Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Register Log in

Why butterworth filter is maximally flat?

Status
Not open for further replies.
N

neoflash

Advanced Member level 1
Joined
Jul 2, 2005
Messages
492
Helped
10
Reputation
20
Reaction score
2
Trophy points
1,298
Activity points
4,759
Some lecture notes states that butterworth filter is monotonic in both pass band and stop band.

However, I believe it is not true, only if all poles's angle >45°.

Then, why some people call this type of filter, maximally flat?

thanks,
Neoflash
 

HI, I thought Bessel was maximum flat.

regards,

Paul.
 

Because the first N derivatives of the amplitude polynomial are zero at the origin.

There are also maximally flat phase and also group delay type filters.
 

neoflash,
An intuitive way of looking at the Butterworth:
Of all the n-pole filters that are monotonic in both the passband and the stopband, the Butterworth filter has the least attentuation for all frequencies in the passband, for a specified passband cutoff frequency.
Regards,
Kral
 

Karl:

I think i prove butterworth is not monotonic only if the pole angles are larger than 45.
 

neoflash,
The pole locations, and, therefore, the pole angles define the Butterworth low pass filter. For a Butterworth filter, the poles are located at equal angles around a circle. For a 2-pole Butterworth filter, the poles with negative real parts are located at angles of +/- 135 degrees. If the angles are not at +/- 135 degrees, the filter is not a Butterworth. The angle between poles of a Butterworth filter is 180/n, where n is the order of the filter. Of course, the poles that have positive real parts are unstable, and are not used in the filter design.
Regards,
Kral
 

    N

    neoflash

    Points: 2
    Helpful Answer Positive Rating
Status
Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Back
Top