TDD (version 0.4)

MakeRespSP: Calculate Poles and Zeros of Short-Period Sensor

Description

Many mechanical short-period seismometers are characterized by three parameters: the natural angular frequency (omega naught), damping coefficient (h), and sensitivity. The response of these sensors to a velocity impulse has two poles and two zeros; the response is zero at the origin, increases roughly proportionately with f^2 up to a low corner, and is flat above the low corner.

The differential equation describing this, where y is the output voltage and v is the velocity of the ground, is

y'' + 2*h*omega_0*y' + omega_0^2*y = Sense * v'' Some short-period sensors are customizable, so it is very important to make sure you use the correct parameters for your installation here.

Usage

MakeRespSP(h, omega0, Sense, f_Sense = NULL)

Arguments

h

Damping coefficient (unitless, 1 for critical damping)

omega0

Natural angular frequency (rad/s)

Sense

Sensitivity in passband (V * s/m)

f_Sense

If given, the frequency (Hz) at which Sense is valid. If NULL (which should ordinarily be the case), Sense is assumed to be valid at frequencies much higher than the low corner.

Value

Sense

Sensitivity of instrument (V * s/m)

Knorm

Normalization constant

poles

Poles of Laplace transform of instrument impulse response (rad/s)

np

Number of poles

zeros

Zeros of Laplace transform of instrument impulse response (rad/s)

nz

Number of zeros

See Also

GetPZ ReadInstr

Examples

# L4C3D
omega0 = 2*pi # 1 Hz natural frequency * 2pi
h = 0.707
Sense = 171
MakeRespSP(h, omega0, Sense)