# Very low noise high pass filter design

We are trying to design a high pass filter, which mainly goals are:

• very low noise. Low noise is the first concern.
• suppresses 1kHz by around 50dB and passes 2kHz.
• Gets rid of DC
• Dont care on other frequencies.

## Description of our project:

We are to measure a very weak 2kHz signal in accompany with very large 1kHz signal(70dB larger than 2kHz signal) with a 16-bit ADC based Lock-in Amplifier.

Since the 2kHz signal is too weak and we need to achieve a resolution coming from a 16-bit ADC, 2kHz signal has to be amplified first. However, since 1kHz is too large, we have to filter it out first, in order to prevent saturation, before amplification.

About specifications of "how low the noises should be". The requirement is as low as possible. We are willing to try ANY method/combination/components to reduce the noises.

## Here are points that I know:

passive filters:

• Need inductors, and at low frequency it may be very hard to find a large and accurate one? (I do not want to make inductor by hand)
• low noises comparing with active filters.

active filters:

• easy to implement
• relative larger noises...

Since the noises are our most important concern, could I ask for some suggestions on tradeoffs of choosing:

• active filter based on OpAmp,
• active filter based on BJT/MOSFET or
• passive filter?
• implement active filters based on IC
• implement active filters based on switched capacitors

Could I have some general comments?

Any suggestions are appreciated.

Regards, Richie

• (1) How much noise is low noise? (2) What attenuation do you need other than at 1 kHz? (e.g. would a notch suffice? If so, look at Cauer filters) Apr 5, 2014 at 12:30
• This signal is screaming "Digitize and run me through an FIR filter!" Apr 5, 2014 at 16:35
• Asking for general comments is far too much for this Q&A site. If you want help solving a problem take note what people are saying - what is low noise? I'll also add - what bandwidth are you wanting and is the 1kHz a single point attenuation or everything below say 1.5kHz. At the moment this question is interesting but badly quantified. Apr 5, 2014 at 17:11
• @BrianDrummond (1)I cannot specify how low the noises. The requirement is "as low as possible", since we do not care cost, complexity. (2)We do not care other frequencies and I will sure check Cauer filters. I hope they donot need tuning that much.. Apr 6, 2014 at 11:00
• @MattYoung Thanks for your reply. The reason that we are not using FIR is because a lock-in Amp will be used after filter. And the reason for us to use high-pass filter is because we want to get rid of 1kHz signal, which is much larger(70dB) larger than our target signal. 1kHz signal has to be filtered out, in order to avoid saturation, before amplifiers. Apr 6, 2014 at 11:03

Yes, we only want to eliminate 1kHz

A notch filter can be used for this: -

This is a 10 kHz design and note figure 6 - how it responds as you get between 9 kHz and 11 kHz with the input signal.

This article describes the circuit in more detail and provides examples of other notch filters across the audio range. The article is by TI and is entitled: -

An audio circuit collection, Part 2

Regarding the op-amps, because you are using a lock-in amplifier it's not critical BUT just in case go for op-amps that are below 10 nV/$\sqrt{Hz}$ specified on noise. Devices that spring to mind are OP1177, AD8605, ADA4528 but there are plenty with lower noise.

• Thanks a lot for your reply. But we also need to get rid of the DC component.. Maybe also with a high pass filter? And is this kind of filter very hard to tune? Apr 6, 2014 at 11:37
• C4 removes DC in the picture in the answer. To maintain low dc values use the ADA4528 I mentioned in my answer - it has an input offset of about 2uV. Apr 6, 2014 at 11:39
• I love this forum.. It seems this is what we want. One last question.. Is it hard to tune? Apr 6, 2014 at 11:41
• And yeah, we currently are using ADA4004, which has noises of 1.8nV/squareHz Apr 6, 2014 at 11:43
• If you are happy with the dc level going in then get rid of C4. If you need the dc level coming out get rid of C5. You can get 1% 10nF and 22nF cog/np0 cause I've used them. Using a number in parallel aint a crime either!! You probably should develop a small spreadsheet for entering values that predicts the centre frequency. Or... use this tool sim.okawa-denshi.jp/en/TwinTCRtool.php Apr 7, 2014 at 19:12

I am going to recommend an L-C filter with a notch at 1 kHz, followed by a low noise amplifier, then an active filter (either Sallen&Key or a twin-T notch filter as Andy suggests).

After the amplifier, the Johnson noise of the resistors in that active filter will be less of a problem, and between the two filter stages it ought to be possible to attenuate the 1kHz component by more than 70dB, to make best use of the dynamic range of the 16-bit ADC (after which digital filtering can provide any further required signal conditioning.

To me, low noise in the audio band means 1 nV/rtHz or less, which cannot be achieved with 10kilohm or even 1kilohm resistances ahead of the first gain stage. But if you can tolerate the noise of the relatively high value resistors in an active filter, there are simpler solutions as Andy suggests.

EDIT for more detail:

The purpose of an initial L-C filter is to reduce the amplitude of the unwanted component, with minimal added noise to the wanted component, so that a low noise amplifier can be used to add gain without saturating. Assume you can attenuate the 1kHz component by 40dB : then the low noise amplifier can provide 40dB gain. The overall signal level is unchanged but the wanted component is 40dB stronger, and the noise introduced by further processing (active filtering, ADC etc) is less important.

There are some available inductors, but winding by hand is not so difficult! There are adjustable and fixed ferrite cores and bobbins available that ought to be suitable. If you use a fixed inductor you may have to tune the notch by adding capacitors during test (bad for a production run but OK for small numbers)

Designing a coil takes some work : to beat 1 nV/rtHz you need to keep resistances well below 100 ohms (though this should be easy), to handle several volts without saturating the core, you need a reasonable core size and here it's not obvious if you have a problem : a pure AC waveform saturating an inductor will generate 3rd harmonic components (3 kHz) and higher.

• It is such a good suggestion! For the first passive filter, is it for giving less noises for amplification? Could I ask if I have to make the inductor by hand at frequency of 1kHz? Or there are factories providing inductors? Sorry I have no experience designing passive filters containing inductors....Regars, Richie Apr 6, 2014 at 12:08
• Thanks for the EDIT, which is quire informative.. And actually our project is designed for mass production around 10k.. That is the reason why I prefer not to make inductors by hand.. Probably we have to stick on active band pass filter? Apr 6, 2014 at 12:47
• You may have the same problem tuning an active filter. With an adjustable inductor, tuning it is a simple step during test. With a fixed one, you may have to measure, select a capacitor, and add it at test. I would wind my own prototypes, then talk to an EPCOS or Murata or Toko sales person for production : they will wind whatever you want, in quantity! Apr 6, 2014 at 12:55
• Thank you Brian! By the way, why not only use passive notch filters instead of passive filters in combination with active filters? Apr 6, 2014 at 16:50
• Because active filters ARE easier, and after a gain stage their noise is less important. The simpler the passive stages can be, the better (and probably cheaper!) but if you can get what you want with just passive filters, there's nothing wrong with that approach. Apr 6, 2014 at 18:30

You mention a corner frequency of 2kHz with 50dB of attenuation at 1kHz. That's a steep filter - why do you need so much attenuation? 50dB from 1 to 2 kHz means a filter roll-off of about 170dB/decade.

Are you sure this is what you want? What are you trying to accomplish here? It's pretty ludicrous, and will require some serious filter design concerns. If implemented as a cascade of first order filters, for example, that's a ninth-order filter. You might be able to implement it as a cascade of Sallen-Key topology Butterworth filters, but your component values will have to be very precise.

You say "low noise." What level of noise is acceptable?

Finally - if you do require this level of precision, why not implement it as a digital filter?

EDIT: Also, what are the phase constraints?

• Thanks for the reply 1) We do need filter as steep as this.Since we want to get rid of unwanted 1kHz signal which is 70dB larger than 2kHz signal. The more detailed description can be found in the modified question in section of "Description of our project" 2) We are not using digital fiters, because the 2kHz has amplitude ranging from 0V to 0.85mV. And it has to be measured with a 16bit ADC. Therefore it has to be amplified first and an analog Lock-In Amplifier will be used to measure the amplitude. 3) Could You please introduce why digital filters are more appropriate for such applications? Apr 6, 2014 at 11:34

You might like to consider using a differential amplifier for your amplification stage, with the inputs being your original signal (from your lockin) and the signal from your experiment. You will need to match the amplitudes of the components of these that are at $f$. Does your lock-in have differential inputs?

I would be tempted to proceed as follows. Set up the diff amp/lockin differential inputs with a potential divider on the reference input. Detect at $f$ and minimise the lockin output by adjusting the amplitude and phase (with a single pole LC filter maybe?) of the reference until it matches those of the signal. Now you should be able to detect at $2f$ without saturation.

This assumes your signal is a voltage, rather than a current, but that seems to be the case looking at the above.

## Block diagram

Here is a block diagram of the sort of scheme I mean. You need to be sure that the ref frequency that the lock-in sees is correct - depending on how good it is, the bandwidth might be very narrow indeed.

I cannot predict how well this will work without knowing the nature of your lock-in - but it's worth a try!

• Sorry, I did not get what you mean. We built our own lock-in, since we know the exact frequency of our signal. Could you please explain a little on the reasons why the inputs of the diff amp are "original signal from Lock-in(actually what is this?)" and "signal from your experiment"? Really appreciated. Apr 7, 2014 at 2:52
• @richieqianle I've added a diagram, which I hope clarifies things. Incidentally, most commercial lock-ins have a differential input mode, in which the signal is the difference between two inputs - like here. (Although it may not be implemented exactly like this!) Let me know if further clarifications are necessary. Apr 7, 2014 at 9:11
• Thanks NLambert, it seems to be a quite interesting idea. However, it also seems to be pretty hard to tune 1kHz to match the amplitude and phase..Could you comment on this? Apr 7, 2014 at 9:41
• @richieqianle To tune this, have a variable LC filter (with a varcap) and a variable voltage divider, take out the frequency doubler and minimise the signal, ie the 1 kHz component at the lock-in input, by adjusting the variable components. It may be worth putting them on an oscilloscope to get them roughly right. Apr 7, 2014 at 9:53
• Although it seems there are smarter ways to phase shift audio frequency signals - see here. Apr 7, 2014 at 13:34