Filter orders

Discussion in 'General Electronics Chat' started by Dritech, Oct 5, 2014.

1. Dritech Thread Starter Well-Known Member

Sep 21, 2011
756
5
Hi all,

Can someone please explain what is exactly the filter order? What is the difference between 2nd order, 4th order, 10th order etc.. filters?

I did some online research but did not actually understand its meaning.

2. MrAl Distinguished Member

Jun 17, 2014
2,551
515
Hi,

Usually the 'order' of a filter refers to the order of the differential equation that would necessary to completely describe the filter.

The effect of going up in order is usually to obtain more selectivity or a sharper response, which gets closer and closer to an ideal filter response.

For example, for a low pass filter the ideal response would be to pass all frequencies up to the cutoff frequency, and then greatly attenuate all frequencies above that. Since no analog filter can accomplish this, we try to get as close to that as possible, or at least as close as we need for a given application, and as we go up in order we get closer and closer to that ideal response. For example, a first order filter can only get somewhat close, while a second order filter can get closer, and a third order filter closer yet. The down side is the component values get more critical as we go up in order.

Dritech likes this.
3. Dritech Thread Starter Well-Known Member

Sep 21, 2011
756
5
Thanks for the reply. What determines the highest order? For instance is it possible to have a 20th order filter or is there a limit?

Apr 5, 2008
15,799
2,385
Hello,

Have a look at the attached PDF.

Bertus

File size:
171.6 KB
Views:
25
5. Papabravo Expert

Feb 24, 2006
10,340
1,850
In a passive analog filter, it is the number of reactive elements. The number of reactive elements is of course related to the differential equation describing the filter response in magnitude and phase. Reactive elements are inductors and capacitors because they both have reactance. Reactance is like resistance for resistors, but it depends on the frequency of the signals it sees. The only real limit is a practical one of how many components you wish to string together; a 20th order filter is certainly possible.

6. MrAl Distinguished Member

Jun 17, 2014
2,551
515
In theory there is no limit given unlimited computing precision, but in the real world there are several secondary effects that set in that will limit the practical filters. For example, if we designed a band pass filter for a given center frequency with 20 stages and only one of those stages was not tuned right due to component tolerances, we end up with a second order filter (one that could have been built with only two stages) rather than the intended twentieth order filter. So even one bad stage can ruin the whole filter.

7. MrAl Distinguished Member

Jun 17, 2014
2,551
515
Hi there,

Strictly speaking, that's not really correct although that is most often what we find in the real world.

For example, a passive RC low pass filter with a single resistor in series with two capacitors that are also in series (all three elements in series) and we take the output from across the cap that is lowest in the string (one end connected to ground). There is one resistor and two capacitors, yet the response is only first order because the differential equation required to describe this circuit is only first order.

This example is easy to spot, but others are not as obvious. One of the rules i like to throw out there is if there are at least two caps in the circuit and any two of them happen to have one lead from each connected together, the order of the filter *might* be one order less because of that. Note that i say *might* because it's not a hard and fast rule that works every time, but does alert us to the possibility that the true order could be lower than the number of energy storage elements in the circuit.
Of course this rule is a heuristic and it's more complicated than that. If we had two sets of caps where both sets had two caps with one lead in common, then the order might be reduced by *two* instead of just one.
A simple example where even that's not enough, if we had one single resistor in series with three caps so all four elements are in series, and we take outputs from across the top cap, center cap, and bottom cap, all three individual responses are first order even though there are three caps in the circuit.

Last edited: Oct 6, 2014
Dritech likes this.
8. crutschow Expert

Mar 14, 2008
13,475
3,362
To add to what has already been said, the rolloff voltage response after the filter's corner frequency is equal to the filter order times 6db/octave of frequency change (20dB/decade), Thus a first order filter rolls off at 6dB/octave, a second order at 12dB/octave, etc.

9. Dritech Thread Starter Well-Known Member

Sep 21, 2011
756
5
Thanks a lot for the replies. I was told that the filter order (n) has to be an odd number. Is this true for a particular filter (ex: chebyshev) ?

10. MrAl Distinguished Member

Jun 17, 2014
2,551
515
Hi,

I'd like to ask who told you that, and if they might have been referring to a certain application.

I dont think there is a parity requirement for any filter, but i wont presume to know every single kind of filter in the universe, especially since a new type could be developed tomorrow that does have this property. But i will say that i think that there are some filters that have a MINIMUM order of 2, one of which is the bandpass filter. I dont think you can create a bandpass filter with order less than 2 unless the system it is being inserted into already has some sort of reactive response, and then it wouldnt really be a bandpass anyway.
So a rule of thumb is no parity, but minimum order of 2 for bandpass and bandstop for example.

11. Papabravo Expert

Feb 24, 2006
10,340
1,850
Filters of even order have no pole on the negative real axis. Filters of odd order have a single pole on the negative real axis and the remaining poles occur in conjugate pairs.

12. MrChips Moderator

Oct 2, 2009
12,624
3,451
In the attenuation band, a 1st-order low-pass filter will attenuate the power by 6dB per octave, or 20dB per decade.

A 2nd-order low-pass filter will attenuate the power by 12dB per octave, or 40dB per decade.

An nth-order low-pass filter will attenuate the power by 6xn dB per octave, or 20xn dB per decade.