I'm looking over a document by TI that's a guide to active low pass filter design, found here:
At the bottom of page 4 it defines the FSF (frequency scale factor) as sqrt(a_0). I may be missing something obvious here, but I don't understand why then the FSF in the second term of the equation for P(f)is not squared? Thanks for any insight!
"Bitrex" schrieb im Newsbeitrag news:ibidnc0AOcpfGPbWnZ2dnUVZ snipped-for-privacy@earthlink.com...
Well, Ithink you refer to equation 1 on page 3. There is a mistake in this equation. In a 2nd order Laplace Transform, which desribes the transfer function H(S)=Vout/Vin of a lowpass we have 3 terms in the denominator:
1/(S^2 + S/Q +1)=H(S) The factor K in the pdf is the gain at DC in the numerator which I have put to 1 for convenience, also FSF=1. S is the normalized frequency, at the pole frequency of the filter it is one. S= jf/(FSF x fc) , you can see that in the second term of the denominator of the pdf. When you square it, the j*j gets negative (-1). That's where they missed in the 1st term. Lets try it out with Q=0.71 (Butterworth) Gain at DC --> S=0 1/(-0^2 + 0/Q + 1) = 1 Gain at 0.5*fc 1/(-0.25 + j*0.5/0.71 +1) = 1/ (0.75 + j*0.71) The modulus of that vector is 0.97 Gain at fc 1/(-1 + j*1/Q + 1) = jQ =1/( j*1.414) modulus=0.71 Gain at 10*fc !/(-100 + j*7.1 + 1) = 1/(-99 + j*7.1) modulus= 0.010075The complex numbers are needed because of the phase shift. the high frequencies are inverted as you can see on the negative numbers. At t5he cutoff frequency we have only an imaginary part, so the phase shift is 90°
ciao Ban
Thank you for your reply! Yes, I see the error they made there now as well. They have the minus sign kind of floating in front of the whole fraction, which makes it seem as if the whole fraction is negative, and not the first term in the denominator. As I mentioned I also think there's another error on page 4, remembering that wc also = sqrt(a_0) the denominator of the second term should have a square root as well.
It seems mistakes like this are pretty common in manufacturer's guides, which sure makes it hard to learn. The name of the PDF file ends with a "B" which indicates that this was a second revision of the document too...:(
In the second equation is missing a square root, of course you're right. And your observations are right. The first error is worse tho, because it's confusing where that minus ended up. The guy who wrote it seems to be an application engineer, he knows the practical stuff quite well, but the math seems not to be his expertise. ciao Ban Apricale, Italy
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Found another glitch on page22 top Here the minus is in the right place, instead he messed up the coefficients of the 3rd stage. porca miseria Ban
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