## PSN-L Email List Message

Subject: Re: Damping CDR for HS10-1
From: Bob McClure bobmcclure90@.........
Date: Sat, 25 Jun 2011 14:11:40 -0400

```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

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.
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 G=
eoff's latest results, but also allows for the loading provide by the a=
mplifier itself.

HS-10 propertiesSensitivity, E =3D 2.99 V/ips =3D 117.7 volts p=
er meter per secondNatural Frequency =3D 1 Hz =3D 2*PI radians per seco=
ndNatural damping =3D 0.031Inertial Mass =3D 33 oz =3D 0.936 kilogr=
am

Erhard Wielandt, in his chapter "Seismic Sensors and their Calibration=
"=A0 in the Manual of Observatory Practice presents a formula for =
electromagnetic damping.The formula is h =3D (E^2 / 2* M * wo * Rd)=
, where

=A0=A0 E is the output in volt-seconds/meter,=A0=A0 h is the damping co=
efficient (0.5/Q),=A0=A0 M is the effective pendulum mass in kilograms,=
=A0=A0 wo is the natural frequency of the pendulum in radians/sec, and<=
br>=A0=A0 Rd is the total shunt resistance.

The recommended total damping is 0.707. Since the HS-10 has an open cir=
cuit damping of 0.031, we want the electromagneticcontribution to be 0.=
707 - 0.031 =3D 0.676.so,Rd =3D E^2 / (2*h*M*wo) =3D (117.7=
)^2 / (2 * 0.676 * 0.936 * 2 * PI) =3D 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 =
=3D 1302 ohms. The 1302 value is that of the external shunt resistor in par=
allel with the amplifier input

resistance. Say the amplifier input resistance is 10K ohms.=A01/Rex=
t =3D 1/Rt - 1/Ramp=A01/Rext =3D 1/1302 - 1/10000 =3D 0.000768 - 0.0001=
00 =3D=A0 0.000668 =A0Rext =3D 1497 ohmsThe applied load wi=
ll reduce the sensitivity of the geophone. The output will be Rshunt/(Rcoil=
+ Rshunt) times the open

circuit value.
```