frequences ratio in diagram (fig 3.18)

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mfcooper

Joined Jun 14, 2017
1
Hi.
In my book (Analog Circuit Techniques by T.H.Wilmshurst) I have fig 3.18 and equation f0=fu/Aoz. I can't get into f0=fu/Aoz. I can get that is relating to exponenta law but that's all on me. Can you explain to me why there is f0=fu/Aoz? Can you recommend to me book that describe mathematica in this fully? Fig 3.18 I set in this post.


Thanks in advance.
 

Papabravo

Joined Feb 24, 2006
21,094
It is just the equation for the slope of a line in the logarithmic domain. Note that both the horizontal and vertical scales are linear in the logarithm of frequency for the horizontal axis and the logarithm of gain for the vertical axis. fu is the frequency for which the gain is one. fo is the frequency where the gain is Aoz. The slope of the line is just:

\(\frac{log(A_{oz})-log(1)}{log(f_o)-log(f_u)}\)
 

MrAl

Joined Jun 17, 2014
11,342
Hi,

It also looks like the graphic is not exactly to scale on one axis. It looks like the Aoz crossing point on the y axis for example should be slightly lower, so that may throw you off too. That is unless we believe that Aoz crosses at exactly 1000*sqrt(1000), which it may depending on how you read the graph.
 
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