# How to select a low-pass filter

1. May 27, 2012

### Niles

Hi

I have a general question: When I want to choose a low-pass filter, then what parameters of the signal determine what frequency it should have? I know my question is broad, but I would appreciate some pointers.

Best,
Niles.

2. May 27, 2012

### yungman

The important thing is first to know what is the cut off frequency.....the -3db frequency. Then if you know the frequency that that is giving you trouble and how much lower you want to attenuate that frequency.

For example, you set the -3db at say 10KHz. You have an unwanted frequency peak at 20KHz. Then the important question is how much attenuation you need for the 20KHz frequency. This govern what kind of filter, how many poles you need.

Of cause, depend of the application, you need to worry about the input output impedance.

With that, you can look up in the filter graph to find the attenuation of the frequency you want to avoid ( 20KHz here).

More detail is the pass band ripple, that is variation of the response in the pass band ( 0 to 10KHz here).

Then you have to worry about the phase change and all the other details.

3. May 28, 2012

### Niles

Hi

Thanks, that is a good explanation. It answered many of my un-asked questions. A LPF is also an integrator: Is there a relation between the cutoff frequency for a LPF and its integration period?

Best,
Niles.

4. May 28, 2012

### yungman

No, a LPF is not an integrator at all. Integrator integrats the signal and present a voltage to the total charge from the period of integration, LPF is a LPF.

You must saw an opamp integrator with a feedback cap called integrating capacitor. You see a large value in parallel with the cap and you think that is like a low pass filter. But it is not. The resistor in the integrator is very high value just to keep the opamp in DC close loop. In LPF, the resistor is part of the calculation of the pole and zero.

Besides, when I talk LPF, I don't even think of these kind of simple opamp. I am thinking of the multi pole passive LC filters or active filters. It is a totally different animal. You can write a book just on the filters.

5. May 28, 2012

### rbj

the words "at all" are an overreach. an LPF need not be an integrator, but an integrator is an example of a low-pass filter since the gain at lower frequencies is more than the gain at higher frequencies.

certainly not all low-pass filters are integrators. but i would say that every integrator, by itself, can be classified as a low-pass filter of some sort.

6. May 28, 2012

### yungman

Even if you consider only the inverted opamp type, the time constant has to be so different and they not doing the same thing.

LPF can be of different configuration as I stated. I designed integrator before, usually you need a reset switch like a mosfet switch.

7. May 29, 2012

### the_emi_guy

Dude, an integrator is a low pass filter.

8. May 29, 2012

### the_emi_guy

Niles,
Are you interested in digital filters, analog discrete filters, or analog op-amp filters?
If you are not sure what these are, that's o.k. too, just let us know as much as you can.
Are you trying to build something is particular? Do you know about what frequency range you are working in?
There are many (probably in the hundreds) of parameters that potentially come up when designing a low pass filter. This is a big topic. Help us out and we can narrow down the list. If you have a particular interest in integrators we can discuss that.

9. May 29, 2012

### yungman

Only one of the most basic type of integrator looks like a low pass filter. A lot of the integrators comprise of a reset switch to discharge the integrating capacitor and that absolutely cannot be a low pass filter.

As I said before, even the simple integrator that looks like a low pass filter will have the frequency response so different it is miss leading to think of them as two of the same.

10. May 29, 2012

### the_emi_guy

I think if we are discussing an integrator, the assumption is that we are talking about the mathematical function of integration, or a circuit that realizes it. If you have a second input in your circuit that is resetting your capacitor voltage than you have something more than an integrator.

11. May 29, 2012

### yungman

We are talking about real signal and real filter, not a theoretical integrator in calculus or theoretical LPF. Many real integrators particular the precision ones do not have a breeding resistor to breed off the charge. Any breeding resistor cause error in the integration. A physical switch is used to reset the integrator at the end of the integration period.

An integrator that look like an inverted op-amp with a very large feedback resistor and an integration cap is only an approximation of an integrator. The resistor, no matter how big is, will cause error. A true precision integrator cannot have that resistor. The only way to reset is to use a switch. This integrator will look nothing like a low pass filter.

12. May 30, 2012

### the_emi_guy

Yungman,
Not everything that contains an integrator is an integrator. The integrate and dump circuit that you are describing *contains* an integrator. When you dump at the end of your integration period you are no longer integrating, you are doing something else. The response of this circuit is, consequently, not that of an integrator.

There are plenty of examples of integrators used to integrate continuously without the need for a dump. (state variable filters, PLL loop filters ..). These are commonly modeled as mathematically pure integrators (transfer function K/s) for first order analysis.

Everything we do involves approximation, we all know this.

Last edited: May 30, 2012
13. May 30, 2012

### yungman

My name is Yungman.

I am talking about a real integrator. We are talking about real LPF, real signal here. Not mathematical equation. This is real world, not in the class room in the university.

Any integrator implemented using low pass approximation, you are charging by the input on one hand, but you are discharging by the circuit on the other hand be it much slower. AND you will have the limitation of the recovery time so you can get back to ground zero before you can start integrate for the second time. Also REAL circuit has leakage current that will charge up the integrating cap. You need to hold the integrator at ground state, then start integrating on command and then reset to get ready for the second integration. These don't show in you mathematical formula. This is real life circuit, that's where the university ends and the real world begin.

I design plenty of close loop control type of circuit that involve low pass filter or integrator if you like to call it, control system similar to PLL stuff. In fact one of the paper I published in the Review of Scientific Instrument is based on a self reset integrator that I designed. An integrator to capture and hold the total charge of an in coming sub nS pulse and hold for 15nS and self reset to 0V level and ready to accept another pulse. Without the reset mechanism, the integrator would be render useless for over 100nS before it is ready for another integration( this is call dead time in scientific instruments). Even worst, using a LPF integrator, if the next event arrive when the integrator yet to recover, you pile on the error. It goes down hill from here.

Theoretical integrator don't need to worry about efficiency, just worry about integration, that's the easiest part. The biggest thing about real life integrator is the through put, dead time, how fast can you make it ready for the second event. That's where the rubber hits the road, that's where math don't have to worry about. Designing a basic integrator is a cake walk. The settling time, reset recovery time, leakage consideration are where you earn your keep.

Last edited: May 30, 2012
14. May 30, 2012

### the_emi_guy

Yungman,
Sorry for the spelling error of your name, it was not intentional (and I edited my post to correct).

15. May 30, 2012

### psparky

I've said this many times before, but without a transfer function you're just twiddling your thumbs.

Vo/Vi equals your transfer function or gain.

IF it's just a series RC circuit....and you are looking LPF....a simple voltage division across the cap will yield 1/(jwrc+1)......your break happens when w=1/rc

Same for an op amp type LPF. (CAP AND RESISTOR IN PARALLEL IN FEEDBACK) Take your -rf/ra and you will get same result except your active filter will have a gain number out front. -rf/ra*1/(jwrc+1)

Take a real op amp integrator.....cap in feedback and resistor in input....and your transfer function will be 1/jwrc.......(plugged into -rf/ra)

Again.....the question you need to ask is....what's the transfer function? Once you've found this....test when w=0....and when w=infinity to get a feel for what your filter looks like. Then look in the middle somewhere...at this point you will need vector math with the "J" in there....this will also give you gain AND angle in your bode plot. (Edit...you WILL need to worry about "J" for any value other than w=0. Take infinitey for example.....big vector at angle ninety...therefore you phase angle will be -90....for example. You gain will be 1....but phase of -90. Will also be close to -90 for any decade higher than break frequency in this case)

And don't worry about that pesky minus sign....since dB is 20 log |gain|

Last edited: May 30, 2012
16. May 30, 2012

### DragonPetter

An integrator can be a low pass filter. I can use my textbooks as reference. Also, this shows the filter effect of integrating in the time domain: https://www.physicsforums.com/showthread.php?t=593423

Here is a transfer function for an integrator, and it clearly has the properties of a LPF.
http://www.etotheipiplusone.net/pics/seg/seg_angle_3_integrator.png

Here is a good reference that explains how an integrator acts as a low pass filter, and how a LPF with a cutoff frequency can approximate integration far beyond that frequency.
http://www.swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/Filters.html

Its true that there are other LPFs than an integrator, but no one gets to decide what is a "true" LPF and what isn't when they both do the definition of a low pass filter. You can't discriminate between low pass versions of chebychev, bessel, elliptical, butterworth, or an integrator, and say only one or some of them are low pass filters just because they have different parameters/characteristics or specific implementations that someone considers a LPF.

Edit: none of this really matters for the OP's question though, just think its misleading if someone gets wrong ideas about integrators. I think the reason integrators are so important is because of their place in the laplace domain as 1/s, and how this tool of integration is used in filter design whether you see it by itself in a transfer function or not. A transfer function is a way of looking at or manipulating special cases of differential equations, and differential equations are combinations of derivatives and integrals of functions. That thread I linked was also started by Niles, so maybe he is sick of talking about integrators haha.

Last edited: May 30, 2012
17. May 30, 2012

### rbj

yungman, i am sorta surprized and a little entertained to see you sticking to your guns with such.

try taking your argument to the USENET group comp.dsp and see how far it gets you.

a LPF is any Linear and Time-Invariant (LTI) system that has higher gain at lower frequencies than it has at higher frequencies. you come up with a filter of any sort that has this property and i will classify it as a low-pass filter.

because that is what it is.

BTW, i know as much about analog filters with ideal op-amps as anyone here, even though in the past 3 decades i was doing only DSP. all LTI systems are built out of adders (or subtractors), scalers (multiplication by a coefficient), and some frequency-dependent block. in analog filters that frequency-dependent block is usually an integrator (it could be a CCD, instead) and in digital filters that frequency-dependent block is a unit delay. otherwise, it's all the same. sorta.

18. May 30, 2012

### rbj

i think you mean "bleeding resistor". sheep breed, but i don't think that resistors breed.

and that is simply wrong. the integrator will look something like other low-pass filters in that with both, the gain of the filter at high frequencies is less than the gain at lower frequencies.

19. May 30, 2012

### DragonPetter

We knew what he meant! Maybe he is being a little stubborn about his definition/philosophy of what defines a LPF, but no need to mock an honest spelling mistake :) He's trying to be helpful, even though some times we are not all on the same page, but its good to just help each other understand nicely.

Anyway, you probably do know more than most of us with signal processing, and what you said about the LTI stuff definitely made it clearer for me.

20. May 30, 2012

### psparky

I was going to say something to this effect.....but I'll put it even simpler.

An integrator is always a low pass filter.......a low pass filter is somtimes an integrator.

Or....

A differentior is always a high pass filter....a high pass filter is sometimes an differentiator.

21. May 30, 2012

### yungman

Read my post #13 again. The integrator is much more than a LPF. If you don't care about real life through put, dead time, and accuracy, then yes, you can use a LPF.
We are not talking about scalers, adders here, we are talking about real life integrator in real circuit.
The math behind the integrator is the easy part, try implement a real integrator in real project. Think application. I do real life analog integrator design, not DSP simulating design. I am sure resetting the integrator and get it ready for the next event is only a single line code in your DSP design. Try doing it in a real integrator.

Last edited: May 30, 2012
22. May 30, 2012

### yungman

Again, read #13. This math stuff is only the basics. Try do an integrator that receive random event for a period of time. If you use a LPF, it start to droop between events and you loss accuracy.

Last edited: May 30, 2012
23. May 30, 2012

### yungman

No, only by definition. As I repeat over and over, read #13 about the real life circuit application and the defect of the simple integrator.
I never argue about the math, I said that is the easy part. Implementation is the key and that's where the rubber hit the road. This is EE forum, not the Calculus or physics forum. BTW, I know the math, but that's not the point.

24. May 30, 2012

### psparky

I'm behind you 100% on this. We all start with the classroom and once we utilize it in the field.....all the "ideal" situations we had no longer exist.

25. May 30, 2012

### DragonPetter

Is a bessel LPF much more than a LPF by your definition too? It maintains constant group delay, while many LPFs do not. Its a special LPF, but it still acts as an LPF.

Why does a real integrator in a real project in real life have any distinction from a mathematical model of an integrator that does the same thing in math language? A real life LPF of any class/implementation has lots of nonlinearities and other non-ideal factors that need to be accounted for to implement it - this is not special to integrators. Other LPF can be used in non-linear applications. Take a charge pump with diodes for example. The RC components are LPFs, regardless if the end goal of the circuit is to give a non-linear voltage boost. An integrator is behaving as a LPF (and its LPF function is why its used in the first place), even if your charge/discharge circuit is making it do something not directly related to filtering. I could be wrong, but I have always thought of a LPF (or any other transfer function) as what it does to frequencies represented as a black box with an input and output, rather than what its end goal/application is.

An even greater question for you: Is a shock absorbing system on a car a signal filter? Certain force signal frequencies are attenuated, just not electrically. Filtering is a more broad concept than what you make it out to be, and if you want to make a distinction between engineering and the theory behind engineering, then you can consider mechanical and other practical filters and you are opening yourself to a lot of ambiguity that only confuses things. Filtering is both a physical and mathematical process, and so you can't do the "dirt-n-grit, get your hands dirty, practical is what it boils down to" good ol boys approach to define something that is abstract.

I can respect where you're coming from, and I think this disagreement is more down to philosophy and application than definition. I just think you're fighting a losing battle when so many EE professors and engineers teach and work with integrators in a purely filtering/signal&system approach.

Last edited: May 30, 2012