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Design >> Analog Design >> Unity Gain Frequency(and filters)
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Message started by Turin on Jul 28^th, 2008, 8:10am

Title: Unity Gain Frequency(and filters)
Post by Turin on Jul 28^th, 2008, 8:10am

This might sound a silly question but i'm a little mixed up at the moment...Let's say we have an intergrator with a certain unity gain frequency.If we had a Gm-c filter with this intergrator how would the unity gain frequency relate to the filter frequency.Would it be the same or would just be depened on it in a cetain way...?

Title: Re: Unity Gain Frequency(and filters)
Post by buddypoor on Jul 28^th, 2008, 9:13am

Well, a general answer cannot be given since it certainlydepends on the filter order and topology. However, for a second order stage very often the pole frequency wp is identical to the square root taken from the product of the integrators unity gain frequencies.

Title: Re: Unity Gain Frequency(and filters)
Post by Turin on Jul 28^th, 2008, 9:26am

What i had in mind is an elipictal 3-rd order Gm-c filter

Title: Re: Unity Gain Frequency(and filters)
Post by buddypoor on Jul 28^th, 2008, 9:38am

OK, but what is now your question ? I suppose you have a circuit diagram and corresponding formulas, don´t you ?

Title: Re: Unity Gain Frequency(and filters)
Post by Turin on Jul 28^th, 2008, 10:11am

My question is how is the unity frequency or the Gm of the intergrator for that matter affect the filter behavior,frequences and responce.

You see i have a completed filter and i'm to redesign it in a different technology.I need to now what parameters i need check in the different parts of it to make sure I end up with the "same" responce.

What i understand is that from the passive prototype you can get the block diagram and from that the intergrators Gm.So can I use the Gm or even better the unity frequencies to determind the filter behaviour?

Title: Re: Unity Gain Frequency(and filters)
Post by buddypoor on Jul 28^th, 2008, 10:44am

At first, I assume you speak about a LOWPASS response, right ?
(because it could be also highpass or bandpass).

For elliptic lowpass filters there are some different topologies available (that means different circuit diagrams) - even when they are derived from a passive prototype.
Each circuit alternative has it own design parametrrs - that means, without a circuit diagram nobody can give you any information.
Sorry, but that´s the problem of filter design: A lot of alternative solutions with different and mostly conflicting pro´s and con´s.
But I suppose you have got some design formulas, don´t you ?

Title: Re: Unity Gain Frequency(and filters)
Post by Turin on Jul 31^st, 2008, 10:37am

Yes...I'm talking of a lowpass filter.This is the topology of the filter and the passive prototype

Title: Re: Unity Gain Frequency(and filters)
Post by loose-electron on Aug 3^rd, 2008, 3:24pm

For the active amplifier version of the filter a general rule should be to keep the amplifiers parastic responses well outside the bandwidth of the active filters ole placement.

For example a 500MHz filter should be done using amplifier that have at least 800MHz BW at the worst PVT corner.

That way the response of the amplifier does not interere with the response of the filters defined poles (Bessel, Elliptic, or Whatever pole constellation)

Generally, that tends to be the approach used, FWIW.

-Jerry

Title: Re: Unity Gain Frequency(and filters)
Post by buddypoor on Aug 12^th, 2008, 2:29am

Turin wrote on Jul 28^th, 2008, 10:11am:

My question is how is the unity frequency or the Gm of the intergrator for that matter affect the filter behavior,frequences and responce.

In order to answer this question it is necessary to derive the filters transfer function from the active circuitry.
Another way would be to evaluate the steps which have led from the passive to the active structure. In this case, you could use the internal differential equations (passive state space equations) to find the relations to the integrator stages of the active circuitry.
These are the only alternatives available to find the relations between flter parameters and the various integrator time constants.

Title: Re: Unity Gain Frequency(and filters)
Post by vivkr on Aug 12^th, 2008, 7:06am

As already mentioned in various replies,

(a) you will need the active element to have a bandwidth a fair bit larger than the highest passband frequency.
(b) the filter topology chosen has a decisive influence on the exact amount.

You could do a sensitivity analysis. This can be done either by solving equations, or else, you just build a simple model of the filter, modelling the nonideal parameters of interest for your active elements (such as bandwidth), and simply do a little bit of parametric simulations to see the effect of the finite bandwidth on overall TF. You know the limits you must fulfil. You can get an idea of the required bandwidth.

However, atleast a very crude analysis on paper is good because then you know what influence you can expect from the finite bandwidth. Also, this allows you a good comparison between different topologies (of course, that can also be simulated, and much faster too).

Regards
Vivek

Title: Re: Unity Gain Frequency(and filters)
Post by buddypoor on Aug 12^th, 2008, 7:34am

Finally, after vivek´s reply, I`ve got the impression that there is a kind of misunderstanding between the questioner "turin" and the answering person(s) - perhaps only me ?

If turin speaks about the "integrator unity gain frequency" I assume he means what it sounds like: The frequency at which the integrator stage has a gain of unity - and the integrating time constant Ti is the reverse of this frequency.
But, of course, this is NOT the unity gain frequency of the active element alone, which - as it was stated - has to be much larger than the integrator unity gain frequency 1/Ti.
Hello turin, can you clarify this ? What do you mean with "unity gain frequency" ?

Title: Re: Unity Gain Frequency(and filters)
Post by Turin on Aug 15^th, 2008, 6:12am

Thanks for the replies everyone.....

When i say unity gain frequency of the intergrator in Gm-c filters i mean:

ω=Gm/C....(with Gm and C refering to the transconductor and capasitor of the intergrator )

Title: Re: Unity Gain Frequency(and filters)
Post by buddypoor on Aug 16^th, 2008, 5:03am

Turin wrote on Aug 15^th, 2008, 6:12am:

Thanks for the replies everyone.....

When i say unity gain frequency of the intergrator in Gm-c filters i mean:
ω=Gm/C....(with Gm and C refering to the transconductor and capasitor of the intergrator )

OK, that was already - and still is - my opinion. In this case, my reply No. 8 from august 12th is valid. That means, your question was NOT related to any parasitic amplifier influences and you are interested instead in the relation between the integrator time constant (it´s a better term that its reverse: integrator unity gain frequency) and the characteristic filter parameters. But, as I have mentioned, a general answer is not possible - it mainly depends on the chosen filter structure and the element dimensioning.