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Design >> Mixed-Signal Design >> what is the relation between corner frequency and damping factor
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Message started by Mallikarjunarao T on Mar 19^th, 2009, 3:22am

Title: what is the relation between corner frequency and damping factor
Post by Mallikarjunarao T on Mar 19^th, 2009, 3:22am

Hai,

I have small doubt, can you explain any one please. what is the relation between corner frequency and damping factor(critical,underdamped and overdamped) which one is better for design and at what values ??

Regards,
Mallikarjunarao T

Title: Re: what is the relation between corner frequency and damping factor
Post by pancho_hideboo on Mar 19^th, 2009, 5:53am

Mallikarjunarao T wrote on Mar 19^th, 2009, 3:22am:

what is the relation between corner frequency and damping factor(critical,underdamped and overdamped) which one is better for design and at what values ??

What do you mean as "corner frequency" ?
What circuit or function do you mean ? Loop Filter of PLL ?

Title: Re: what is the relation between corner frequency and damping factor
Post by buddypoor on Mar 19^th, 2009, 7:05am

Mallikarjunarao T wrote on Mar 19^th, 2009, 3:22am:

There is NO relation between damping factor and 3-dB-corner frequency.
Take a lowpass of 2nd order as an example:
(1) the damping factor d determines if - and if yes - how large the overshoot of the step response will be and how long the settling time of the damped wave is. This factor is inversely proportional to the pole Q.
In the frequency domain the peaking of the transfer curve in the region of the pole frequency is proportional to the pole Q=1/2d

(2) The 3db-corner frequency is approximately equal to the pole frequency (for Q=0,7071 , d=0.7071 both are identical). This is the FREQUENCY of the damped step response, but has nothing to do with its duration (damping).

I forgot to recommend some values:
In case you like a good compromize between acceptable overshoot and no peaking in the 2nd order transfer curve d=0.707 (Butterworth approximation) is used very often. But any value around d=0.7 looks good.

Title: Re: what is the relation between corner frequency and damping factor
Post by pancho_hideboo on Mar 19^th, 2009, 7:10am

If this corner frequency is for phase noise characteristics of PLL, there is a relation with Q or damping factor.

Title: Re: what is the relation between corner frequency and damping factor
Post by Peruzzi on Mar 19^th, 2009, 11:02am

Mallikarjunarao T,

I started to write a quick explanation of damping factor versus corner frequency but paused and did a quick Google search of "second order transfer functions". There are so many examples and tutorials you can find in a few seconds, written better than I could in the time I'm willing to give.

So I encourage you to use Google, skim a few articles, then sit down for an hour or two with your chosen tutorial and an open Matlab session and become an expert.

Best of luck,

Bob Peruzzi

Title: Re: what is the relation between corner frequency and damping factor
Post by Mallikarjunarao T on Mar 20^th, 2009, 7:32am

Hai ,

Corner frequency means w0 . I asked generally for any circuit ????

With Regards,
Mallikarjunarao T

Title: Re: what is the relation between corner frequency and damping factor
Post by buddypoor on Mar 20^th, 2009, 8:40am

Mallikarjunarao T wrote on Mar 20^th, 2009, 7:32am:

Hai ,

Corner frequency means w0 . I asked generally for any circuit ????

With Regards,
Mallikarjunarao T

Mallikarjunarao T,

The name "w0" can mean a lot (pole frequ, natural frequ, corner frequ, center frequ,......)
That means, we learn NOTHING from you by using only a symbol !
You must spend some time and place and use a description which is as complete as necessary to understand your problem.
In addition, see my contribution from yesterday. I told you that there is NO relation between damping and corner frequency.
As a good example, take a low pass 2nd order:
It can have a damping factor of 0.707 (Butterworth response) and at the same time a corner frequency of 1 Hz or 100 MHz.

Title: Re: what is the relation between corner frequency and damping factor
Post by raja.cedt on Mar 20^th, 2009, 10:35pm

hi,
i understand w0 means natural frequency of undamped second order system.There is no relationship between these two term,in fact there shouldn't.if so system becomes non linear because damping factor is like control input to oscillator(like when it is very low it will oscillate,when is very high it wont oscillate) and natural frequency indicate at what frequency it has to oscillate(lets take an oscillator...its oscillating frequency is any where depends on the design,but damping factor should be ideally zero..i guess conveys you that there is no relationship between these two ).
And another thing up to my knowledge there is no need to find all these damping factor,Quality factor..because these are the another way of quantifying the pole location.
but there is a relation between damping factor and oscillating frequency of well damped system..this u can appreciate from some text books
I hope i delivered some use full stuff to you..let me know any issue's or clarification's

Thanks,
rajasekhar

Title: Re: what is the relation between corner frequency and damping factor
Post by Mallikarjunarao T on Mar 23^rd, 2009, 9:03am

Thanks to buddypoor and raja.cedt for giving of valid information to me.

Best Regards,
Mallikarjunarao T

Title: Re: what is the relation between corner frequency and damping factor
Post by loose-electron on Apr 5^th, 2009, 5:19pm

I would dig out a book on control systems and keep it handy. Stick a copy of a book on continuous time filtering nearby.