[sdiy] 8th order?

[Magnus Danielson]

From: flightofharmony at comcast.net
Subject: Re: [sdiy] 8th order?
Date: Tue, 05 Jun 2007 06:17:43 -0700
Message-ID: <46656277.2090300 at comcast.net>

> James Dunn wrote:
> > Magnus Danielson wrote:
> >> From: James Dunn <james at 4thharmonic.com>
> >> Subject: [sdiy] 8th order?
> >> Date: Tue, 05 Jun 2007 10:40:03 +0100
> >> Message-ID: <46652F73.3050707 at 4thharmonic.com>
> >>
> >>  
> >>> What does 8th order mean? Is it simply another way of describing the 
> >>> number of poles in a filter or db/oct?
> >>>     
> >>
> >> It relates back to the theoretical background of linear diffrential 
> >> system
> >> and describes the degree of the system. The order of the system also 
> >> descibes
> >> how many poles and how many zeros the system can have. The placement 
> >> of the
> >> zeros gives the db/Oct number, but the school-book examples with all 
> >> zeroes in
> >> a bunch over at infinity for a low-pass makes the db/Oct being -6.02 
> >> db/Oct
> >> times the order. An n-pole system is of the n:th degree.
> >>
> >> You require at least n reactive components (capacitors, inductors) to 
> >> acheive
> >> a n:th order system, but it is not always that you get that order, 
> >> you can get
> >> less. For example will a dual-PI notch filter with RC links have 3 
> >> capacitors
> >> but only show up as a 2:nd degree system. The db/oct measure does not 
> >> give a
> >> good measure here.
> >>
> >> I hope you see the difference and also apprechiate why we talk about 
> >> 8th order
> >> rather than 48 db/Oct systems.
> >>
> >>   
> > er, I'm afraid not! Thanks very much for your in-depth answer though - 
> > I think I need to spend some more time with the Arts of Electronics.. 
> > :) I also think I have a good enough understanding for what I need for 
> > the time being though.

Let's take another example. The Oberheim Xpander filter is a 4th order filter,
but you may use it as a 4-pole Low Pass (-24 dB/Oct),
or a 3-pole Low Pass (-18 dB/Oct) and a 1-pole High Pass (+6 dB/Oct),
or a 2-pole Low Pass (-12 dB/Oct) and a 2-pole High Pass (+12 dB/Oct),
or a 3-pole Low Pass ( -18 dB/Oct) and a 1-pole All Pass (0 dB/Oct). 

Please notice how the multiples of 6 in the low and high pass parts is never
higher than 4, but may be lower!!!

They are all 4th order systems, having 4 poles but how these are placed and
where the zeros are places makes all the difference in the world. The dB/Oct
number is certainly not telling all the truth either.

> > Thanks again

Please keep asking! I enjoy answering these questions. :)

> > James
> So, in short form, the order of the filter refers to the number of poles 
> and zeroes. The dB performance is based on filter type. The 
> characteristic equation specifies the performance ( cutoff frequency, 
> etc.) of the circuit, then you build a circuit to match that 
> specification. To build an 8th order filter you cascade four 2nd order 
> stages.

Almost true. You can cascade 8 first order filters and that is also a valid
8th order filter. Infact, by summing the input and outputs of all those you can
acheive all the zeros you want, and by feedbacking a sum of all the outputs
and add to the input signal you can acheive all the poles you want. If the
first-order system happends to be an integrator, you got yourself a state-
variable filter.

Cheers,
Magnus