some questions on the amplifier in the RC Active filter

[lily1981216]

how to adjust filters on amplifier

Hi,everyone,I have to design two filters having cutoff frequencies of 100kHz and 1.2Mhz. And I don't know how to select the amplifiers in the filters. And what is the requirement on the gain, bandwidthand so on?Thanks!!

 

[LvW]

calculate multiple r,c filter

Hi,everyone,I have to design two filters having cutoff frequencies of 100kHz and 1.2Mhz. And I don't know how to select the amplifiers in the filters. And what is the requirement on the gain, bandwidthand so on?Thanks!!

It depends on the filter structure selected by you. However, as a general rule the GBW of the opamp should be 50...100 times larger as the pole frequency of a second order filter stage.

 

[lily1981216]

3rd order rc filter calculator

what's the relation between the filters structure and the amplifier? Could you explain that in greater detail?Thanks?

 

[LvW]

what's the relation between the filters structure and the amplifier? Could you explain that in greater detail?Thanks?

Some filters use the opamp as an amplifier with "infinite" gain (multiple feedback structure) and some other use the opamp with feedback (limited gain, like Sallen-Key-structure). Another topology is based on impedance converters.
Each alternative has its own advantages and disadvantages. That is the reason that all alternatives are in use and no general recommendation can be given.
For filters with orders higher than 2 there is another attractive topology: active simulation of inductors in a passive reference filter .
In all cases the amplifier influence on the exactness of the transfer function is different. Those are the reasons that filter design is a task which requires a certain knowledge of the properties of all alternatives . It always results in a compromize.
Hope this helps a bit.

 

[mengcy]

Hi,LvW, I am confused by your explanation: GBW of the opamp should be 50...100 times larger as the pole frequency of a second order filter stage.

50~100 times larger is obscure and why?
I think the 0dB bandwidth of the amplifier set more than the product of the bw of the filter miltiply the gain is enough.

 

[FvM]

As you regard the answer as obscure, you're invited to calculate the exact transfer function of a second order filter build with a band limited (let's assume first order for convenience) amplifier by yourself. I hope, you'll immediately believe without calculation, that the transfer function must be of third order then.

As the most interesting question, in which way and how severe will the ideal filter transfer function be affected by the finite GBW? To anticipate part of the result, the filter cutoff respectively center frequency as well as it's Q are changed. The said factor 50 to 100 is a rule of thumb if you want to keep the ideal filter parameters with acceptable tolerance.

If the factor isn't feasible, you can adjust the filter dimensioning to consider the real amplifier. Because the real transfer function is actually third order, you possibly can't fit exactly the intended characteristics.

 

[LvW]

I completely agree with the above explanations.

A short remark/addendum to the last part of FvM´s contribution:
If the factor isn't feasible, you can adjust the filter dimensioning to consider the real amplifier

There is one special method to find the corrected component values in order to "adjust" the real filter transfer function (with a real amplifier) to the IDEAL value at one specific frequency, which e. g. can be the pole frequency.
This method makes use of a simulation program like SPICE and compares the ideal with the real response. From this it can compute and display the new component values.

 

[lily1981216]

Thank you very much! But I'm a little puzzled. Do you mean the amplifier should be selected according to the structure of filters(sallen-key,MFB,leap-frog)? And if I want to design a filter and I have known the cutoff frequency of the filter, should I determine the order of the filter first? Then compute the cutoff frequency of second order filters constituting the filter. And I use the cutoff frequency of the second order filters to determine the gain and bandwidth? At last determine the structure of the amplifier. Is the procedure right?

Added after 23 minutes:

As you regard the answer as obscure, you're invited to calculate the exact transfer function of a second order filter build with a band limited (let's assume first order for convenience) amplifier by yourself. I hope, you'll immediately believe without calculation, that the transfer function must be of third order then.

As the most interesting question, in which way and how severe will the ideal filter transfer function be affected by the finite GBW? To anticipate part of the result, the filter cutoff respectively center frequency as well as it's Q are changed. The said factor 50 to 100 is a rule of thumb if you want to keep the ideal filter parameters with acceptable tolerance.

If the factor isn't feasible, you can adjust the filter dimensioning to consider the real amplifier. Because the real transfer function is actually third order, you possibly can't fit exactly the intended characteristics.

Hi, do you mean the transfer function of the second order filter with a real amplifier
will become a transfer function of the third order filter?

 

[LvW]

Thank you very much! But I'm a little puzzled. Do you mean the amplifier should be selected according to the structure of filters(sallen-key,MFB,leap-frog)? And if I want to design a filter and I have known the cutoff frequency of the filter, should I determine the order of the filter first? Then compute the cutoff frequency of second order filters constituting the filter. And I use the cutoff frequency of the second order filters to determine the gain and bandwidth? At last determine the structure of the amplifier. Is the procedure right?
i

Yes, that´s the procedure - if I understood you correctly.
1.) Of course, the 1st step is to determine the order and the cut-off of the filter - according to the damping requirements
2.) Then, the structure has to be selected (cascade of 2nd order stages or based on a passive ladder structure). That is the most critical step as several aspects have to be considered (technical, economical, operational, ...), resulting in a compromize.
3.) Then, suitable active devices are to be selected. During this 3rd step it can be very helpful to use circuit simulation in order to proove if the amplifier chosen cause only deviations from the ideal response which are acceptable.