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<META content=3D"Erik Cheever, Swarthmore College" name=3Dauthor>
<META content=3DALL name=3DROBOTS>
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<BODY>
<DIV id=3DoverDiv=20
style=3D"Z-INDEX: 1000; VISIBILITY: hidden; POSITION: =
absolute"></DIV><!-- #BeginEditable "MainText" -->
<H1>Bode Plot Examples</H1>
<UL id=3DNavHeader>
<LI><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/Bode.html=
">Overview</A>=20
<LI><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeWhat.=
html">Freq=20
Domain</A>=20
<LI><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeWhy.h=
tml">Why=20
Bode?</A>=20
<LI><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeHow.h=
tml">Asymptotic=20
plots</A>=20
<LI><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeRules=
.html">Making=20
Plot</A>=20
<LI id=3Dcurrent><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeExamp=
les.html">Examples</A>=20
<LI><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodePlotG=
ui.html">BodePlotGui</A>=20
<LI><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeRevie=
wRules.html">Rules=20
Table</A>=20
<LI><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeAll.h=
tml">Printable</A>=20
</LI></UL>
<P>Several examples of the construction of Bode Plots are included in =
this=20
file. Click on the transfer function in the table below to jump to =
that=20
example.</P>
<DIV class=3DskinnyTable>
<TABLE class=3DskinnyTable>
<TBODY>
<TR>
<TH class=3DskinnyTable style=3D"HEIGHT: 21px" =
colSpan=3D6>Examples (Click=20
on Transfer Function)</TH></TR>
<TR>
<TD class=3DskinnyTable style=3D"HEIGHT: 66px"><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeExamp=
les.html#ex1"><STRONG>1<BR></STRONG><IMG=20
=
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/eqs/imgFF.=
gif"></A></TD>
<TD class=3DskinnyTable style=3D"HEIGHT: 66px"><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeExamp=
les.html#ex2"><STRONG>2<BR></STRONG><IMG=20
=
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/eqs/img101=
.gif"></A></TD>
<TD class=3DskinnyTable style=3D"HEIGHT: 66px"><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeExamp=
les.html#ex3"><STRONG>3<BR></STRONG><IMG=20
=
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/eqs/img103=
.gif"></A></TD>
<TD class=3DskinnyTable style=3D"HEIGHT: 66px"><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeExamp=
les.html#ex4"><STRONG>4<BR></STRONG><IMG=20
=
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/eqs/img105=
.gif"></A></TD>
<TD class=3DskinnyTable style=3D"HEIGHT: 66px"><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeExamp=
les.html#ex5"><STRONG>5<BR></STRONG><IMG=20
=
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/eqs/img107=
.gif"></A></TD>
<TD class=3DskinnyTable style=3D"HEIGHT: 66px"><A=20
=
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/BodeExamp=
les.html#ex6"><STRONG>6<BR></STRONG><IMG=20
=
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/eqs/img109=
.gif"></A></TD></TR></TBODY></TABLE></DIV>
<P> </P>
<DIV class=3DskinnyTable>
<TABLE class=3DskinnyTable>
<TBODY></TBODY></TABLE></DIV>
<HR class=3DfullWidth>
<A name=3Dex1></A><!--webbot bot=3D"Include" =
U-Include=3D"Example1/index.html" TAG=3D"BODY" startspan -->
<DIV id=3DoverDiv=20
style=3D"Z-INDEX: 1000; VISIBILITY: hidden; POSITION: =
absolute"></DIV><!-- #BeginEditable "MainText" -->
<H1>Example 1</H1>
<HR>
<P class=3Dequation><A href=3D"javascript:history.go(-1)"><IMG =
alt=3DBack=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/images/LeftArro=
w.gif">=20
Back <IMG alt=3DBack=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/images/LeftArro=
w.gif"></A></P>
<HR>
<P>Draw the Bode Diagram for the transfer function:</P>
<P class=3Dequation><IMG height=3D39 alt=3D"Transfer Function"=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/Example1/B=
odeEx1TF.gif"=20
width=3D84></P>
<H2>Step 1: Rewrite the transfer function in proper =
form. </H2>
<BLOCKQUOTE>
<P>Make both the lowest order term in the numerator and denominator=20
unity. The numerator is an order 0 polynomial, the denominator =
is order=20
1.=20
<P class=3Dequation><IMG height=3D58 alt=3D"Rewritten Transfer =
Function"=20
=
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/Example1/i=
ndex.3.gif"=20
width=3D184> </P></BLOCKQUOTE>
<H2>Step 2: Separate the transfer function into its constituent =
parts.</H2>
<BLOCKQUOTE>
<P>The transfer function has 2 components:</P>
<UL>
<LI>
<P>A constant of 3.3 </P>
<LI>
<P>A pole at s=3D-30 </P></LI></UL></BLOCKQUOTE>
<H2>Step 3: Draw the Bode diagram for each part.</H2>
<BLOCKQUOTE>
<P>This is done in the diagram below.</P>
<UL>
<LI>
<P>The constant is the cyan line (A quantity of 3.3 is equal to 10.4 =
dB). The phase is constant at 0 degrees. </P>
<LI>
<P>The pole at 30 rad/sec is the blue line. It is 0 dB up to =
the break=20
frequency, then drops off with a slope of -20 dB/dec. The =
phase is 0=20
degrees up to 1/10 the break frequency (3 rad/sec) then drops =
linearly down=20
to -90 degrees at 10 times the break frequency (300 rad/sec).=20
</P></LI></UL></BLOCKQUOTE>
<H2>Step 4: Draw the overall Bode diagram by adding up the results =
from=20
step 3.</H2>
<BLOCKQUOTE>
<P>The overall asymptotic plot is the translucent pink line, the exact =
response is the black line. </P></BLOCKQUOTE>
<P class=3Dfigure><IMG height=3D659 alt=3D"Bode Plot"=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/Example1/i=
ndex.4.gif"=20
width=3D653></P>
<P> </P>
<HR>
<P class=3Dequation><A href=3D"javascript:history.go(-1)"><IMG =
alt=3DBack=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/images/LeftArro=
w.gif">=20
Back <IMG alt=3DBack=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/images/LeftArro=
w.gif"></A> &n=
bsp; =20
<A=20
href=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Bode/Example2/=
index.html"><IMG=20
alt=3DNext=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/images/RightArr=
ow.gif">Example=20
2<IMG alt=3DNext=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/images/RightArr=
ow.gif"></A></P>
<HR>
<P> </P><!-- #EndEditable -->
<HR class=3DfullWidth>
<DIV id=3DsiteInfo>
<P class=3Dequation>=A9 Copyright 2005-2007 <A=20
href=3D"mailto:erik_cheever@swarthmore.edu?subject=3DLinear Physical =
System Analysis (Copyright notice)">Erik=20
Cheever</A> This page may be freely used for =
educational=20
purposes.<BR></P>
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</P><A href=3D"http://www.swarthmore.edu/NatSci/echeeve1">Erik=20
Cheever</A> <A=20
href=3D"http://www.engin.swarthmore.edu/">Department of=20
Engineering</A> <A=20
href=3D"http://www.swarthmore.edu/">Swarthmore College</A> =
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<H1>Example 2</H1>
<HR>
<P class=3Dequation><A href=3D"javascript:history.go(-1)"><IMG =
alt=3DBack=20
src=3D"http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/images/LeftArro=
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