The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Analog Design >> limit cycle
https://designers-guide.org/forum/YaBB.pl?num=1328461593

Message started by raja.cedt on Feb 5^th, 2012, 9:06am

Title: limit cycle
Post by raja.cedt on Feb 5^th, 2012, 9:06am

hello,
can any one please tell me about limit cycle, and what it's significance...at least give me some reference or some thing.

Thanks,
Raj.

Title: Re: limit cycle
Post by boe on Feb 7^th, 2012, 10:32am

Raj,
a (stable) limit cycle is a kind of oscillation. An important example is an oscillation of a recursive digital filter in fixed-point arithmetic stimulated and sustained by the rounding error.

Which context interests you?
- B O E

Title: Re: limit cycle
Post by raja.cedt on Feb 7^th, 2012, 10:47am

hello boe,
thanks for the reply, i am getting this word very repetitively when i am studying discrete system stability and about jitter. So could you please explain what is limit cycle, i am guessing it is a root-locus of some thing.

Thanks,
raj.

Title: Re: limit cycle
Post by thechopper on Feb 7^th, 2012, 8:30pm

Hi Raja,
This is more or less what I remember...
Typically in non-linear systems, the solutions to differential equations representing such systems have singularities around which the trajectory of such solution (in the plane defined by the state variables) cycle around such point.
As boe suggested they represent oscillations conditions that can be reached depending on the initial conditions of your non-linear system: a typical limit cycle is the switching of a buck converter when analyzed as a non-linear system, or idle tones on a sigma delta converter when also analyzed as non-linear feedback system.

Best
Tosei

Title: Re: limit cycle
Post by boe on Feb 8^th, 2012, 4:34am

Raja,
Tosei's explanation seems OK to me; however, the difference to instability of linear systems is that they are oscillations of fixed amplitude.

- B O E

Title: Re: limit cycle
Post by RobG on Feb 26^th, 2012, 5:14pm

Raja - The idle tones in a delta sigma modulator can be thought of as limit cycles, although I'm not sure if they are the same thing as what you are researching. See page 41-45 of Schreier/Temes's book.

rg