fixing freq response of geophone

Forget the buzzwords (Linkwitz Riley et al), go back to basics.

Consider the geophone with given termination (perhaps 4K per the datasheet) as a pure voltage transducer of volts/velocity, followed by a transfer function H(s). Deduce from the freq response and damping factor in the datasheet what H(s) is, and replicate that in an electrical transfer function. It probably wil be a 2-pole function. It'll only be as accurate as your characterization of the geophone from the datasheet, but that'll probably be close enough for most purposes.

Put that inside a feedback loop having a gain block. The resulting output will then closely replicate the (frequency independent) theoretical voltage source in both phase and amplitude until frequencies get low enough that you run out of gain in the feedback amp. Nearly any opamp has ample gain to flatten your response to well below 0.4 Hz if you get the feedback H(s) right.

A LF gain boosting circuit is a filter with gain.

An active filter with a response that is the inverse of this curve, used to amplify the signal, will produce a flat response. Unfortunately, the inverse response involves gain heading toward infinity as the frequency approaches zero. So it becomes impractical to produce the inverse for noise reasons below some minimum frequency.

If you damp the device to the C curve with a resistive load, you can approximate the inverse filter with a pair of cascaded integrators with a resistor in series with the feedback capacitor such that the RC time constant is about 1/(4.5Hz)*2*pi = .035 seconds.

You can also limit the boost to a decade or so (about .45 Hz) by paralleling the cap with a resistor that is at least 10 times the resistance of the one in series with the cap.

Look at this example with a fixed width font, like courier:

390k ___ ___ +-|___|-+--|___|-+ | 36k | | | | || | | +----||--| | V+ 1u || | ___ | |\\| | in -|___|-+----|-\\ | 10k | >--------+-- out +-|+/ | |/| gnd V-

(created by AACircuit v1.28.4 beta 13/12/04

You would make 2 of these, probably with a dual opamp like an LM358.

If you use this filter directly connected to the geophone, change the input resistor to 1.8k to act as the damping resistor.

except the latter has a gain that goes to 0 at high freq, which I don't want because the s/n will get worse.

Thanks for the suggestion, but that's basically what I had already done before posting. I have a few resistors in parallel and in series with capacitors to give the appropriate low and high freq cutoffs. My question is basically if this should be considered "close enough".

ok. how do you do this?

>

Devise a 2-pole highpass filter with Q and corner freq the same as your geophone. The transfer fn of a feedback driven by impedance Zi (the geophone) and having feedback impedance of Zf is approximately Zf/Zi if the gain of the amp is high enough to make other terms negligable. Nearly any opamp will suffice.

The frequency dependencies of Zi and Zf cancel, giving you flat response. If Zf = K*Zi then the gain of the stage will be K, providing the amplifier's gain is >> K.

Did you use two stages in series? The fall off in response of the geophone is a two pole roll off.

The definition of "close enough is up to you. What do you require. The actual inverse response would probably require a 2 pole filter that shows some resonant peaking to match that of the resonance of the geophone. But I don't have the exact solution to hand you, and there would be only a minor (another word that needs definition) difference in the total effect.

Here's a question for you: Why are you trying to flatten the response in the analog domain? Analog filter circuits down at those frequencies tend to be noisy and involve mechanically large capacitors. If this signal is going into an ADC, you may be better to do the frequency processing there.

Chances are you also want to get the phase right. If you go the digital route, be careful of this issue. In analog circuits you almost have to work at it to not get the phase close when you get the amplitude right.

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kensmith@rahul.net   forging knowledge

The usual reason for doing it in analogue, at least to some level of approximation, is to avoid SNR loss due to very different dynamic ranges at different frequencies. Sometimes you can just use enough bits in the digitizer, but not always--usually on account of additive noise elsewhere, as in RIAA preemphasis.

Cheers,

Phil Hobbs

[...]

He's trying to boost the low frequency end. Usually this is where the 1/F noise is already bad.

Also, I expect that the filter he will be adding will make the noise worse.

If his reason is that he needs to trigger the start of recording when the signal passes some point or something, the case for a bass boost would be a better one.

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kensmith@rahul.net   forging knowledge

Given the low dc resistance of Geophones, one has already struggled to maintain the amplifier noise below the Geophone's Johnson noise. Trying to boost the gain by 12dB/octave or more will quickly raise the amplifier's level noise beyond the sensor's Johnson noise. For your Geophone that rolls off at ~6Hz, using 12dB/octave, a dramatic gain of 225 at 0.4Hz will be needed to correct its response. Ouch!

Whew, noise city!

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 Thanks,
    - Win

I'd say it depends on where you are; we've taken measurements with similar 6Hz geophones where the ambient noise was well below the amplifier plus Johnson noise in the 2Hz region. In such a case, the latter would determine our measurement limit. We solved this using a set of French, Sercel, Mark Products L-4 1.0-Hz geophones.

I have an additional 4-page datasheet with curves.

Agreed.

Ouch.

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 Thanks,
    - Win

Thanks for the response. I did consider going the digital route, however, I'd have to get some kind of a real-time board so that there wouldn't be any kind of hiccups in the output.

So is it true that in analog design, if you get the amplitude almost right, the phase will also be almost right?

pretty much

The fall off in response of the

yes, at the extremes, but at the corner, a circuit with some "q" has a faster rolloff

I have been playing around in matlab, and simply using 2 RC's makes the response off by ~50% at the corner. So what I need is some guide that tells me how to make filters with a given Q. I have started looking at active filter design guides, but they tend to have preset Q's. So far, I have resorted to solving a S-K filter by hand and then plotting it in matlab, but this might be a time sink for me. Maybe the easiest might be to construct a SK filter in some spice variant and tweak the values until the amplitude response seems about right. Thanks for the help so far.

hey wait, I actually want a circuit that creates a dip at the corner freq, not a peak...

In article , Winfield Hill wrote: [...]

In real life, the Johnson noise of the geophone isn't going to be the noise floor. When the geophone is in use, you have to contend with the noise of ants scratching themselves. :)

In real life, the wind blowing on the trees nearby makes noise you can see.

Still it isn't easy because the input from the goephone needs to be about

1nV/sqrt(Hz) and yet not get destroyed if lightning strikes the ground some distance away.

In the oil exploration sort of seismograph you sometimes see a voltage spike from the rocks when the explosives go off.

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kensmith@rahul.net   forging knowledge

In article , alan wrote: [...]

What are you using for an ADC?

If you are plugging into a PC you can run Linux or DOS and get timing that is fairly uniform. It is likely that it won't be as good as you need. If you need fairly jitter free timing, you can use hardware to trip off the ADC at the constant rate and then just make sure that the software takes the number away before it gets overwritten.

If you need better than that, you may want to look at getting the development PCB for a DSP (analog devices Shark) or micro-controller (cygnal)

Like I said, you almost have to work at making this false. Try modeling the geophone as an anlog filter with the same shape in LTSpice. You can then see what the phase of the complete system will look like.

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kensmith@rahul.net   forging knowledge

I have been keeping my eyes open for one of the HS-10-1 units on this page, for sale, second hand, but I haven't seen any.