https://imgur.com/a/sDrv0

I do not understand how the part of the transfer function associated with the constant magnitude offset is calculated. Looking at the farmost left side of the plot, it has a slope of -20db/decade, meaning that the graph intersects the x-axis at 40w if you ignore all poles except for 1/s. This means that, in order to calculate the constant magnitude offset, you have to figure out how much of a gain would put the intersection back at 1w, the place where a pole of 1/s would have put it.

Don't you need a magnitude offset of 39db to set the intersection back at 1w? That means that the value of K is equal to the solution of the equation 20log(x) = 39. Can someone explain where my reasoning is wrong?

 

Hi,
The farmost left line with -20dB/dec is the Bode plot of Av/s.
If you look at the line, at w = 0.4 rad/s the magnitude is 40dB. You can use this information to find Av.

 

The problem was that I thought 40 to 1 db was a decade change of 1.4 decades, when it's really a decade change of 1.6 decades, due to logarithmic scales being different from linear scales. That was the key to the problem.