Tuesday, October 02, 2007

Phase Relations in Active Filters

In applications that use filters, the amplitude response is generally of greater interest than the phase response. When a filter is used inside a process control loop, however, the total phase shift is of concern, since it may affect loop stability. This article looks at first- and second-order filters, comparing phase response as a function of topology, order, and Q. Higher-order filters are treated as cascades of lower-order blocks.


At 10:56 PM, Anonymous Anonymous said...

This article is very well written, the subject matter is important and failure to understand phase relationships of signals passing through a filter will cause design failure, often the failure will be unexplained.
Too often design is just a matter of plugging some numbers into a CAD program, if a person will go to the trouble to build a prototype and probe the amplitude and phase relationships they will learn much.
A great article like this is on par with "Dr. Leif", Bob's mailbox or the writings of Steve Woodward.
Thanks, a really thought provoking, deep article written in a condensed, elegant fashion.
John Peterson, or as known to his friends, "Analog Genius".

At 5:07 PM, Blogger LvW said...

For my opinion, this contribution is a kind of “refresher” as it summarizes only the basics of the phase characteristics, e. g. it reminds the reader that an inverting circuit shifts the phase by 180 degrees. Thus, it discusses – more or less – the ideal filter response which can be derived from the various textbooks as well.
However, it would be much more interesting to learn something about the nonideal characteristics of the various filter topologies resulting from the opamps parasitic phase contribution. Which filter topologies are sensible and which are less sensible to opamp parasitics ? Therefore, it would be advantageous to extend table 1 by another columne containing these information. And what about some other topologies not mentioned in the text (GIC, FDNR, FLF) ?
Regarding the BESSEL-response it is important to realize that this characteristic is chosen in most cases because of its quasi-linear phase characteristics. In this context it is more important to discuss the definition of a “corner frequency in the time domain” taking into account the group delay characteristics. Normally, the 3-dB-corner frequency of the Bessel-response is only of secondary interest.
One final remark: It is confusing to choose for the 3-dB-point of a first order lowpass the name “center frequency”. It should be “pole frequency” – consistent with all filter functions, independent of its order.


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