Designer’s Guide Community

raja.cedt

Senior Fellow

Offline

Posts: 1516
Germany

Question on loop bandwidth
Jun 02^nd, 2009, 7:42am

hi,
i just want to know when a zero is introduced into 2nd order system and zero frequency is lower than system natural frequency.Now can any body please tell me at what rate loop will respond (assume the above system is in some loop), I think answer for this question is wu in the following , but all papers are saying natural frequency.
can any body please explain where i am wrong.

Thanks,
Rajasekhar.

Back to top

delete_001.png

IP Logged

vivkr

Community Fellow

Offline

Posts: 780

Re: Question on loop bandwidth
Reply #1 - Jun 3^rd, 2009, 12:04am

Hi,

My knowledge of control systems is a bit rusty but I would support the papers. However, I would say that it would be closer to wn than to wu, and the exact value probably is also dependent on the separation between wn and wu.

This by the way is one of those things which you can beautifully see in MATLAB using very simple models, and is also very instructive. I recommend plotting the step response of the system (closed-loop) and looking at the root locus plot. That way, you will get a very clear understanding.

Best regards,

Vivek

Back to top

IP Logged

buddypoor

Community Fellow

Offline

Posts: 529
Bremen, Germany

Re: Question on loop bandwidth
Reply #2 - Jun 3^rd, 2009, 1:01am

raja.cedt wrote on Jun 2^nd, 2009, 7:42am:

hi,
i just want to know when a zero is introduced into 2nd order system and zero frequency is lower than system natural frequency.Now can any body please tell me at what rate loop will respond (assume the above system is in some loop), I think answer for this question is wu in the following , but all papers are saying natural frequency.
can any body please explain where i am wrong.
Thanks,
Rajasekhar.

I assume you didn�t realize that you, of course, change the natural frequency by introducing a zero. Thus, you are right and the "papers" as well. The "rate of loop response" will be the new natural frequency - and for my opinion that�s wu.
Regards
Lutz

Back to top

LvW (buddypoor: In memory of the great late Buddy Rich)

IP Logged

raja.cedt

Senior Fellow

Offline

Posts: 1516
Germany

Re: Question on loop bandwidth
Reply #3 - Jun 3^rd, 2009, 2:19am

hi vivkr,
thanks for you r reply, actually this is a pll basics question.Generally in books they generally loop bandwidth is 1/10 of the reference frequency, but what i am asking is here loop bandwidth is wu(it should not wn). Another basic question i have is in this case why wn is coming into picture, up to my knowledge if any system is crossing 0db with -40db then wn will come into picture, in this case it is crossing 0 db with -20db?

Thanks,
Rajasekhar.

Back to top

IP Logged

buddypoor

Community Fellow

Offline

Posts: 529
Bremen, Germany

Re: Question on loop bandwidth
Reply #4 - Jun 3^rd, 2009, 3:15am

raja.cedt wrote on Jun 3^rd, 2009, 2:19am:

hi vivkr,
thanks for you r reply, actually this is a pll basics question.Generally in books they generally loop bandwidth is 1/10 of the reference frequency, but what i am asking is here loop bandwidth is wu(it should not wn). Another basic question i have is in this case why wn is coming into picture, up to my knowledge if any system is crossing 0db with -40db then wn will come into picture, in this case it is crossing 0 db with -20db?
Thanks,
Rajasekhar.

I don�t understand your last sentence - what do you mean with "come into the picture" ? If the loop gain crosss the 0dB line with -40dB/dec. the closed loop will be unstable ! That�s the only reason for incorporating a zero. Was this your question ?

Back to top

LvW (buddypoor: In memory of the great late Buddy Rich)

IP Logged

raja.cedt Senior Fellow Offline Posts: 1516 Germany	Re: Question on loop bandwidth Reply #5 - Jun 3^rd, 2009, 3:38am hi buddypoor, what your are saying is correct but what is the significance of wn? i think the answer is if your loop is really unstable then it oscillate with this frequency.But now zero is introduced but still all PLL papers are using wn is loop bandwidth? why it is? thanks, Rajasekhar.
Back to top	IP Logged

buddypoor

Community Fellow

Offline

Posts: 529
Bremen, Germany

Re: Question on loop bandwidth
Reply #6 - Jun 3^rd, 2009, 6:17am

raja.cedt wrote on Jun 3^rd, 2009, 3:38am:

hi buddypoor,
what your are saying is correct but what is the significance of wn? i think the answer is if your loop is really unstable then it oscillate with this frequency.But now zero is introduced but still all PLL papers are using wn is loop bandwidth? why it is?

thanks,
Rajasekhar.

OK, it seems in my first reply at 10:00 I have expressed myself not clear enaugh. I try again:
Wn is the natural frequency of the loop without the additional zero.
After introducing this zero the open loop response changes and we get the 0dB crossing at another frequency (which you call Wu) with another slope. However, this is the new natural frequency of the closed loop - and we should call it again Wn. (The "old" Wn now has no practical meaning and no significance
anymore since the circuit has changed !).
Did you get it now ?
Thanks, Regards
Lutz

Back to top

LvW (buddypoor: In memory of the great late Buddy Rich)

IP Logged

raja.cedt Senior Fellow Offline Posts: 1516 Germany	Re: Question on loop bandwidth Reply #7 - Jun 3^rd, 2009, 8:08am hi buddy poor, � � � � � � � � � �exactly that's what even i am hoping, but all papers are telling previous wn is the rate at which PLL corrects error in closed loop. Now where is the mistake? If you have time just read go through some self bias pll's. thanks, Rajasekhar.
Back to top	IP Logged

buddypoor

Community Fellow

Offline

Posts: 529
Bremen, Germany

Re: Question on loop bandwidth
Reply #8 - Jun 3^rd, 2009, 8:17am

raja.cedt wrote on Jun 3^rd, 2009, 8:08am:

hi buddy poor,
exactly that's what even i am hoping, but all papers are telling previous wn is the rate at which PLL corrects error in closed loop. Now where is the mistake? If you have time just read go through some self bias pll's.
thanks,
Rajasekhar.

Please, can you give me a link to such a paper you are speaking of ?

Back to top

LvW (buddypoor: In memory of the great late Buddy Rich)

IP Logged

raja.cedt Senior Fellow Offline Posts: 1516 Germany	Re: Question on loop bandwidth Reply #9 - Jun 3^rd, 2009, 8:48am hi, please refer this reference. http://www.truecircuits.com/images/pdfs/maneatis03.pdf http://www.truecircuits.com/images/pdfs/maneatis96b.pdf in this papers or even pll books like gadner book you can find 'loop bandwidth wn' Thanks, rajasekhar.
Back to top	IP Logged

buddypoor

Community Fellow

Offline

Posts: 529
Bremen, Germany

Re: Question on loop bandwidth
Reply #10 - Jun 3^rd, 2009, 11:15am

Hi rajasekhar.

thanks for the links to the documents.
I am sorry , but at the moment I have no time to read it carefully.
However, I had a short look and I�ve seen that wn includes the term RC1
(see Equ. 16) which obviously (see Fig. 9) is the loop filter which contains a zero ! Thus, for my understanding the frequency called wn in the paper is related to a frequency response which includes the zero.
Perhaps there is only a misunderstanding regarding terminology between you and me and the paper.
Regards.

Back to top

LvW (buddypoor: In memory of the great late Buddy Rich)

IP Logged