# Which resistors control the gain of this filter?

Update2: Nevermind the update1, question went far beyond its scope. Accepted answer was my expectation.

Update1: I have the filter(bandpass) design below, created using texas instruments filter design tool. I am also adding my specs to the question, in case it helps.

• Gain at center freq = 1 V/V

• Center freq = 1160

• Passband width = 80 Hz( I figured lowering this made filter design more easy, more possible, though I would expect the other way around)

• Stopband width = 400 Hz ( because of to be able to attenuate -/+ 300 Hz by 20dB, I chose 400 instead of 600 just in case, thinking about the non-ideal problems may occur)

• Stopband attenuation = -40dB ( I have chosen 40dB just for in case, 20 or so is enough)

• Allowable passband ripple = 1dB (not sure what this affecta, this was standard on filter designer software)

• I can reach E12 resistors(%10) and E12 capacitors(%10)

These are the specs I have also used in the design tool.

The filtering action of the circuit below is close to desired. I have examined freq response with an oscilloscope + signal generator combination. I was expecting a gain close to 1 V/V , but it is actualy 0.15 V/V or so. Therefore, I want to increase the gain without affecting the center frequency. Is this possible? I have thought that gain can be arranged by the ratio of R5_S3 and R4_S3, and changed R5_S3 to 10k, but it did not affect gain, actually it did no difference, I can say.

So, I wonder which resistors can control the gain of this filter, if it can be controlled of course.

• Comments are not for extended discussion; this conversation has been moved to chat. Any conclusions reached should be edited back into the question and/or any answer(s). Dec 29, 2019 at 2:21

Every resistor in that filter impacts both the gain and the frequency response. Ditto the capacitors. I'd just put a gain stage in front of it, or behind it.

• Hmm, it's also my backup plan. I just wanted to know if I can do it within this filter or not. Dec 28, 2019 at 0:39
• You'd have to redesign the filter, in which case it'd probably be easier to just look up some op-amp filter topologies in a book and roll your own. Dec 28, 2019 at 0:44
• Consider you have 3 op amps there. They don't tend to come in packages of 3, but rather 2 (OPA2743) or 4 (OPA4743). So you can probably use a 4th for gain. Dec 28, 2019 at 1:54
• @ChrisStratton actually, all scope of this question was to know whether I can bypass using one more stage of amplification or not. It looks using one more stage will be easier. Dec 28, 2019 at 2:03
• ACtually Tim, This suggestion does not fix the real problem which does not need a flat gain fix but rather a bandpass ripple tolerance fix, where certain combinations of error tolerance result in horrible ripple gain errors by shifting high Q poles. So the fix is lower all Q's and tolerance errors simultaneously with increasing number of stages to reduce overall sensitivity. Any fixed 20dB gain added will likely drift with small 'C changes caused by small tolerance errors Dec 28, 2019 at 19:57

rant: The 1st stage attenuates almost 60dB . WHy? and you want gain??? or are you misreading in 0.15 dB is pretty close to unity gain. What's wrong with this picture and where are your design specs?

High Q pass filters are not easily realized with steep skirts.

Analysis

OK now reason with your critical specs. Your design has -60dB 1st stage then +30dB with two more stages to try and get the step skirts you asked for. Bad idea.

Your BPF specs had BWp=80 Hz (pass) yet BWs=400 Hz(stop) @ -40dB

Recall 1 order = -6dB per octave and 400/80=5f or just more than two (2) octaves or -15dB but you need -40dB which demands high Q

• so high and ultra-precision low tolerance caps are needed (\$) <1% means just over 2 octaves attenuate. What the TI filter did to realize this was very high Q to get step skirts then attenuate the front end stage 1 with -60dB , when you should have realized you need high Q so make it high gain (40dB) and use a pad attenuator if necessary.

If you try 1% parts and realize your gain error is too high then you need more stages like 8th order or more .

Conclusion: inexperienced specs. NO sanity checker on TI Filter designer. but does have tolerance selector but sub-optimal error analysis.

You may have to go higher order stages or more expensive lower tolerance parts.

Inverting filter amplifiers use only negative feedback. Sallen-Keys uses positive feedback

Always balance your Rin values to eliinate DC input offset voltage from bias current when required and if using CMOS Op AMps , scale all parts to use 5k Min. or 10k Min.

This design is incomplete. When filters are near Q=30 , the tolerances and cost of components OR errors are high. Also group delay distortion is also high.

======================================================================

## edit

Last attempt to maximize tolerance and stay within 1dB error in Passband. Sallen-Key design while having fc/fBW =1160/80(min) with steep skirts in TI Profilter.

Conclusion Since all caps are same value , if matched but off by 1%, that's Ok R=10% is terrible for ripple, R=1% can cause> 3dB ripple R=0.5% meets spec of 1dB ripple with 1% caps.

I can zoom XY axis on filters with mouse but it is tricky to see ripple in PB.

• I guess the first thing that strikes me from the above is that the one pole $-6\:\text{dB}$ skirts spec is after quite a distance from the center frequency. With high Q, the shape near the center is different. An off the cuff calculation says that even with three poles, with the center pole set to half the Q of the outer two, we are talking Q values in the hundreds. Insertion loss is huge after getting to the number of poles needed to bring Q into reasonable range and with reasonable precision parts. This is not a neophyte design problem. And the 1 dB spec is harder on Q than maximal flat.
– jonk
Dec 28, 2019 at 9:14
• @jonk if you read the text in my image you can read each pole and Q. But @ Tim is only half right . Not only the R’s but every C affects the gain thru passband (PB) by ratios and positive feedback before 180 deg phase shift of every RC ratios. In math the sensitivity of gain for each part may be computed by partial derivatives. You must improve this by choosing the design with the lowest Q in each stage or as prompted the lowest MAX Q ( Usually Bessel) and then force the design to twice as many stages like 8 using two Quad OA’s instead of 3 or 4. THen examine change withComponent tolerances. Dec 28, 2019 at 17:01
• TL;DR I See @Tim said ditto to the Caps. This explains the problem , I went more after the solution. Dec 28, 2019 at 17:10