Very low noise high pass filter design

Question

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...

Need your help!

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

Answer 1

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.

Answer 2

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.

Answer 3

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?

Answer 4

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!