US 2026/0202564 A1 · MOVING-COIL GEOPHONE ZERO-PHASE CORRECTOR BASED ON STATE VARIABLE SHAPER

Abstract

A moving-coil geophone zero-phase corrector based on a state variable shaper is provided. The zero-phase corrector includes a state variable shaper module, a differential-to-single-ended module, and a single-ended-to-differential module. After a moving-coil geophone signal is input as a differential signal, the differential-to-single-ended module converts the signal into a single-ended signal suitable for filtering, the high-pass filter, band-pass filter, and low-pass filter in the state variable shaper module correct the phase characteristic of the geophone's frequency response to a zero-phase attribute, and finally, the single-ended-to-differential module converts the single-ended signal back into a differential signal for output.

A moving-coil geophone zero-phase corrector based on a state variable shaper, formed by connecting a differential-to-single-ended module, a state variable shaper module, and a single-ended-to-differential module in sequence;

wherein the state variable shaper module is designed for a frequency range of 5-300 Hertz, and comprises a high-pass filter, a band-pass filter, and a low-pass filter, the high-pass filter comprises an adder (U1), the band-pass filter comprises an integrator (U2) and an inverter (U4), and the low-pass filter comprises an integrator (U3);
the adder (U1) of the high-pass filter comprises a first operational amplifier, a resistor (R1), and a resistor (R2), the resistor (R1) serves as a feedback resistor connecting an inverting input terminal of the first operational amplifier to an output terminal of the integrator (U3), the resistor (R2) connects an inverting input terminal of the adder (U1) to an output terminal of the first operational amplifier, the output terminal of the first operational amplifier serves as an output port of the high-pass filter, and a phase at the output port is substantially zero;
the integrator (U2) of the band-pass filter comprises a second operational amplifier, a resistor (R3), a resistor (R4), and a capacitor (C1), the resistor (R3) connects an output terminal of the adder (U1) to an inverting input terminal of the second operational amplifier, the resistor (R4) and the capacitor (C1) are connected in parallel as the feedback resistor and a feedback capacitor between the inverting input terminal and an output terminal of the second operational amplifier, forming an inverting integrator, an output terminal of the integrator (U2) exhibits a frequency characteristic of the band-pass filter and provides a phase lead of approximately 90 degrees, the output terminal of the integrator (U2) is connected to the inverter (U4), the inverter (U4) comprises a third operational amplifier, a resistor (R7), a resistor (R8), and a resistor (R24), the resistor (R7) connects an inverting input terminal of the third operational amplifier to the output terminal of the integrator (U2), the resistor (R24) connects a non-inverting input terminal of the third operational amplifier to an input reference voltage or ground, the resistor (R8) serves as the feedback resistor connecting the inverting input terminal and an output terminal of the third operational amplifier, and the constituted inverter (U4) ensures a band-pass filter phase characteristic unaltered;
the integrator (U3) of the low-pass filter comprises a fourth operational amplifier, a resistor (R5), a resistor (R6), and a capacitor (C2), the resistor (R5) connects the output terminal of the integrator (U2) to an inverting input terminal of the fourth operational amplifier, the resistor (R6) and the capacitor (C2) are connected in parallel as the feedback resistor and the feedback capacitor between the inverting input terminal and an output terminal of the fourth operational amplifier, and the output terminal of the integrator (U3) exhibits a frequency characteristic of the low-pass filter and provides a phase lead of approximately 180 degrees;
outputs of the high-pass filter, the band-pass filter, and the low-pass filter are connected to a resistor (R9), a resistor (R10), and a resistor (R11) respectively, the resistor (R9), the resistor (R10), and the resistor (R11) serve as resistors determining weighting coefficients for summing the low-pass filter, the band-pass filter, and the high-pass filter respectively to set filter multiplication factors for summation, and the resistor (R9), the resistor (R10), and the resistor (R11) are connected to an adder (U5) and an inverter (U6);
a resistor (R12) in the adder (U5) serves as a feedback resistor connecting an output terminal of a fifth operational amplifier and an inverting input terminal of the fifth operational amplifier in the adder (U5), determining an amplification factor during the summation, and a resistor (R21) connects a non-inverting input terminal of the fifth operational amplifier to the input reference voltage or the ground;
the inverter (U6) ensures phase stability despite adder presence, the inverter (U6) comprises a sixth operational amplifier, a resistor (R13), a resistor (R14), and a resistor (R22), the resistor (R13) connects an inverting input terminal of the sixth operational amplifier to an output terminal of the adder (U5), the resistor (R22) connects a non-inverting input terminal of the sixth operational amplifier to the input reference voltage or the ground, and the resistor (R14) serves as the feedback resistor connecting the inverting input terminal and an output terminal of the sixth operational amplifier;
a transfer function of the state variable shaper module is as follows:
H
⁡
(
s
)
=
K
⁢
1
*
H
H
(
s
)
+
K
⁢
2
*
H
B
(
s
)
+
K
⁢
3
*
H
L
(
s
)
(
1
)
wherein s represents a frequency in a Laplace transform domain, K1, K2, and K3 are summation coefficients for the high-pass filter, the band-pass filter, and the low-pass filter respectively, different summation coefficients correspond to different linear combinations, by changing the summation coefficients, a transfer function constructed by a circuit is altered to achieve phase characteristic correction for an output frequency response of different geophones, and the summation coefficients K1, K2, and K3 adhere to a following relationship:
{
K
⁢
1
=
R
12
R
11
K
⁢
2
=
R
12
R
10
K
⁢
3
=
R
12
R
9
(
2
)
wherein R9 represents a resistance value of the resistor (R9), R10 represents a resistance value of the resistor (R10), and R11 represents a resistance value of the resistor (R11);
in equation (1), HH(s), HB(s), and HL(s) are transfer functions of the high-pass filter, the band-pass filter, and the low-pass filter respectively, expressed as:
H
H
(
s
)
=
R
1
+
R
2
R
1
⁢
(
R
6
⁢
C
2
⁢
s
+
1
)
⁢
(
R
4
⁢
C
1
⁢
s
+
1
)
(
R
6
⁢
C
2
⁢
s
+
1
)
⁢
(
R
4
⁢
C
1
⁢
s
+
1
)
+
R
2
⁢
R
4
⁢
R
6
R
1
⁢
R
3
⁢
R
5
(
3
)
H
B
(
s
)
=
-
R
1
+
R
2
R
1
⁢
R
4
R
3
⁢
(
R
6
⁢
C
2
⁢
s
+
1
)
(
R
6
⁢
C
2
⁢
s
+
1
)
⁢
(
R
4
⁢
C
1
⁢
s
+
1
)
+
R
2
⁢
R
4
⁢
R
6
R
1
⁢
R
3
⁢
R
5
(
4
)
H
L
(
s
)
=
R
1
+
R
2
R
1
⁢
R
4
R
3
⁢
R
6
R
5
(
R
6
⁢
C
2
⁢
s
+
1
)
⁢
(
R
4
⁢
C
1
⁢
s
+
1
)
+
R
2
⁢
R
4
⁢
R
6
R
1
⁢
R
3
⁢
R
5
(
5
)
in transfer functions equations (3) to (5), C1 represents a capacitance of the capacitor (C1), C2 represents a capacitance of the capacitor (C2), R1 represents a resistance value of the resistor (R1), R2 represents a resistance value of the resistor (R2), R3 represents a resistance value of the resistor (R3), R4 represents a resistance value of the resistor (R4), R5 represents a resistance value of the resistor (R5), and R6 represents a resistance value of the resistor (R6);
H1(s) represents a target transfer function used for zero-phase correction, and H2(s) represents a transfer function after cascading the moving-coil geophone zero-phase corrector, expressed as:
H
1
(
s
)
=
s
2
+
2
⁢
ξ
0
⁢
ω
0
⁢
s
+
ω
0
2
s
2
+
2
⁢
ξ
1
⁢
ω
1
⁢
s
+
ω
1
2
(
6
)
H
2
(
s
)
=
S
0
⁢
s
2
s
2
+
2
⁢
ξ
1
⁢
ω
1
⁢
s
+
ω
1
2
(
7
)
in equation (6), ω0 and ξ0 are a cutoff frequency and a damping ratio of a transfer function of a moving-coil geophone respectively, ω1 and ξ1 are a cutoff frequency and a damping ratio of a transfer function of a zero-phase correction circuit respectively;
and in equation (7), A0 is a gain of the transfer function of the moving-coil geophone;
H(S)=H1(s) is set, and reasonable design and selection of resistor and capacitor parameters are combined, then the parameters C1, C2, R1, R2, R3, R4, R5, R6, R9, R10, R11, K1, K2, and K3 in above transfer function equations are solved, thus zero-phase correction of a geophone is enabled using solved circuit parameters;
and
a phase characteristic φ2(ω) of the transfer function H2(s) after cascading the geophone and the zero-phase correction circuit is set to have a phase magnitude of F at 5 Hertz, as follows:
φ
2
(
ω
)
=
arctan
⁡
(
-
2
⁢
ξ
1
⁢
ω
1
⁢
ω
ω
1
2
-
ω
2
)
=
ε
with ξ1 and ε known, ω1 is solved to determine the target transfer function H1(s) for the zero-phase correction.

401 more elements

Moving-coil geophone zero-phase corrector based on state variable shaper

Life of this patent

Moving-coil geophone zero-phase corrector based on state variable shaper

Life of this patent

Abstract

Claims5