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Lilylily

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question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Oct 21^st, 2009, 6:34pm

Hi, everyone.If I design a active RC filter with 1MHz cutoff frequency, it is said that the unity gain bandwidth of oamp in the filter structure must be 100MHz at least. Why? What is the relation between the bandwidtn of the filter and the unity gain bandwidth of the amplifier? Thanks to everyone!

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buddypoor

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #1 - Oct 22^nd, 2009, 2:28am

Lilylily wrote on Oct 21^st, 2009, 6:34pm:

Hi, everyone.If I design a active RC filter with 1MHz cutoff frequency, it is said that the unity gain bandwidth of oamp in the filter structure must be 100MHz at least. Why? What is the relation between the bandwidtn of the filter and the unity gain bandwidth of the amplifier? Thanks to everyone!

Sorry, but there is no fixed relation beween filter BW and the UGBW of the opamp. The problem is relatively involved and is caused by the non-idealities of the opamp gain and phase (!!!) when the frequency increases. More than that, the amount of influence of opamp "errors" on the filter transfer function depends on the filter structure - e. g. whether you use the opamp
a) as a VCVS (Sallen-Key)
b) an "infinite" amplifier (Multi-feedback)
c) as an impedance converter (GIC structures).

By the way, the last alternative is by far the best which means it is the least sensible topology to opamp errors. But it needs two opamps instead of one.
In general, the factor of 100 is relatively safe. For the case c) perhaps a factor of 20....50 may be sufficient - depending on your requirements regarding acceptable errors. Any further question ?

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

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Mayank

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #2 - Oct 22^nd, 2009, 8:55am

Hi Lily,

� � � � Quote:

What is the relation between the bandwidtn of the filter and the unity gain bandwidth of the amplifier?

�

� � I agree with Buddypoor that there's no direct relation between filter BW & reqd. Opamp BW. But would like to add a few things :--

1. �

A_∞ = -1/sRC = - w₀ / s
A(s) = V_out(s)/V_in(s) = A_∞ T(s) / ( 1+T(s) )

T(s) = -a(s) R/( R + 1/sC ) = ^a₀ / ( 1 + 1/w_p) �* ^s/w₀ / _{( 1 + s/w0 )} � where w_p ≈ w₀ / s

....aah, that was a pain...to type it out... Sad

Is from my notebook...had done this analysis sometime back...

So now you can see, there a magnitude fn A(s) which is close to desired function A_∞ as long as T(s) is large....

Ohh This eqn will make it more clear....

we can write from above --> �A(s) = -w₀/s �* � 1/(1+w₀/w_u) � * �1/(1+s/(w₀ + w_u))

The first term is the desired ideal term...
The second term shows magnitude error due to finite GBW
The Third term shows undesired shift in pole frequency(both mag+phase error) due to finite GBW..

I hope that makes it a bit more clear...through the mathematical analysis....

thanx,
Mayank.

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Mayank

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #3 - Oct 22^nd, 2009, 9:10am

Hi,

Extending the previous post [ tryin to be more elaborate ],

1. The first term A_∞ modifies only magnitude --> only integration time affected...

2. High Q filters are very sensitive to variations in the effective value of w₀. Hence we keep w_u ≈ 10x~50x w₀

3. Now assuming w_u >> w₀ ,

A_approx(s) ≈ -w₀/s * 1/(1+s/w_u)

so POLE_ideal = POLE_actual * (1+POLE_actual/w_u)

Do some more math...putting POLE = a + j*b
you willl find out :-----

1. Negligible change in POLE's imaginary part.
2. Real part affected by finite GBW.

BOTTOMLINE --

1. Finite BW -- Leads to Quality Factor Enhancement -- seen as excess peaking.

2. Finite Gain -- Leads to Quality Factor Degradation -- seen as droop in filter's magnitude response.

There are some ways to reduce amp BW requirements in high speed filters if you need them.

thanx,
Mayank.

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Lilylily

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #4 - Oct 22^nd, 2009, 6:48pm

Thanks to Buddypoor and Mayank!Thank you very much! I think I should study what you said carefully! Then talk about that with you!
Mayank, I can't see the picture! Maybe there is something wrong with it when you upload it. Could you upload that again or send it to my email? My email is lilei_81@163.com. And thanks again!

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buddypoor

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #5 - Oct 23^rd, 2009, 12:37am

Mayank wrote on Oct 22^nd, 2009, 9:10am:

.....................
There are some ways to reduce amp BW requirements in high speed filters if you need them.
..............................

Yes, that�s correct, there are some ways:
1.) Selection of a non-sensible topology
2.) Passive or even active phase compensation
3.) Method of "pole tuning": Replacement of a suitable part of the circuit (R or C) by an appropriate RC combination - using a simulation program based on the substitution theorem of network theory. But this method requires a realistic opamp macro model.

Regards

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

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Mayank

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #6 - Oct 23^rd, 2009, 10:37am

Hi,

@ everyone : some1 please tell me how to upload a picture here ? I have never been able to do it successfully.

@buddypoor : Yeah, you are right....These methods can be used to reduce opamp BW requirements...But there's one thing....Technique 2 & 3 are very diffcult to keep a track across PVT variations...If you know some really good method for compensation which tracks along with PVT....Please elaborate on it....non-sensitive topology

& as for 1. where you say , topology insensitive( well i wont say non-sensibile :P ) please elaborate on some non-sesitive topology ??

regards,
Mayank.

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Mayank Community Fellow Offline Posts: 334	Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp. Reply #7 - Oct 23^rd, 2009, 11:35am Hey Lily, Mailed you the picture...But received some mailback in some other language...Didnt understand it...Probably some Auto-reply from your account...Anyways, Tell me if got the image or not.... regards, Mayank.
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raja.cedt Senior Fellow Offline Posts: 1516 Germany	Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp. Reply #8 - Oct 23^rd, 2009, 7:11pm hi mayank, i didn't understand the understand the analysis what you have given? could you please send to raja.cedt@gmail.com... i feel for every filter architecture we can derive the relations and UGB depends on the input signal freuqency alsooooo Thanks, Rajasekhar.
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Mayank Community Fellow Offline Posts: 334	Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp. Reply #9 - Oct 23^rd, 2009, 8:31pm Hi , @ raja : that's correct...You can derive the relations for every filter arch. --- What i presented was for Active RC But, I didnt understand how UGB depends on input signal frequency ?? :o Please explain...
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buddypoor

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #10 - Oct 24^th, 2009, 3:07am

Mayank wrote on Oct 23^rd, 2009, 10:37am:

Hi,
@buddypoor : Yeah, you are right....These methods can be used to reduce opamp BW requirements...But there's one thing....Technique 2 & 3 are very diffcult to keep a track across PVT variations...If you know some really good method for compensation which tracks along with PVT....Please elaborate on it....non-sensitive topology

& as for 1. where you say , topology insensitive( well i wont say non-sensibile :P ) please elaborate on some non-sesitive topology ??
regards,
Mayank.

Mayank, I am not sure if I could understand you correctly (with PVT, do you mean "product verification testing"?).
There is a common understanding in the world of analog filters that the GIC topology is the best as far as sensitivity to opamp non-idealities is concerned. Regarding sensitivity to passive tolerances all circuits derived from passive ladder structures are the best (leapfrog or FDNR).
Was this your point?
Regards

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

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duncandu

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #11 - Oct 24^th, 2009, 10:02am

Lilylily wrote on Oct 21^st, 2009, 6:34pm:

Hi, everyone.If I design a active RC filter with 1MHz cutoff frequency, it is said that the unity gain bandwidth of oamp in the filter structure must be 100MHz at least. Why? What is the relation between the bandwidtn of the filter and the unity gain bandwidth of the amplifier? Thanks to everyone!

It's a rough estimation, and you can find several papers regarding to it. You can find some intuitive conclusion by analyzing the 1st or 2nd order filters by yourself, and you can then get some feeling. The analysis can be built on the classic 2-pole operational amplifier theory.
It is interesting that, actually, we just need the operational amplifier has a very large gain within your bandwidth, so if you can find some clever ways, you don't have to design a high-GBW operational amplifier. Because, in fact, the high-GBW requirement is based on the classic 2-pole operational amplifier, and you can design some novel operational amplifiers with transmission zeros. Remember, what you design is a continuous-time systems, you don't need to care the so-called doublet problem caused by zeros.

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Lilylily

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #12 - Oct 25^th, 2009, 8:43pm

duncandu wrote on Oct 24^th, 2009, 10:02am:

Lilylily wrote on Oct 21^st, 2009, 6:34pm:

Hi, everyone.If I design a active RC filter with 1MHz cutoff frequency, it is said that the unity gain bandwidth of oamp in the filter structure must be 100MHz at least. Why? What is the relation between the bandwidtn of the filter and the unity gain bandwidth of the amplifier? Thanks to everyone!

It's a rough estimation, and you can find several papers regarding to it. You can find some intuitive conclusion by analyzing the 1st or 2nd order filters by yourself, and you can then get some feeling. The analysis can be built on the classic 2-pole operational amplifier theory.
It is interesting that, actually, we just need the operational amplifier has a very large gain within your bandwidth, so if you can find some clever ways, you don't have to design a high-GBW operational amplifier. Because, in fact, the high-GBW requirement is based on the classic 2-pole operational amplifier, and you can design some novel operational amplifiers with transmission zeros. Remember, what you design is a continuous-time systems, you don't need to care the so-called doublet problem caused by zeros.

Hi, do the words "has a very large gain within your bandwidth" mean designing a op amp with large gain and a 3dB bandwidth equaling to the cutoff frequency of the filter I will design? and the amplifier used in the filter usually has one pole in the unity gain bandwidth, hasn't it?

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Mayank

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Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp.
Reply #13 - Oct 26^th, 2009, 9:51am

Hi buddypoor,
By PVT, i meant Process-Voltage-Temperature Variations... say Supply Voltage variation of 10 % , Process Corners-FF/SS/FS/SF(or monte-carlo), and Temperature range of operation(-40~125^oC)....

Well, but you got me almost right...GIC is by far the best topology insensitive to opamp non-idealities.... & the very reason i wanted to go for LeapFrog was because it's most tolerant against passive component variations...

BUT, GIC is quite a complex design...When should we chose to go for GIC ??

thanx,
Mayank

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Mayank Community Fellow Offline Posts: 334	Re: question on the bandwidtn of the filter and unity-gain bandwidth of the oamp. Reply #14 - Oct 27^th, 2009, 9:49pm Hi lilei & raja, I have mailed you guys the document, in case you dont check your mails regularly...Hope it helps... --Mayank.
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