<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=Windows-1252">
<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
</head>
<body dir="ltr">
<div id="divtagdefaultwrapper" style="font-size:10pt;color:#000000;font-family:Arial,Helvetica,sans-serif;" dir="ltr">
<p style="margin-top:0;margin-bottom:0"></p>
<div style="mso-element:para-border-div;border:none;border-top:solid #CCCCCC 1.0pt;
mso-border-top-alt:solid #CCCCCC .75pt;padding:11.0pt 0in 0in 0in;background:
white;margin-left:34.5pt;margin-right:7.5pt">
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;padding:
0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size:10.5pt;
font-family:"Helvetica",sans-serif;color:#333333"><o:p> </o:p></span></p>
<span style="font-size: 12pt;"></span>
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
tab-stops:.5in 49.5pt;background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;
padding:0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size:10.5pt;
font-family:"Helvetica",sans-serif;color:#333333"><o:p><span style="font-size: 12pt;"> </span></o:p></span></p>
<span style="font-size: 12pt;"></span>
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;padding:
0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size: 12pt; font-family: Helvetica, sans-serif; color: rgb(51, 51, 51);">Magnus –<o:p></o:p></span></p>
<span style="font-size: 12pt;"></span>
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;padding:
0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size:18.0pt;
font-family:"Helvetica",sans-serif;color:#333333"><span style="font-size: 12pt;">I think we would agree that there may be reasons for considering bandpass responses of order greater than 2 – but getting a higher Q (sharper peak)
is</span><span style="font-size: 12pt;"> </span><span style="font-size: 12pt;">not likely to be one of them.</span><span style="font-size: 12pt;">
</span><span style="font-size: 12pt;">Usually the sharper Q is obtainable just by increasing the performance Q of the second-order.</span><span style="font-size: 12pt;">
</span><span style="font-size: 12pt;">It’s not like the case with low-pass where extra poles give you a sharper roll-off rate JUST BEYOND the corner (like 24 db instead of 12).</span><span style="font-size: 12pt;">
</span><span style="font-size: 12pt;">With a high-Q BP, the “skirts” begin well after the response is well below the peak.
</span><o:p></o:p></span></p>
<span style="font-size: 12pt;"></span>
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;padding:
0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size:18.0pt;
font-family:"Helvetica",sans-serif;color:#333333"><span style="font-size: 12pt;">If you DO want sharper “skirts” (say 12 db on each side of the peak instead of the 2</span><sup><span style="font-size: 12pt;">nd</span></sup><span style="font-size: 12pt;">-order
6db on each side), then a cascading of identical BPs is the ticket. The Q increases in such cases, but distressingly slowly- if I recall. So it is probably not even a good way to sharpen a BP.</span><o:p></o:p></span></p>
<span style="font-size: 12pt;"></span>
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;padding:
0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size:18.0pt;
font-family:"Helvetica",sans-serif;color:#333333"><span style="font-size: 12pt;">The real use of (and meanings of) higher-order BP is to achieve a flatter passband.</span><span style="font-size: 12pt;">
</span><span style="font-size: 12pt;">The poles are slightly offsets so that when we move away from one, with a declining gain, the next pole takes over.</span><span style="font-size: 12pt;">
</span><span style="font-size: 12pt;">This is so-called “stagger-tuning” - a difficult design.</span><o:p></o:p></span></p>
<span style="font-size: 12pt;"></span>
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;padding:
0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size: 12pt; font-family: Helvetica, sans-serif; color: rgb(51, 51, 51);"> </span></p>
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;padding:
0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size: 12pt; font-family: Helvetica, sans-serif; color: rgb(51, 51, 51);">But the design is easy if one uses a lowpass-to-bandpass transformation for Butterworth or Chebyshev:
<o:p></o:p></span></p>
<span style="font-size: 12pt;"></span>
<p style="margin-top:0in;margin-right:0in;margin-bottom:7.5pt;margin-left:0in;
background:white;border:none;mso-border-top-alt:solid #CCCCCC .75pt;padding:
0in;mso-padding-alt:11.0pt 0in 0in 0in">
<span style="font-size:18.0pt;
font-family:"Helvetica",sans-serif;color:#333333"><span style="font-size: 12pt;"> </span></span><span style="color:black;mso-color-alt:
windowtext"><span style="font-size: 12pt;"> </span><a href="http://electronotes.netfirms.com/AN336.pdf" id="LPlnk802802" class="OWAAutoLink" previewremoved="true"><span style="font-size: 12pt;">http://electronotes.netfirms.com/AN336.pdf</span></a></span><span style="font-size:18.0pt;font-family:"Helvetica",sans-serif;color:#333333"><o:p></o:p></span></p>
</div>
<br>
<p></p>
</div>
</body>
</html>