
Home  Forums  Rules  Articles  diyAudio Store  Blogs  Gallery  Register  Donations  FAQ  Calendar  Mark Forums Read 
Everything Else Anything related to audio / video / electronics etc) BUT remember we have many new forums where your thread may now fit! .... Parts, Equipment & Tools, Construction Tips, Software Tools...... 

Please consider donating to help us continue to serve you.
Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving 

Thread Tools 
1st July 2021, 04:21 PM  #1 
diyAudio Member
Join Date: Aug 2020

Laplace transfer function, poles and quality factor
Hello,
I am working on my theoretical skill, and I struggle a bit understanding the geometric interpretation of splane regarding eigenfrequency (natural frequency ?) and quality factor. On this document (cf screenshot), I read that poles at constant frequency move on a circle when modifying the quality factor? Is it because of this "natural frequency" term ? It goes strongly against my intuition that constant frequency is equivalent to constant imaginary part of the pole. http://jahonen.kapsi.fi/Audio/Papers/Equalization.pdf I am understanding wrong ? is the document a bit inaccurate ? Would you have some recommendation about resources I could use to understand those thing ? (signal theory, linear stuff, DSP, and so on). I am not too scared of maths, but I really enjoy pedagogical stuff that gives intuitions. Thank you very much :) 
1st July 2021, 05:54 PM  #2 
diyAudio Member
Join Date: Oct 2008
Location: Vancouver

I had to look up "natural frequency" to find its the same as resonant frequency. Thats the freq. an object vibrates when you hit it, or the freq where a circuit has max amplitude. It doesn't normally change so in that paper for any system the natural freq. Wn stays constant. The freq. of the signal w, is not constant. Its contained in the S as jw+rho.
If you want THE book, its here for free. [PDF] Network Analysis and Synthesis By Franklin F. Kuo Book Free Download – EasyEngineering Last edited by cbdb; 1st July 2021 at 06:03 PM. 
1st July 2021, 06:48 PM  #3 
diyAudio Member
Join Date: Apr 2011

That's a good one. I don't think they even teach this stuff anymore, sad.

1st July 2021, 08:01 PM  #4 
diyAudio Donor
diyAudio Member

For me, Norman Nise's textbook is the gold standard: amazon link
It covers stability (and instability) very thoroughly. BTW the "natural frequency" omega sub 0, is seldom observed in real world physical systems, because real world systems contain nonzero amounts of damping. Instead, what is observed in real world systems is the "damped natural frequency" omega sub d omega_d = omega_0 * sqrt(1  (zeta squared)) where zeta is the damping factor. If for example an LC resonator contains any resistance R at all, then zeta>0 and omega_d < omega_0. 
4th July 2021, 08:32 PM  #5 
diyAudio Member
Join Date: Aug 2020

Thank you very much all.
I think I understood. So, on circle centred on 0, we have "constant damped natural frequency", and on line parallel to the imaginary axis, constant "undamped" natural frequency ? 
Thread Tools  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Transfer Function  Measurement and Use  Brian Steele  Subwoofers  3  11th March 2020 09:25 AM 
Determining the Laplace Transform for Inverse Equalization Curves in LTSpice?  benman94  Software Tools  8  24th February 2019 11:36 PM 
Laplace behavioural source vs passive INV RIAA  Mosquito  Analogue Source  36  16th August 2016 11:26 AM 
Easiest and fastest way to measure a crossover's transfer function?  454Casull  Analog Line Level  3  26th August 2009 07:52 AM 
Transfer function. Poles not where expected  Raka  MultiWay  35  29th July 2008 01:20 PM 
New To Site?  Need Help? 