fixing freq response of geophone

[alan]

Hello people,

I have a geophone whos specs are given here:
http://www.geospacelp.com/c_gs11da.shtml

I would like to build a circuit that makes the freq response flat down
to say .4 Hz. I called the company and got a forumla for the response,
which I believe looks like a damped oscillator. I tried making a filter
that has 2 poles at the kink, but it still leaves a small lump in the
frequency response. I think this has something to do with the fact that
an oscillator's rolloff is not the same as two cascaded RC filters.
OK, so I know from H&H and others that there are 2 pole filters that you
can make that have different Q's, e.g. Butterworth, Linkwitz Riley, etc.

So here are some issues/questions:

Even though the 2 RC's don't exactly flatten out the freq response, it's
still reasonably close. Will the phase response also be reasonably
close? Will the response be more RC-like if I increase the damping of
the geophone? (I think if I turn the damping waaaaay up, the response
will only fall off as one pole.)

I don't really want to build a filter per se, but rather a LF boosting
circuit (i.e. G>1). Is there a guide I can look towards for doing this?
I'm sure there must be other people out there that want to do this with
their geophones.

Ok, I just did a little searching, and I realise that there are very
complicated things that can be done to improve performace, e.g. install
capacitive plates, etc. Let's just say that for now I want to be done
with this in a day's worth of labor, so I'm only looking for boosting
the LF response with a simple circuit and making sure the phase is
reasonable. I think this will be some kind of a 2 pole circuit with a Q
in there somewhere.

Thanks

 

[John Popelish]

Hello people,

I have a geophone whos specs are given here:
http://www.geospacelp.com/c_gs11da.shtml

I would like to build a circuit that makes the freq response flat down
to say .4 Hz. I called the company and got a forumla for the response,
which I believe looks like a damped oscillator. I tried making a filter
that has 2 poles at the kink, but it still leaves a small lump in the
frequency response. I think this has something to do with the fact that
an oscillator's rolloff is not the same as two cascaded RC filters.
OK, so I know from H&H and others that there are 2 pole filters that you
can make that have different Q's, e.g. Butterworth, Linkwitz Riley, etc.

So here are some issues/questions:

Even though the 2 RC's don't exactly flatten out the freq response, it's
still reasonably close. Will the phase response also be reasonably
close? Will the response be more RC-like if I increase the damping of
the geophone? (I think if I turn the damping waaaaay up, the response
will only fall off as one pole.)

I don't really want to build a filter per se, but rather a LF boosting
circuit (i.e. G>1). Is there a guide I can look towards for doing this?
I'm sure there must be other people out there that want to do this with
their geophones.

A LF gain boosting circuit is a filter with gain.

Ok, I just did a little searching, and I realise that there are very
complicated things that can be done to improve performace, e.g. install
capacitive plates, etc. Let's just say that for now I want to be done
with this in a day's worth of labor, so I'm only looking for boosting
the LF response with a simple circuit and making sure the phase is
reasonable. I think this will be some kind of a 2 pole circuit with a Q
in there somewhere.

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 www.tech-chat.de)

You would make 2 of these, probably with a dual opamp like an LM358.
http://focus.ti.com/lit/ds/symlink/lm358.pdf

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

 

[Don Foreman]

Hello people,

I have a geophone whos specs are given here:
http://www.geospacelp.com/c_gs11da.shtml

I would like to build a circuit that makes the freq response flat down
to say .4 Hz. I called the company and got a forumla for the response,
which I believe looks like a damped oscillator. I tried making a filter
that has 2 poles at the kink, but it still leaves a small lump in the
frequency response. I think this has something to do with the fact that
an oscillator's rolloff is not the same as two cascaded RC filters.
OK, so I know from H&H and others that there are 2 pole filters that you
can make that have different Q's, e.g. Butterworth, Linkwitz Riley, etc.

So here are some issues/questions:

Even though the 2 RC's don't exactly flatten out the freq response, it's
still reasonably close. Will the phase response also be reasonably
close? Will the response be more RC-like if I increase the damping of
the geophone? (I think if I turn the damping waaaaay up, the response
will only fall off as one pole.)

I don't really want to build a filter per se, but rather a LF boosting
circuit (i.e. G>1). Is there a guide I can look towards for doing this?
I'm sure there must be other people out there that want to do this with
their geophones.

Ok, I just did a little searching, and I realise that there are very
complicated things that can be done to improve performace, e.g. install
capacitive plates, etc. Let's just say that for now I want to be done
with this in a day's worth of labor, so I'm only looking for boosting
the LF response with a simple circuit and making sure the phase is
reasonable. I think this will be some kind of a 2 pole circuit with a Q
in there somewhere.

Thanks

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.

 

[alan]

A LF gain boosting circuit is a filter with gain.

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.

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 www.tech-chat.de)

You would make 2 of these, probably with a dual opamp like an LM358.
http://focus.ti.com/lit/ds/symlink/lm358.pdf

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

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".

 

[alan]

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.

ok. how do you do this?

 

[Don Foreman]

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.

 

[John Popelish]

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".

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.

 

[Ken Smith]

Hello people,

I have a geophone whos specs are given here:
http://www.geospacelp.com/c_gs11da.shtml

I would like to build a circuit that makes the freq response flat down
to say .4 Hz.

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.