Hey all

I have an issue with the response from a BPF I created, however I do not know how to approach explaining it. The issue is this;

I have a very narrow bandwidth BPF (4-7Hz - for an EEG brainwave filter), I designed it using the sallen-key topology and using a buttersworth response and its 4th order. Simulated using multisim the passband region is pretty much flat and then drops off nicely at the transition.

However in reality when breadboarded the response was much more like a bell curve, where there was a peak in gain at the centre frequency (above the gain calculated for) and the gain expected was seen much closer to the -3dB points. So in essence, my buttersworth response wasn't very 'maximally flat'


I have spent a good few days trying to find a way to explain this but haven't found very much. My thoughts are; that either there is some issue due to how small the bandwidth is, which is resulting in the fact that transitioning from the stopband to passband and visa-versa creates the curve. Or that its something more to do with the design?

However I have nothing other than assumptions to back this up, any input would be greatly appreciated
Rob

 

If you would post a schematic diagram of your filter, exactly as you built it, people might be able to help you; as it is, I can't even hazard a guess...

 

Schematic, schematic, schematic. And... From 4 to 7 Hz is less than 1 octave, so the centerpoint of your passband is less than 1/2 octave from each corner frequency. Flatness takes more width in the bandwidth to manifest. You probably could get about the same response with a resonant-tuned circuit. Also, real world components have tolerances that mess up sensitive designs. The amplitude response at your two corner freqs will not be exactly as predicted, even with 0.1% resistors and 1% capacitors. Several octaves away the passband will be flat and the attenuation slopes will be right on track, but no way within 1/2 octave.

ak

 

I have spent a good few days trying to find a way to explain this but haven't found very much. My thoughts are; that either there is some issue due to how small the bandwidth is, which is resulting in the fact that transitioning from the stopband to passband and visa-versa creates the curve. Or that its something more to do with the design?

Your pass band is very narrow and the frequencies are very low. Simulations don't take all important factors into consideration; for instance, the ability to find precision components. You probably need more stages and/or sacrifice some pass band signal.

 

I suspect it's the tolerance on the components that makes the difference between the simulation and the real world.
Run some Monte Carlo simulations in Multisim with varying component tolerances to see this effect.

 

OT: I once worked in an R&D lab back in the late 70's and had a newly minted PhD ask me where he could get some 100 micron prisms. I had to explain to him that he was now in the real world and his theory and simulations would need to be adjusted for reality... Definitely highly educated, but I wasn't at all impressed with his common sense...

We used SPICE for some simulations back then, but computers were so slow that we still did most of our design work in our head... Seems that is now discouraged... Pretty soon, maybe already, people will be doing the equivalent of using a calculator to add 200 + 200. No joke, I've seen people do it...

Okay, I'll get off my soap box now and the flaming can begin

 

Don't need a calculator when you have one of these around

 

No Problem
I wasn't sure whether this was a phenomena that was a general attribute found in electronics or something more specific. My Filter; Except I used OPA4277 not the OP07



And oh don't worry, im only just out of an engineering apprenticeship and ive seen some physicists ask some very silly questions I am doing a degree in electronics and I never expected my in real life results to reflect my simulations, but I was looking for a way to explain the differences I will run the simulations mentioned in multisim, I hadn't realised you could do that in mutltisim, but thinking bout it, it would make sense to have a function like that

I am sure component tolerances did have an effect, but what are your thoughts on what I said about how tight the bandwidth is? how quickly can an op-amp transition from the pass to stop band? surely it is limited. So with a bandwidth of 4-7Hz (in my not so experienced) opinion I wouldn't have been surprised if it took a couple Hz to transition.

 

Ops, mistake in first post, its Multiple feedback, not sallen-key

 

how quickly can an op-amp transition from the pass to stop band? surely it is limited. So with a bandwidth of 4-7Hz (in my not so experienced) opinion I wouldn't have been surprised if it took a couple Hz to transition.

Op-amps have surprisingly fast response, so I think this is not the problem at less than 10 Hz.
Look at GBW (Gain Bandwidth Product) or SR (slew rate). These are both limits on the speed of an op-amp.

The slew rate of a sine wave is 2 Pi F Vpeak
The gain-bandwidth listed on the datasheet is divided by your gain to get bandwidth.
Sorry. That sounds like a dumb thing to say.

 

No, No, thank you guys you've given me some stuff to think about which is exactly what I wanted I know its not the GBP, as the bandwidth is absolutely tiny and im at unity gain. my GBP is currently like 3

I will have a look into octaves so thanks AK, somehow I missed your post first time round

 

An opamp doesn't "transition" from one part of a frequency response curve to another. Nanosecond to nanosecond it is solving the feedback equation and presenting an answer based on its inputs. In a Bode plot the gain is cruising along until it hits a nice sharp corner, then it moves along the next plot segment until it hits the next corner, etc. That is a representation of the real world, not the world itself. The actual amplifier is running at maximum gain all the time at every frequency. Negative feedback turns down the inputs until the outputs are what is desired, but the subtraction that makes that work happens *outside* the opamp's transistor circuits, usually at the inverting input pin and the input differential pair. A standard opamp is a differential amplifier - the difference happens at the input emitters and doesn't amplify anything, followed by an amplifier running flat out max gain all the time. Everything else is outside. It seems like a trivial point, but it is critical when trying to understand why opamp circuits are not working. The device pins and their connections are not part of the amplifier itself, they are external components.

ak

 

Ahh indeed, thank you AK, that is some very useful information. I have learnt something today It may be trivial and probably won't help with my write-up at present, but its certainly something that I think will help me in the future I much prefer to understand something to a more fundamental level than to simply be able to do/calculate said thing. I think I need to spend more time looking at the internals of an op-amp, we barely scratched the topic in regards to this in my course.

 

Some random thoughts...

At the frequencies you're working at and with the opamps you've chosen, I can't imagine that opamp GBW could be an issue. If the frequencies were a hundred times higher, yes; but not down in the single-digit Hz.

In my experience, simulation programs such as PSPICE, LTSpice IV and (I assume) Multisim can give terribly off-the-wall, screwy results for some circuits under some conditions; but one thing they typically do NOT screw up on is the frequency response characteristics of filter designs, especially when opamp GBW is not an issue. If the simulation results you've obtained do not match what you're seeing from the hardware, my best guess is that component tolerances (especially capacitors) are the culprit. If you're not using capacitors at least as tight as +/- 5%, you're going to have problems. +/- 1% capacitors would be even better.

As has been pointed out, your range of frequencies of interest doesn't even cover a full octave and that's a pretty narrow range; I question whether you will be able to obtain adequate filter performance (passband flatness + stopband attenuation + sharpness of transition) with only 4 poles. 6 poles, or even 8, might be more like it. Unfortunately, the more poles you try to stack up, the more critical component tolerances become, and in the end you could just make the problem worse.

Have you considered digital filtering? At low frequencies like these, it might be worth considering and you could get REALLY high performance.