# Is there a preferred order in which to apply (analog) filters in a chain?

I'm working on a project where a very weak signal need to pass through a bunch of filters. However, I am seeing quite a lot of different ways in which the order of the various filter stages are applied. So my question is:

Is there a preferred order in which to apply different filters in an analog signal chain?

For example:

[weak signal sensor] (input)
--> [10 kHz LPF]
--> InAmp
--> [50Hz Notch (active)]
--> [500 Hz LPF-2]
--> [20 Hz HPF]


There is a similar question here but clear answers are lacking and is not related to very weak signals.

I'm looking to understand why, for example (above), one want to pre-filter the input before the IA, or in other cases where people decide to place a HPF before LPF. The only thing I have read (from Texas Instruments docs) is that one should apply the greatest gain as late as possible, but that also seem to vary.

• With a weak signal, I think you would usually amplify the signal a bit first. Any passband attenuation (in dB) prior to the first amplifier will come directly out of your SNR (in dB). But if the incoming signal contains high amplitude high frequency components, it may be necessary to LPF first, as you have shown. Also this is not my area of expertise, so... – mkeith Apr 25 at 21:49

There is no 'one size fits all' solution.

It depends on the detail of your individual amplifiers, and your input signal.

First, you have to see whether it's even theoretically possible to build a signal processing chain from your chosen amplifiers, for your chosen specification. Your specification should allow you to derive a dynamic range for the system. This is the difference between the minimum signal (usually defined by noise and signal offsets) and the maximum signal (usually defined by some measure of distortion (harmonic, intermodulation, spectral growth) slew rate, or even clipping against the rails). Each of your amplifiers will have a dynamic range. All amplifier dynamic ranges should be greater than your specification dynamic range, the greater the margin the better. The amplifier with the smallest margin is the one to worry about first. If your signal, or your specification has a small dynamic range, then your job is easy.

The amplifier dynamic ranges will apply at an optimum signal level. As you move lower than this level, the effect of noise will increase, higher and you get more distortion, both decreasing the dynamic range. This defines a signal level profile through the signal processing chain.

Does your input signal have any defects? Much HF noise? Put a LPF first, to protect the slew rate of later stages. Much DC offset? Put a HPF first, or a differential stage, to remove the DC and centre-up the signal for subsequent stages.

Finally, arrange your stages in an order that meets the signal level profile. If there are lots of ways to do this, lucky you, your job is easy. If there is only one way (let's say it's an off-air signal, so you need a bandpass filter and LNA first) with subsequent stages of gain with increasing signal level handling, then it's straightforward. If there are no ways, then find the limiting element, the one with the lowest dynamic range, build or buy a better one, rinse and repeat.

• PDP11 - Respect! Oh man, this sound pretty complicated. I don't have the faintest idea what slew rate is. Also, how do you define and measure defects in this case? – not2qubit Apr 26 at 12:54
• Here is a pretty good explanation of Slew Rate. But which begs the question. What are a good and bad OpAmp slew rates for input signals in the range 70 - 500 Hz, lets say? – not2qubit Apr 26 at 13:14

The instrumentation amp generally converts a differential signal to a single-ended signal. The input impedance is high, and equal on both inputs. It has great CMRR. It's generally first in my signal path.

The high-pass filter removes any offsets. I generally put this next, as amplification at my InAmp will amplify offsets as well. Any further amplification may saturate any subsequent amplification.

The caveat of this approach is that if the input has substantial offsets, the InAmp needs to be capped at modest gain.

I tend to not prefilter before the InAmp (other than RF filters usually recommended in data sheets). I don't want to do anything that might dork around with CMRR. If the inputs are people-mounted electrodes, I do put current limiting resistors in place to comply with NFPA99.

ADC, of course is last, and is preceded by low pass filters. There may be more LPF's in other stages, as well, and other HPF's, if a large gain stage generates large offsets.

• That's the thing. I'm not sure why RF filters have to be applied before the InAmp as some designs show. What exactly is causing problem for the InAmp with RF? – not2qubit Apr 26 at 12:46
• @not2qubit the problem with RF is that CMRR is frequency-dependent for InAmps. It's not so hot at RF. Best to get rid of the stuff before it goes in to the amp, and because you're talking about (or should be talking about) frequencies much higher than those of interest, you're not hurting CMRR where its' important. – Scott Seidman Apr 26 at 13:29
• Aha, I see. Thank you for clarifying. – not2qubit Apr 26 at 15:10
• It improves RF noise immunity. If some RF source (like a cell phone) gets close to your device, some of the RF could couple in and saturate the high gain amp or simply manifest as noise. – mkeith Apr 27 at 3:57

As @Neil_UK said, the answer will depend on the details of your application.

In your particular case, it seems like you're trying to capture a very weak signal of low frequency (20Hz~500Hz) that may be susceptible to AC power line coupling (50Hz). I would also assume that you don't care about the DC component.

In this case I would use a simple AC coupling first that could be as simple as a series capacitor (that may give you the 20Hz HPF you want) followed by a very low noise audio pre-amp (probably using discrete transistors) so you get the best system noise figure you can get. Then I would follow with the LPFs (I'm not sure why you need two LPFs with two different cutoff frequencies) and the notch filter.

• I don't think audio amp is suitable for these signals. There's only 1 HPF in my example. But the second LPF relates to what Scott said, that there could be some mysterious problem with RF on InAmp input... – not2qubit Apr 26 at 12:49
• The Notch is for filtering out AC coupling. – not2qubit Apr 26 at 12:55
• I meant to say two LPFs - fixed the typo. Thanks for pointing that out. – joribama Apr 26 at 17:13

Sometimes there is. One audio system I remember generated quite a lot of broadband white noise from the thermal noise of some unavoidable high value resistors in one filter stage.

The simple solution was to move that stage ahead of a low pass filter like your 500Hz LPF, which then attenuated almost all of that broadband noise.

I absolutely agree with Neil, there is no one-size-fits-all solution.