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<span style="font-size:14.0pt">FIVE POINTS <o:p> </o:p></span></p>
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<span style="font-size:14.0pt"><o:p> </o:p></span></p>
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<span style="font-size:14.0pt">(1)<span style="mso-spacerun:yes"> </span>(just an aside)<span style="mso-spacerun:yes">
</span>A “digital” 90-Degree-PDN is called a “Hilbert Transformer”.<span style="mso-spacerun:yes">
</span>In contrast to an implementation with analog all-pass (flat magnitude but imperfect phase difference) the HT has a perfect phase of 90-degrees phase difference but a non-flat magnitude response (trade-off):<span style="mso-spacerun:yes">
</span><o:p> </o:p></span></p>
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<a href="http://electronotes.netfirms.com/EN199.pdf"><span style="font-size:14.0pt">http://electronotes.netfirms.com/EN199.pdf</span></a><span style="font-size:14.0pt"><o:p> </o:p></span></p>
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<span style="font-size:14.0pt">EN Vol 20 No. 199 pp 10-12<span style="mso-spacerun:yes">
</span>Sept 2001<o:p> </o:p></span></p>
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<span style="font-size:14.0pt"><o:p> </o:p></span></p>
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<span style="font-size:14.0pt">(2)<span style="mso-spacerun:yes"> </span>Keep in mind that all PNDs have a TRANSIENT response because of the poles.<span style="mso-spacerun:yes">
</span>They take time to reach steady-state; - the longer the cascades, and the higher the pole-Q, the longer the delay, and possible artifacts.<span style="mso-spacerun:yes">
</span><o:p> </o:p></span></p>
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<span style="font-size:14.0pt"><o:p> </o:p></span></p>
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<span style="font-size:14.0pt">(3)<span style="mso-spacerun:yes"> </span>Consider using “Inverse Chebyshev” to set the phases error instead of equiripple (Cauer).<span style="mso-spacerun:yes">
</span>At a small expense in upper frequency error, (larger than equiripple), you should be able achieve near zero in the audio band ALL THE WAY TO ZERO frequency if that is your desire.<span style="mso-spacerun:yes">
</span><o:p> </o:p></span></p>
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<span style="font-size:14.0pt"><o:p> </o:p></span></p>
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<span style="font-size:14.0pt">4)<span style="mso-spacerun:yes"> </span>I have previously mentioned EN#168:.
<o:p> </o:p></span></p>
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<a href="http://electronotes.netfirms.com/EN168-90degreePDN.PDF"><span style="font-size:14.0pt">http://electronotes.netfirms.com/EN168-90degreePDN.PDF</span></a><span style="font-size:14.0pt"><o:p> </o:p></span></p>
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<span style="font-size:14.0pt">This approach allows a designer to build with second-order sections and do the entire design with even just ONE selected capacitor value, while cutting the number of op-amps in half, and avoiding extremes of RC products.<span style="mso-spacerun:yes">
</span><o:p> </o:p></span></p>
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<span style="font-size:14.0pt"><o:p> </o:p></span></p>
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<span style="font-size:14.0pt">(5) There is time-honored concept called “Classical Sensitivity“ (CS).<span style="mso-spacerun:yes">
</span>It is: the CS of a performance-parameter, X, to a variation of (tolerance of) a component, y, is:
<o:p> </o:p></span></p>
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<span style="font-size:14.0pt">SXy<span style="mso-spacerun:yes"> </span>= (y/ X) [ (delta)X / (delta)y ]<o:p> </o:p></span></p>
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<span style="font-size:14.0pt"><span style="mso-spacerun:yes"> </span>= [
<span style="mso-spacerun:yes"> </span>(delta)X/ X <span style="mso-spacerun:yes">
</span>/ <span style="mso-spacerun:yes"> </span>(delta)y/ y<span style="mso-spacerun:yes">
</span>]<o:p> </o:p></span></p>
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<span style="font-size:14.0pt">This can be estimated fairly easily by incrementing the relevant design equation a small amount, OR better by calculation via partial derivative since X(y,….) is generally available:<o:p> </o:p></span></p>
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<span style="font-size:14.0pt">SXy = (y/X) [ partial(X)/(respect to y ) ] <span style="mso-spacerun:yes">
</span><span style="mso-spacerun:yes"> </span><span style="mso-spacerun:yes"> </span><o:p> </o:p></span></p>
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<span style="font-size:14.0pt">For example, a pole frequency might be p=1/RC at first-order [SpR = -1], but p = 1/sqrt(R1R2C1C2) at second-order [SpR=-1/2] which says that a second-order approach is better.<span style="mso-spacerun:yes">
</span>For more on tuning with Sensitivity see:<o:p> </o:p></span></p>
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<span style="font-size:14.0pt"><o:p> </o:p></span></p>
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<a href="http://electronotes.netfirms.com/AN361.pdf"><span style="font-size:14.0pt">http://electronotes.netfirms.com/AN361.pdf</span></a><span style="font-size:14.0pt"><o:p> </o:p></span></p>
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