Infinite Gain Multiple Feedback Active Filter

You need to understand that OP AMPS are not the 'ideal components' of theory so you can't go wild with resistor values and expect it to work.
I havn't read through the tutorial, but hopefully it should explain the theory, and the practical limitations.
If you are looking a the audio spectrum you should find it relatively easy. At higher frequencies it all becomes a mess where layout is as important than components, which is why I hate RF.
I'm not trying to give a full answer just give you a nudge in the right direction.
The 'gain bandwidth' product of an opamp may be a useful concept to check out.
It may help us all to help you if you tell us what you are playing with. Are you just starting out with electronics or you have some formal education in the subject or it's relevant to your job or what?
Del

I am not playing around with electronics, and yes I have read and worked with electronics. I wanted to understand the reason/concept of calling it an infinite gain filter.

I presently want to build a good bandpass filter with high Q, low bandwidth for 10-11 kHz. I was wondering if using IC 741 in the circuit would be a good idea. If yes, I could proceed to calculate the optimum values of the resistors and capacitors (from the standard values available in the market) for passing only the required frequency.

'Playing' was not meant as a derogatory term, many of us in the field started out, and still learn by playing.
A quick google suggests that the gain bandwidth product of a 741 is about 1 million. Therefore at 11khz the maximum gain would be about 91 which is a long way below infinite.
Personally I think the name Infinite Gain etc is silly and confusing.
There are people on CR4 vastly better qualified than I to comment, I was just trying to get this party started.
Del
<exits left singing>

"Personally I think the name Infinite Gain etc is silly and confusing."

Me too. It just goes to say that "ideally" it can be as high as possible right?

Sorry if I sounded rude Del, or if I thought you sounded rude

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The use of the terms "infinite gain" is not silly but it clearly can be confusing. As you highlighted Del, the article is implying that the analysis that they are presenting assumes infinite gain of the amplifier. No amplifier rolloff effect comes into play in this analysis but depending on the frequency and amplifier chosen it certainly can become a noticeable effect. Another frequently ignored difference between an ideal and real amplifier in filter usage is the input and output impedance characteristics of the amplifier. It is because of the subtle effects that an amplifier can make that I applaud and support the idea of playing with filter design circuits. Op-amps are cheap today, also the pin configuration is fairly well standardized today. So I recommend that one should try different amplifiers in identical circuits to see what, if any, effect the choice of different amplifiers will have on a circuit.

So why exactly is the term "Infinite gain" used? And what does it mean in this context?

"Infinite gain" is used as an assumption that for all frequencies the gain of the amplifier in open loop will be infinite. So that the components closing a feedback loop will be the only thing setting the actual gain of the circuit. In the case for the cited, reliable but antiquated μA741 op-amp it has an open loop gain of about 104 dB with a ±12V supply. This puts the voltage gain of the amplifier at about 160,000 for a DC signal. So if you have a 1V DC output from a 741, then the difference between the + and - input pins will be 1V/160,000≈6μV. (This is not the offset voltage or current parameter.) However, this chip has a gain bandwidth product nominally of 1.5 MHz. So if you are getting a 0.1 VPP 1.5MHz signal on the output then the difference between the + and - pins at 1.5MHz will be 0.1VPP.

Okay, so I will use the resistor between the capacitors' junction and ground.

Let's go to some basic op-amp circuitry usage. If you use the antiquated but reliable 741 op-amp with a gain bandwidth product of 1.5MHz in an inverting gain configuration of just two resistors. Rf=210k and Ri=1k. One would expect that the voltage gain would be -Rf/Ri = -(210k/1k) = -210 This then makes a low pass filter amplifier without any lumped element capacitor of 1.MHz/210≈7.1kHz. There is no capacitor in this part of the discussion.

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The so called infinite gain only apply to the theoretical aspects of the operational amplifier. In reality you need to put or define your circuit's boundary conditions. Almost always, besides the necessary circuit elements needed for it to function properly, the main limiting factor will be your chosen power supply! No matter what the computed gain you may arrive at, you cannot go beyond the level of the supply voltage!

Hi One & All,

Can you give us more detail? Like Min & max inputs levels, what output levels need and what is the Bandwidth need plus what is the over all project?

BEN

Are there anything else I can do to make it closer to the ideal bandpass filter?

As others have pointed out, your real gain is limited by the gain bandwidth product of the op amp. 741 has been around a long time, and there are a lot of faster op amps available.

Proper impedance matching, for both input and outputs should be one of your primary concern in your designs, ie. Hi Q filter. Although OpAmps by themselves can be considered to exhibit very high input impedances, actual designed input parameters /components will alter those characteristics as well as how they will behave with the surrounding circuitries.

Thanks :-) What would be a good value for Q factor, I guess it shouldn't be too high or low. But its specific value?

Your Q of the filter is set by the the bandwidth and center frequency.

B=ω_h-ω_l

ω₀=√(ω_h*ω_l)

Q=ω₀/B

I know the formulae. I mean practically for about 10- 11 khz what would be a good Q factor for the filter?

Okay at the 3dB value for my 10.6 kHz filter, I have kept a tolerance of 0.6 kHz on either side from the center frequency. Which gives me Δf = 1.2 kHz. So Q = fr/Δf ,

thats sets Q at 10.6/1.2 = 8.5. Does this make my filter too choosy, that it wont respond to variations from my oscillator or is the Q factor good?

I cannot say from what you've posted. You've only identified what you want for a pass band for this filter. You did not identify either the stop band or what the following circuitry will receive. The slope out of the pass band for any single pole filter (you have one of your poles for the high frequencies and one for the low frequencies) will be 6 db per octave which is also known as 20 db per decade. So taking the low frequency side, a 5 kHz sine wave will be attenuated by (10 kHz/5 kHz)*6db+3db=9db.

Here is a program for calculating Multiple Feedback Filters for Bandpass.

http://sim.okawa-denshi.jp/en/OPttool.php

It also seems to have links to highpass, lowpass, and others

OOPS!

The link I gave you takes you to the low pass version of the filter. If you go to this one: http://sim.okawa-denshi.jp/en/OPtazyuBakeisan.htm, it will give you a big bunch of various filter types. Look for "MULTIPLE FEEDBACK BANDPASS FILTER DESIGN".

I must confess that I have NOT used this software before. I just grabbed the first thing that looked good, but I am very impressed with it. Just for the heck of it, I ran a filter similar to what you are talking about... f= 11 KHz, Q=5, Gain=10.

I noted that they have shorthand. For example entering "11K" for frequency gives you 11 KHz. It beats the heck out of entering 11,000. On capacitors, .001u for microfarad, p for picofarad, and I assume n for nanofarad.

In entering design values, I had to enter Quality factor Q = 5 and hit the button to keep the program from using damping factor.

In running the program, I noted that the resistor results were all 5% values. As I said earlier, we use 1% resistors. I found a box labeled Select Resistor Sequence. I set the value there to E96 and ran the problem again. This time, it gave me 1% resistor values. I did not fiddle with Capacitor Sequence as it is not really applicable.

If you know little about OP AMPs you might want to take a look at "OP AMPS FOR EVERYONE" by Ray Mancini. I got my copy off the internet when Ray worked for Texas Instruments (a possible source).

Anyhow, have fun

Bill

WOOPS!

That last link takes you to the lowpass section. The GENERAL filter section is here.

http://sim.okawa-denshi.jp/en/Fkeisan.htm