Electronic – How to determine the order of filter

filtersignalsignal processingsignal-theory

This is my first study about signal analysing. I'm very confused about filter order.
My reference book says that this graph shows 4-th order filter.

And, there are also 2th-order and 12-th order

My problem is how can I know whether its 4-th order, 12-th order, or 2nd order like the book says so? I'd like to know the process behind it.

Best Answer

The order, n of a filter is the number of reactive elements (if all are contributing.)

Using the linear slope (on log-log grid) away from f breakpoint it will be 6dB/octave per order of n.

An n= 4th order is 24dB/octave slope as in both of 1st examples .

I might think it appears to a 10th order filter Butterworth -60dB/oct and 8th order Chebychev -40dB/oct. There is visual ambiguity here from the lack of range after break, to estimate the filter slope when the graph is cutoff near 1 octave above. Also these are filter examples with low&high Q so the breakpoint slopes are very different.

So I agree it is hard to estimate in figure1.12. Whereas Fig 1.11 is easier to measure the slope.

Graphical Method

Use a straight edge to go through the Y axis intercept and fit a linear slope to curve. Then measure the slope in n multiples of -6n dB/oct or better if possible -20n dB/dec.

It gets complicate when the Y axis is not big enough.

A decade is 1/10= 20 log 0.1 = -20dB x n order.
An octave is 1/2 = 20 log 0.5 = -6.02dB x n order.

So from Fig 1.11 12th order filter

The graphical method has some uncertainty but is closest to 12th order. enter image description here