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 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. 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 properties

Sensitivity, E =3D 2.99 V/ips =3D 117.7 volts p= er meter per second

Natural Frequency =3D 1 Hz =3D 2*PI radians per seco= nd

Natural damping =3D 0.031

Inertial 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 electromagnetic

contribution 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 ohms

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

circuit value.