How to find cutoff frequencies from Bode plot?

[dominicfhk]

Homework Statement

http://img832.imageshack.us/img832/7517/captureax.jpg
According to the solution, the cutoff frequencies are 1, 20, 80, 500 and 8000. I don't understand how to get those answers by inspecting the plot.

Homework Equations

None

The Attempt at a Solution

I think the cutoff frequency is defined as the frequency at which the ratio of input/output equals to 0.707, or whenever the magnitude of the frequency breaks downward. However, I don't see why 1, 20, 80, 500 and 8000 are the cutoff frequency for this bode plot. So how exactly can I tell what the cutoff frequencies are by inspecting the plot? Thank you so much.

 

[gneill]

The term is "corner frequency", and describes where the slope of the magnitude plot "turns a corner". This manifests as places where the slope alters from its previous "trend", for example going from convex to concave in shape.

If you look at the plot of a simple first-order filter (say a low pass filter), it can be represented schematically as a horizontal straight line which turns a corner and thereafter follows a new straight line that slopes down to the right with increasing frequency. (In reality the "corner" is rounded curve, but schematically you can picture the intersection of the two line segments).

If you cascade a number of filter sections with different "corners", the slope changes are cumulative and cause the bode plot to undulate accordingly. Picking out the corners from the plot is a matter of looking for the (sometimes subtle) slope changes.

 

[NascentOxygen]

According to the solution, the [STRIKE]cutoff[/strike] corner frequencies are 1, 20, 80, 500 and 8000. I don't understand how to get those answers by inspecting the plot.

Well, it is certainly a help to be told what the corner frequencies are. It makes finding them just that much easier. :tongue:

Try to approximate the amplitude plot by drawing straight-line segments. These can have gradients (in dB/decade) of 0, ±20, ±40, etc. The corners where adjacent line segments intersect define the corner frequencies described above.