PSN-L Email List Message

Subject: Re: Damping CDR for HS10-1
From: Geoffrey gmvoeth@...........
Date: Sat, 25 Jun 2011 20:39:54 +0000

```Interesting Bob,

But I'm using an instrumentation amplifier.
In such an arrangement of three op amps
you are using two positive inputs which means
the input impedance is mega ohms to giga ohms.
The only input is the the resistors which are
split against ground. So in my case the you
have verified my numbers to be basically correct.

I have learned something new to myself in the past

There seems to be common mode signals
of an electrical nature coming in on the
geophone input. The only way to balance out
this unwanted signal has been to
make several pairs of identical split resistors
and see which pair will after installed eliminate the problem.
It seems my test equipment can not resolve the measurements
fine enough to properly match these two resistors.
Therefore it is a matter of chance that the right
combination can be achieved.

I have never been able to do this balancing
act with any configuration other than an instrumentation
amplifier.

It is my ignorance in combination with
which has caused me years of headaches.

In my case the Ge seems to reduce to
(2.99 * 1302)/1742 or 2.234 v/(in/sec)
But this is not how I handle this figure.
I treat it as an overall loss of 20log(2.234/2.99) or -2.53dbv
when calculating the final amplifier gain.

Regards,
geoff

-----Original Message-----
From: Bob McClure
Sent: Saturday, June 25, 2011 6:11 PM
To: psnlist@..............
Subject: Re: Damping CDR for HS10-1

For whatever it is worth, here is my computation of the shunt resistance to be applied to the HS-10 geophone to obtain a
damping coefficient of 0.707. It confirms Geoff's latest results, but also allows for the loading provide by the amplifier itself.

HS-10 properties

Sensitivity, E = 2.99 V/ips = 117.7 volts per meter per second
Natural Frequency = 1 Hz = 2*PI radians per second
Natural damping = 0.031
Inertial Mass = 33 oz = 0.936 kilogram

Erhard Wielandt, in his chapter "Seismic Sensors and their Calibration"  in the Manual of Observatory Practice
presents a formula for electromagnetic damping.

The formula is h = (E^2 / 2* M * wo * Rd) , where
E is the output in volt-seconds/meter,
h is the damping coefficient (0.5/Q),
M is the effective pendulum mass in kilograms,
wo is the natural frequency of the pendulum in radians/sec, and
Rd is the total shunt resistance.

The recommended total damping is 0.707. Since the HS-10 has an open circuit damping of 0.031, we want the electromagnetic
contribution to be 0.707 - 0.031 = 0.676.

so,

Rd = E^2 / (2*h*M*wo) = (117.7)^2 / (2 * 0.676 * 0.936 * 2 * PI) = 1742 ohms

Let us say the coil resistance is 440 ohms. The input resistance of the amplifier and its applied shunt resistor must then
equal 1742 - 440 = 1302 ohms. The 1302 value is that of the external shunt resistor in parallel with the amplifier input
resistance.
Say the amplifier input resistance is 10K ohms.
1/Rext = 1/Rt - 1/Ramp
1/Rext = 1/1302 - 1/10000 = 0.000768 - 0.000100 =  0.000668

Rext = 1497 ohms

The applied load will reduce the sensitivity of the geophone. The output will be Rshunt/(Rcoil + Rshunt) times the open
circuit value.

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