active band-pass filter design

Both limited gain and bandwidth of real OPs affect the filter characteristic. Good filter tools are able to design the filter for known real OP parameters.

lhlbluesky said:

when i change the opamp to a ideal VCVS source (gain=10000), the simulation result is Ok (f=19.9KHz, Q=5.5). why? what other reasons can make the bad simulation result?
thanks all, pls help me again.

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Just for clarification:
All (classical) filter formulas for mid frequency and Q are based on the assumption of IDEAL opamps (infinite GBW).
Therefore the deviations between real and ideal.

'Good filter tools are able to design the filter for known real OP parameters', what is the good filter tool, FvM, can you give me a web link or a copy?
besides, about the following stage's loading equalization, is there any advice? may i use a low-output-resistance opamp? if so, can anyone recommend some related circuit structure (low power consuming structure)?
waiting your help.

Nuhertz Filter Solution can do the design optimization conveniently, but it's not free.

You always have the option to adjust the component values in a SPICE simulation (e.g. using free LTSpice) until you meet the intended filter characteristic. PSpice optimizer can adjust component parameters automatically.

but i use the hspice tool, what other ideas?
thanks all for your help.

Hspice as all required features:
- laplace (s-domain) description of prototype filters
- optimization of circuit parameters to adjust a frequency characteristic or pulse response according to the prototype

thanks FvM. but i also need help. in simulation, i found the simulation result (f0, Q, gain) is far away from the theoretical value of calculation. and i doubt that, the opamp is non-ideal, the opamp introduces the simulation error. so, for the 2-order MFB bandpass filter (as the picture shows in previous post) , can anyone give me the transfer function and f0/Q/gain/BW expressions when considering opamp non-ideal characteristic, such as finite opamp dc gain, etc. i have tried to obtain the expressions, but it is too complicated. so i need your help. thanks.

lhlbluesky said:

can anyone give me the transfer function and f0/Q/gain/BW expressions when considering opamp non-ideal characteristic, such as finite opamp dc gain, etc. i have tried to obtain the expressions, but it is too complicated. so i need your help. thanks.

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Ihlbluesky, that is a very uncommon and a very bad approach. The real opamp not only introduces errors (if compared with calculations) caused by the finite open-loop gain but also due to its phase shift.
That means: The order of your circuit is increased. The main advantage of an opamp is the fact that it can be used WITHOUT considering its real characteristics. Thus, the transfer function is determined by external components only. Because nobody would design such a circuit, no formulas are available for filter parameters including real opamp characteristics.
Why you are using such a "bad" opamp with 40 dB gain only?

i have tried to obtain the expressions, but it is too complicated. so i need your help.

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Help for what? We won't be able to simplify the expressions. They are as they are.

There are basically two methods:
- make the OP gain and gain bandwidth product sufficient high that the ideal transfer function is achieved with acceptable error. This way is e.g. pursued by TI's Filter Pro Desktop and should work at least for medium frequency ranges (e.g. < 100 kHz-1MHz) with recent OPs.

- calculate the real transfer characteristic numerically and adjust the component values to approximate the ideal characteristic. I sketched it as optimization methods with PSpice or Hspice. This approach will be at least necessary for high frequency active filters where comfortable OP bandwidths aren't available.

Nuhertz shows the difference between real and ideal filter characteristics caused by real OP parameters or component variations, but requires a manual optimization.

FvM said:

calculate the real transfer characteristic numerically and adjust the component values to approximate the ideal characteristic.

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I will explain in somewhat more detail what can be done:

1.) Design the filter according to the formulas available for ideal opamps;

2.) Now - using real opamps resp. real opamp macro models the simulation will reveal deviations from the desired behavior (bandwidth smaller, Q larger, pole frequency smaller).
However, these deviations will/must be acceptable - as long as they are within the specification limits (depending on the particular application);

3.) If the operating frequencies (pole frequency) are relatively large in comparison to the transit frequency wt of the opamp used (larger than 1/00 of wt) , the deviations will NOT be acceptable.

4.) In this case, there are, in principle, three alternatives to modify one single path within the passive network surrounding the opamp with the aim to correct (at least: partly) the error.
4a) As mentioned by FvM: Optimization features of the simulation program
4b) Usage of specific formulas (as far as I know available only for Sallen-Key 2nd-order topologies) which allow a kind of "pre-distortion".
That means: The ideal filter structure (parts values) is pre-distorted in such a way that the real opamp will produce smaller errors.
4c) Usage of a specific "optimization" configuration based on the substitution theorem (only little known). As the result - one single ac analysis can tell you, for example, how to replace a resistor by a new RC combination in order to partly compensate the errors.

in my simulation with non-ideal opamp, i adjusted the R and C value to get the right center frequency f0 (20KHz), but the Q value is much smaller than i calculated (less than 2 for a calculated value of 7), and i changed the R and C value as the ideal formula showed, but Q changes only a little (not change basically), it is very strange.
besides, i added a capacitor Cout in the output of MFB bandpass filter as some paper advised, then, the f0/Q/gain value all changed, and Q has a little improvement. why? what is the role of this output capacitor? why can it change the value of f0/Q/gain? and should i add this Cout cap or not? why? the filter's loading is a resistor-type inverting amplifier as i said previously.
finally, i really appreciate for all your help.

in my simulation with non-ideal opamp, i adjusted the R and C value to get the right center frequency f0 (20KHz), but the Q value is much smaller than i calculated (less than 2 for a calculated value of 7)

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Insufficient OP gain is a possible explanation.

Capacitive output load creates an additional pole in loop gain. It tends to increase the filter Q, the same as limited OP bandwidth.

Generally speaking, every deviation from ideal filter circuit will have some effect. It can be either analysed exactly or evaluated by trial and error method.

lhlbluesky said:

in my simulation with non-ideal opamp, i adjusted the R and C value to get the right center frequency f0 (20KHz), but the Q value is much smaller than i calculated (less than 2 for a calculated value of 7), and i changed the R and C value as the ideal formula showed, but Q changes only a little (not change basically), it is very strange.
besides, i added a capacitor Cout in the output of MFB bandpass filter as some paper advised, then, the f0/Q/gain value all changed, and Q has a little improvement. why? what is the role of this output capacitor? why can it change the value of f0/Q/gain? and should i add this Cout cap or not? why? the filter's loading is a resistor-type inverting amplifier as i said previously.
finally, i really appreciate for all your help.

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Ihlbluesky, that is no systematic procedure to correct deviations. I do not recommend to proceed further.
Why do you not answer the question (from FvM) regarding the opamp? Why such a bad unit?

thanks all, especially FvM and LvW. i will try again.