#8211; V<SUB CLASS="Subscript">
t</SUB>
<SUB CLASS="SubscriptVariable">
n</SUB>
) &#8211; 0.5 <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 ]<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
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(2.9)</P>
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<P CLASS="Body">
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The constant k<SUP CLASS="Superscript">
'</SUP>
<SUB CLASS="SubscriptVariable">
n</SUB>
 is the process transconductance parameter (or <SPAN CLASS="Definition">
intrinsic transconductance</SPAN>
):  </P>
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<A NAME="pgfId=377489">
 </A>
k<SUP CLASS="Superscript">
'</SUP>
<SUB CLASS="SubscriptVariable">
n</SUB>
 = <SPAN CLASS="Symbol">
m</SPAN>
<SUB CLASS="SubscriptVariable">
n</SUB>
<SPAN CLASS="EquationNumber">
C</SPAN>
<SUB CLASS="Subscript">
ox</SUB>
 .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
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 </A>
(2.10)</P>
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<P CLASS="BodyAfterHead">
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We also define <SPAN CLASS="Symbol">
b</SPAN>
<SUB CLASS="SubscriptVariable">
n</SUB>
, the <SPAN CLASS="Definition">
transistor gain factor</SPAN>
 (or just <SPAN CLASS="Definition">
gain factor</SPAN>
) as  </P>
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<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=377526">
 </A>
<SPAN CLASS="Symbol">
b</SPAN>
<SUB CLASS="SubscriptVariable">
n</SUB>
 = k<SUP CLASS="Superscript">
'</SUP>
<SUB CLASS="SubscriptVariable">
n</SUB>
<SPAN CLASS="EquationNumber">
(W/L)</SPAN>
 .</P>
</TD>
<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnNumber">
<A NAME="pgfId=377528">
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(2.11)</P>
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</TABLE>
<P CLASS="BodyAfterHead">
<A NAME="pgfId=10486">
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The factor W/L (transistor width divided by length) is the transistor <SPAN CLASS="Definition">
shape factor</SPAN>
.</P>
<P CLASS="Body">
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Equation 2.9 describes the <SPAN CLASS="Definition">
linear region</SPAN>
 (or triode region) of operation. This equation is valid until <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 = <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
 &#8211; <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
t</SUB>
<SUB CLASS="SubscriptVariable">
n</SUB>
 and then predicts that <SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 decreases with increasing <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
<SPAN CLASS="EquationVariables">
,</SPAN>
 which does not make physical sense. At <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 = <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
 &#8211; <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
t</SUB>
<SUB CLASS="SubscriptVariable">
n</SUB>
 = <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
<SUB CLASS="Subscript">
(sat)</SUB>
 (the <SPAN CLASS="Definition">
saturation voltage</SPAN>
) there is no longer enough voltage between the gate and the drain end of the channel to support any channel charge. Clearly a small amount of charge remains or the current would go to zero, but with very little free charge the channel resistance in a small region close to the drain increases rapidly and any further increase in <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 is dropped over this region. Thus for <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
DS</SUB>
 &gt; <SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>
 &#8211; <SPAN CLASS="EquationNumber">
V</SPAN>
<SUB CLASS="Subscript">
t</SUB>
<SUB CLASS="SubscriptVariable">
n</SUB>
 (the <SPAN CLASS="Definition">
saturation region</SPAN>
, or pentode region, of operation) the drain current <SPAN CLASS="EquationVariables">
IDS </SPAN>
remains approximately constant at the <SPAN CLASS="Definition">
saturation current</SPAN>
, <SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="SubscriptVariable">
DSn</SUB>
<SUB CLASS="Subscript">
(sat)</SUB>
, where  </P>
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<TD ROWSPAN="1" COLSPAN="1">
<P CLASS="TableEqnCenter">
<A NAME="pgfId=377599">
 </A>
<SPAN CLASS="EquationVariables">
I</SPAN>
<SUB CLASS="SubscriptVariable">
DSn</SUB>
<SUB CLASS="Subscript">
(sat)</SUB>
 = (<SPAN CLASS="Symbol">
b</SPAN>
<SUB CLASS="SubscriptVariable">
n</SUB>
/2)(<SPAN CLASS="EquationVariables">
V</SPAN>
<SUB CLASS="SubscriptVariable">
GS</SUB>