Hi,

I have stumbled on some analog filter design calculation that puzzles me. We have a transfer function
\[ T(s) = \frac{|1+jw/z|}{|1 + jw/p|} \]
next author says that we can express the magnitude response as:
\[ \alpha = 20log{|1+jw/z|} - 20log{|1 + jw/p|} \]
Next he wants to focus just one the first log of the above formula and says that for a high frequency this can be simplified to:
\[ \alpha = 20log(\sqrt{1 + \frac{w}{z}^2)} = 20 log(w/z) \]
So far this is clear, but the he says, IF we rase the frequency by 10 then \[ \alpha = 20log(10w/z) = 20log(10) + 20log(w/z) = 20 + \alpha_2(w) \]
and he concludes "Thus for an increase of frequency by a factor of 10 the attenuation increased by 20db. Why attenuation? We got +20 not -20, second this part was a numerator of a transfer function so every increase in there should cause an increase in the system response not a decrease. Is it a mistake or I miss something?

Thanks!

 

it is called magnitude. should not magnitude be always positive.

 

It looks like it's a simple slip -- the gain increases by 20 dB/decade for a zero, or, equivalently, the attenuation decreases by 20 dB/decade.

Look at the context of the discussion and see if the rest of it is consistent with this. If it turns out to be consistent with claiming that the attenuation increases, then there's a problem.

Even the best textbooks have silly errors in them.

Heck, notice that your equation has a silly error in it, because it has, in the radical, ω²/z instead of (ω/z)². Easy to make these kinds of mistakes -- we know what we mean and we just slip up on the fine details as we express it.

 

Thank you, @WBahn, I agree with what you said. It is easy to make a mistake (as I did above too), I think in the book he made a digression about what can happen if we increase the frequency 10x and that the magnitude will change, for some reason he decided to call this change "attenuation" despite the fact we were analyzing a numerator of a transfer function so this can clearly only be a gain. Later graphs correctly represent an increase in magnitude according to the transfer function under consideration.